Structured Process Hazard Analysis

Learning objective. Use HAZID, HAZOP, checklists, fault trees and event trees to ask systematically how safeguards fail, including human and common-cause contributions.

Linked synthetic case. A line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover.

What an adequate output contains. A worksheet is a prompt for multidisciplinary reasoning, not proof that the identified scenario list is exhaustive.

Why this unit is needed

Process safety concerns preventing and limiting catastrophic releases of hazardous substances or energy, rather than merely maintaining a low count of routine injuries. A real project cannot infer its safety from a single score, accident-free period or calculation. For this unit, use hazid, hazop, checklists, fault trees and event trees to ask systematically how safeguards fail, including human and common-cause contributions. The basis of this reasoning is the physical configuration of equipment and operations, not the appearance of a matrix or dashboard. Assign each critical assertion an owner and identify how field observations could contradict it.

The case used across the lessons is deliberately hypothetical: A line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover. It contains no named real chemicals, equipment certificates, actual incident frequencies or approved operating limits. That distinction is central to interpreting models. For a plant, process safety information must describe what can be hazardous, how the process can deviate, and which barriers genuinely remain functional in abnormal conditions. A model may reveal sensitivity while omitting the mechanism that actually dominates a serious accident.

The five-layer engineering argument

1. Hazard and inventory: Identify substances, energy and populations or environmental receptors that could be exposed. Document what remains unknown before assigning a numerical risk category.

2. Initiating mechanism: State a credible cause, including external utilities, human-machine interfaces, maintenance, abnormal startup and non-routine conditions; separate initiating cause from the loss-of-control top event.

3. Prevention: Identify physical design limits, independently verified interlocks, procedures and maintenance controls. Do not assume independence without checking power, instruments and common personnel.

4. Mitigation: Assess containment, shutdown, relief and emergency arrangements in the context of the actual consequence mechanism. A mitigation may reduce severity without reducing the initiating frequency.

5. Assurance: Specify evidence, proof tests, field observations and responsible action owners. Controls that are unavailable, bypassed or degraded must not be credited as if fully available.

How to use the three numerical laboratories

These interactive models intentionally isolate individual relationships rather than claiming to predict a hazardous plant. Before moving a slider, write the governing equation and the physical units. Decide which outcomes should rise or fall when one parameter changes. After moving it, check whether the response and the plotted curve agree with that expectation. Export numerical data and calculate one point independently. If a curve seems favorable, identify a missing mechanism that could reverse the real decision.

This unit's laboratories are:

• [Lab 10: Independent OR fault-tree gate](../labs/lab-10.html) — Compute union of two independent basic events. Boundary: Independence assumed and same observation basis; shared causes require separate model.
• [Lab 11: Independent AND fault-tree gate](../labs/lab-11.html) — Compute intersection of independent basic events. Boundary: Does not model dependencies, systematic failures, repair or demand frequency.
• [Lab 12: Event-tree failed-branch frequency](../labs/lab-12.html) — Follow a hypothetical initiating frequency through two conditional failures. Boundary: Frequencies and probabilities are invented; assumes conditional independence and stated branch timing.

How to review evidence

For each lesson prepare a three-column evidence ledger: declared fact, supporting observation/source, and status (measured, specified, assumed, inferred, or unresolved). Do not promote an assumption to a measurement when an equation happens to give a precise answer. In a team review, challenge the source of every probability and time constant. If an engineering standard is cited, verify the correct edition and legal applicability; standards differ by jurisdiction and project date. For serious events, methods used by qualified specialists should replace these elementary illustrations.

The course encourages deliberate disagreement: two reviewers should independently identify the hazardous deviation and potentially defeated safeguards before reconciling their lists. Record both the agreement and remaining uncertainty. The presence of a highly consequential unresolved scenario should not be hidden inside a low composite average. Closure means that a response has been implemented and verified to work, not that a spreadsheet cell has been colored green.

Progression and assessment

Complete the four lessons in order. Each assessment demands a short derivation, a sensitivity or limitation check, a scenario analysis and a documented decision. A numerical result without a stated boundary, units and credible evidence should receive no engineering credit. The final unit project asks for an auditable decision memo that separates a screening observation from an approval to build or operate. Peer review should specifically challenge common-cause failures and untested assumptions.

Lesson 1: HAZOP guidewords and nodes

A structured HAZOP compares design intent with deviations such as no flow, more pressure and reverse flow. The team examines credible causes and consequences, safeguards and recommendations for each important deviation. Key analytical anchor: Deviation = guideword applied to a defined process parameter. Investigate the following case: For a transfer line, investigate NO FLOW with a running pump, then compare with REVERSE FLOW when downstream pressure is higher. The most likely conceptual error is using a guideword list as a substitute for a facilitated multi-disciplinary meeting. In the lesson, assemble updated p&ids, operating procedures, instrument and equipment descriptions, experienced team members before drawing the operational conclusion: record decisions and evidence for actions, including reasons for no recommendation. Further discussion: Write two complete worksheet rows; distinguish cause from safeguard and consequence.

Lesson 2: Fault trees and dependent events

A fault tree starts from a defined top event and uses logic gates for combinations of basic events. OR probability differs from AND probability; independence is rarely automatic and shared utilities can defeat multiple barriers. Key analytical anchor: P(A∨B)=P(A)+P(B)−P(A∩B). Investigate the following case: If independent valve failure and sensor failure probabilities are 0.03 and 0.02, their OR event is 0.0494. The most likely conceptual error is multiplying dependent failure probabilities or mixing demand probabilities with annual frequencies. In the lesson, assemble equipment failure modes, proof test histories and common-cause mechanisms before drawing the operational conclusion: use trees to expose logical structure, then obtain justified failure data. Further discussion: Draw one fault tree in which a common electrical supply invalidates the independent-branch estimate.

Lesson 3: Event trees and conditional branch outcomes

An event tree begins at an initiating event and follows successful or failed protective functions. Branch frequencies are products of initiating frequency and conditional probabilities only when branch assumptions are justified. Key analytical anchor: f_branch = f_initiator × ∏P(branch state | prior states). Investigate the following case: An illustrative initiating frequency of 0.1/y and a 0.1 failure probability of a safeguard yield a 0.01/y branch under the model assumptions. The most likely conceptual error is reporting illustrative conditional branch values as measured event frequencies. In the lesson, assemble initiating data, barrier design, maintenance, testing, bypass procedures and correlation analysis before drawing the operational conclusion: make assumptions and units explicit in every event-tree calculation. Further discussion: Compare a branch with and without a shared-cause failure and state which data are missing.

Lesson 4: FMEA, prioritization and uncertainty

Failure modes and effects analysis is useful for asset-level failure identification and action ownership. A severity-occurrence-detection product is ordinal and not a substitute for quantitative risk or consequence analysis. Key analytical anchor: Illustrative priority index = S × O × D (ordinal ranking only). Investigate the following case: A failure mode with scores 8, 3 and 4 has an index 96; scores are internal meeting scales, not hazard probabilities. The most likely conceptual error is ranking a high-consequence mode low because a detector seems easy to use. In the lesson, assemble asset function, failure history, inspection records, assessor definitions and consequences before drawing the operational conclusion: keep severe single-point failures visible regardless of composite score. Further discussion: Construct two score sets with equal product but different consequence severity and discuss priority.

Unit completion checkpoint

The minimum acceptable submission contains an annotated process boundary for structured process hazard analysis, a cause-to-consequence pathway, a register of assumptions, an independent numerical reproduction of each model, and an unresolved-information list. In the synthetic case, a line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover. Identify which missing single item is most likely to change your recommendation and why. Then state who would have authority to accept or reject the real project after a specialist review.

Unit 4 · Lesson 1: HAZOP guidewords and nodes

[Unit overview](../units/unit-04.html) · [Interactive lab 10](../labs/lab-10.html) · [Assessment](../assessments/unit-04.html) · [Applied project](../projects/unit-04.html)

The engineering question

A structured HAZOP compares design intent with deviations such as no flow, more pressure and reverse flow. The team examines credible causes and consequences, safeguards and recommendations for each important deviation. This lesson belongs to Structured Process Hazard Analysis, where the course objective is to use HAZID, HAZOP, checklists, fault trees and event trees to ask systematically how safeguards fail, including human and common-cause contributions. The governing issue is not whether one can calculate a number; it is whether that number describes the failure mechanism under study. A competent analysis separates a claim about what happens, an argument about why it would happen, and evidence that the safeguards could withstand real operation.

Specific thought experiment. For a transfer line, investigate NO FLOW with a running pump, then compare with REVERSE FLOW when downstream pressure is higher. Work from the equipment boundary outward. Name the initiating event, the operating mode, the top event, the potentially exposed people or environment, and the time over which the consequences could develop. If any one of these is unspecified, maintain the uncertainty rather than inventing a value.

Principles and analytical relationship

The working relation or structured method is Deviation = guideword applied to a defined process parameter. It is useful because it forces an analyst to state inputs and ask whether the units, time basis and conditioning assumptions match. A rate per year cannot be multiplied by an arbitrary probability without asking what event that probability conditions upon. Similarly, an ordinary fraction is not a mass fraction until the relevant mass balance has been declared. In a causal diagram, an arrow represents a proposed physical or organizational dependency; it is not, by itself, proof of causality.

The physical interpretation for hazop guidewords and nodes is the following: A structured HAZOP compares design intent with deviations such as no flow, more pressure and reverse flow. The team examines credible causes and consequences, safeguards and recommendations for each important deviation. Thus the result needs an audit trail back to observations, design documents or a controlled estimate. There is no universal conversion from a neat calculation to safe operation. Where the relationship is qualitative, a complete answer explains the conditions for each step and which alternative cause could produce the same observed symptom. When the relation is quantitative, a complete answer supplies units, ranges and a check against a limiting case.

For the course case, a line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover. Consider three boundaries before deciding whether the model is applicable: the system under study, the observation period, and the intervention boundary. System boundaries determine which inventories and energy flows are included. Observation periods distinguish transient loss of control from a steady process average. Intervention boundaries identify where automatic protection, human response or passive containment can plausibly act. A safeguard that acts after the harm does not prevent the initiating event, although it may limit the consequence.

Worked reasoning example

Unverified numerical or qualitative illustration: For a transfer line, investigate NO FLOW with a running pump, then compare with REVERSE FLOW when downstream pressure is higher. Begin with the stated conditions only. Write the relationships that must hold, then identify at least one variable not specified in the example. If an exact arithmetic result is given, reproduce it independently and add a clear qualifier about the simplified model. If the example is qualitative, draw a two-branch argument: one where the existing barrier is available and one where it is defeated by a plausible condition. Do not fill missing branches with assumed success simply to obtain a final score.

A useful way to test the claim is to ask what change would produce the opposite conclusion. For this topic, the specific analytical trap is using a guideword list as a substitute for a facilitated multi-disciplinary meeting. Try to construct a counterexample with the same nominal process equipment but an altered startup, maintenance, utility, human or instrument condition. A single plausible counterexample indicates that the original claim was conditional. It does not automatically establish that the process is unsafe; it establishes which fact must be investigated before any stronger judgment.

Evidence and traceability

The minimum relevant evidence set is updated p&ids, operating procedures, instrument and equipment descriptions, experienced team members. For each item record source, revision, date, scope, owner and confidence. Separate field-measured values from vendor guarantees, industry generic estimates and deliberately fictional learning inputs. For example, two pumps sold at the same nominal capacity do not necessarily share seal arrangements, failure modes or instrument interfaces. Even an authoritative standard does not substitute for actual testing or determine whether a particular facility falls within its legal scope.

An effective review checks whether evidence is current for the operating mode. Startup differs from steady production; temporary operation after a maintenance outage may differ from both. Procedures, alarms and emergency equipment must be evaluated for those modes explicitly. A reliability assertion based on one short interval must not silently be extended to years of service. Missing evidence should generate a specific work request instead of a generic recommendation to “improve safety.”

Laboratory investigation and sensitivity

Use [Lab 10: Independent OR fault-tree gate](../labs/lab-10.html). The printed equation is P(A ∪ B) = 1−(1−p_A)(1−p_B). Compute union of two independent basic events. Start from each slider's default, record the displayed metric and vary the first parameter over five or more settings. The graph and CSV should agree with your hand calculations. Next, change one other parameter while keeping the first fixed; this distinguishes a mathematical sensitivity from a trend caused by simultaneous input changes.

Investigation target: Check result is at least the larger component probability. The major simplification is Independence assumed and same observation basis; shared causes require separate model.. A good lab report predicts the sign of the derivative or change before observing the plot, then explains what physical process that derivative represents. If an output is nonphysical or a limiting denominator becomes zero, it should be reported as an invalid domain rather than manipulated into a finite reassuring result. Place the lesson's analytical relationship alongside the lab relation; explain whether they describe the same physical quantity or different levels of abstraction.

As a challenge, compare this model with [Lab 11: Independent AND fault-tree gate](../labs/lab-11.html). The second model's relation is P(A ∩ B) = p_A p_B, and its stated limitation is Does not model dependencies, systematic failures, repair or demand frequency.. The comparison is not an invitation to combine numbers blindly. Explain what would need to be measured so the two simplified relationships could appear in one defensible engineering argument.

Failure-first decision review

The unacceptable shortcut is using a guideword list as a substitute for a facilitated multi-disciplinary meeting. Make a table with columns assumption, possible failure, observation that would expose it, cheapest credible check, owner, and decision consequence. For this particular topic the review should prioritize the evidence sources above rather than produce a broad list of every conceivable failure. Then ask what is the most important remaining uncertainty if all routine checks pass. Low-frequency high-consequence scenarios often cannot be validated simply by waiting for an incident.

The recommended analytical action is: Record decisions and evidence for actions, including reasons for no recommendation. This recommendation is a learning exercise, not a control-system change or site-specific directive. Describe its boundaries. What would have to be established by independent qualified review? How would an operator learn that the intended protective measure had become unavailable? Which record would demonstrate closure after a modification? A paper action with no verification is not the same as an effective protective function.

Interpreting uncertainty and competing explanations

Uncertainty enters from input data, model structure, operating variability and human or organizational factors. Input uncertainty might be reduced by a calibrated measurement, whereas model-structure uncertainty demands a different physical model or field trial. Increasing the number of decimal places addresses neither. Separate uncertainty that could reverse the conclusion from uncertainty that changes only the reported numerical precision. The severity of a credible major-accident scenario should influence how urgently an evidence gap is reviewed, even when its probability is difficult to quantify.

For hazop guidewords and nodes, an apparently successful barrier test may demonstrate only the modes exercised by the test. It might not probe lost utilities, common-cause failure, maintenance bypass or the specific initiating condition. A useful counterfactual question is: If the expected result were wrong tomorrow, which observation would reveal it first? Identify an observable precursor and a clear escalation action. This turns an educational calculation into a disciplined evidence requirement without representing it as a plant certification.

Independent exercises

1. Boundary and mechanism: Write two complete worksheet rows; distinguish cause from safeguard and consequence. Label at least one fact, one assumption and one unknown.

2. Quantitative check: Reproduce one result from Lab 10. Show units, the governing relationship and a simple limiting-case or conservation check.

3. Scenario variation: Replace one favorable assumption with an unfavorable but plausible operating condition. Explain which safeguarding claim is weakened and why.

4. Decision note: Summarize in 200–300 words whether record decisions and evidence for actions, including reasons for no recommendation. Specify the additional observation that could change your conclusion.

5. Critical review: Explain why using a guideword list as a substitute for a facilitated multi-disciplinary meeting would be misleading when a high-consequence scenario is involved.

Lesson outcome checklist

• A credible scenario chain is drawn, without conflating initiating cause, top event and outcome.
• Model assumptions and units are explicit and the numerical output is checked independently.
• Any barrier credit is tied to function, independence, availability, evidence and an owner.
• The decision specifies what remains unverified; it does not present an educational model as a safe operating limit.

Unit 4 · Lesson 2: Fault trees and dependent events

[Unit overview](../units/unit-04.html) · [Interactive lab 11](../labs/lab-11.html) · [Assessment](../assessments/unit-04.html) · [Applied project](../projects/unit-04.html)

The engineering question

A fault tree starts from a defined top event and uses logic gates for combinations of basic events. OR probability differs from AND probability; independence is rarely automatic and shared utilities can defeat multiple barriers. This lesson belongs to Structured Process Hazard Analysis, where the course objective is to use HAZID, HAZOP, checklists, fault trees and event trees to ask systematically how safeguards fail, including human and common-cause contributions. The governing issue is not whether one can calculate a number; it is whether that number describes the failure mechanism under study. A competent analysis separates a claim about what happens, an argument about why it would happen, and evidence that the safeguards could withstand real operation.

Specific thought experiment. If independent valve failure and sensor failure probabilities are 0.03 and 0.02, their OR event is 0.0494. Work from the equipment boundary outward. Name the initiating event, the operating mode, the top event, the potentially exposed people or environment, and the time over which the consequences could develop. If any one of these is unspecified, maintain the uncertainty rather than inventing a value.

Principles and analytical relationship

The working relation or structured method is P(A∨B)=P(A)+P(B)−P(A∩B). It is useful because it forces an analyst to state inputs and ask whether the units, time basis and conditioning assumptions match. A rate per year cannot be multiplied by an arbitrary probability without asking what event that probability conditions upon. Similarly, an ordinary fraction is not a mass fraction until the relevant mass balance has been declared. In a causal diagram, an arrow represents a proposed physical or organizational dependency; it is not, by itself, proof of causality.

The physical interpretation for fault trees and dependent events is the following: A fault tree starts from a defined top event and uses logic gates for combinations of basic events. OR probability differs from AND probability; independence is rarely automatic and shared utilities can defeat multiple barriers. Thus the result needs an audit trail back to observations, design documents or a controlled estimate. There is no universal conversion from a neat calculation to safe operation. Where the relationship is qualitative, a complete answer explains the conditions for each step and which alternative cause could produce the same observed symptom. When the relation is quantitative, a complete answer supplies units, ranges and a check against a limiting case.

For the course case, a line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover. Consider three boundaries before deciding whether the model is applicable: the system under study, the observation period, and the intervention boundary. System boundaries determine which inventories and energy flows are included. Observation periods distinguish transient loss of control from a steady process average. Intervention boundaries identify where automatic protection, human response or passive containment can plausibly act. A safeguard that acts after the harm does not prevent the initiating event, although it may limit the consequence.

Worked reasoning example

Unverified numerical or qualitative illustration: If independent valve failure and sensor failure probabilities are 0.03 and 0.02, their OR event is 0.0494. Begin with the stated conditions only. Write the relationships that must hold, then identify at least one variable not specified in the example. If an exact arithmetic result is given, reproduce it independently and add a clear qualifier about the simplified model. If the example is qualitative, draw a two-branch argument: one where the existing barrier is available and one where it is defeated by a plausible condition. Do not fill missing branches with assumed success simply to obtain a final score.

A useful way to test the claim is to ask what change would produce the opposite conclusion. For this topic, the specific analytical trap is multiplying dependent failure probabilities or mixing demand probabilities with annual frequencies. Try to construct a counterexample with the same nominal process equipment but an altered startup, maintenance, utility, human or instrument condition. A single plausible counterexample indicates that the original claim was conditional. It does not automatically establish that the process is unsafe; it establishes which fact must be investigated before any stronger judgment.

Evidence and traceability

The minimum relevant evidence set is equipment failure modes, proof test histories and common-cause mechanisms. For each item record source, revision, date, scope, owner and confidence. Separate field-measured values from vendor guarantees, industry generic estimates and deliberately fictional learning inputs. For example, two pumps sold at the same nominal capacity do not necessarily share seal arrangements, failure modes or instrument interfaces. Even an authoritative standard does not substitute for actual testing or determine whether a particular facility falls within its legal scope.

An effective review checks whether evidence is current for the operating mode. Startup differs from steady production; temporary operation after a maintenance outage may differ from both. Procedures, alarms and emergency equipment must be evaluated for those modes explicitly. A reliability assertion based on one short interval must not silently be extended to years of service. Missing evidence should generate a specific work request instead of a generic recommendation to “improve safety.”

Laboratory investigation and sensitivity

Use [Lab 11: Independent AND fault-tree gate](../labs/lab-11.html). The printed equation is P(A ∩ B) = p_A p_B. Compute intersection of independent basic events. Start from each slider's default, record the displayed metric and vary the first parameter over five or more settings. The graph and CSV should agree with your hand calculations. Next, change one other parameter while keeping the first fixed; this distinguishes a mathematical sensitivity from a trend caused by simultaneous input changes.

Investigation target: How does common power failure invalidate this product? The major simplification is Does not model dependencies, systematic failures, repair or demand frequency.. A good lab report predicts the sign of the derivative or change before observing the plot, then explains what physical process that derivative represents. If an output is nonphysical or a limiting denominator becomes zero, it should be reported as an invalid domain rather than manipulated into a finite reassuring result. Place the lesson's analytical relationship alongside the lab relation; explain whether they describe the same physical quantity or different levels of abstraction.

As a challenge, compare this model with [Lab 12: Event-tree failed-branch frequency](../labs/lab-12.html). The second model's relation is f_branch = f_i p_A p_B, and its stated limitation is Frequencies and probabilities are invented; assumes conditional independence and stated branch timing.. The comparison is not an invitation to combine numbers blindly. Explain what would need to be measured so the two simplified relationships could appear in one defensible engineering argument.

Failure-first decision review

The unacceptable shortcut is multiplying dependent failure probabilities or mixing demand probabilities with annual frequencies. Make a table with columns assumption, possible failure, observation that would expose it, cheapest credible check, owner, and decision consequence. For this particular topic the review should prioritize the evidence sources above rather than produce a broad list of every conceivable failure. Then ask what is the most important remaining uncertainty if all routine checks pass. Low-frequency high-consequence scenarios often cannot be validated simply by waiting for an incident.

The recommended analytical action is: Use trees to expose logical structure, then obtain justified failure data. This recommendation is a learning exercise, not a control-system change or site-specific directive. Describe its boundaries. What would have to be established by independent qualified review? How would an operator learn that the intended protective measure had become unavailable? Which record would demonstrate closure after a modification? A paper action with no verification is not the same as an effective protective function.

Interpreting uncertainty and competing explanations

Uncertainty enters from input data, model structure, operating variability and human or organizational factors. Input uncertainty might be reduced by a calibrated measurement, whereas model-structure uncertainty demands a different physical model or field trial. Increasing the number of decimal places addresses neither. Separate uncertainty that could reverse the conclusion from uncertainty that changes only the reported numerical precision. The severity of a credible major-accident scenario should influence how urgently an evidence gap is reviewed, even when its probability is difficult to quantify.

For fault trees and dependent events, an apparently successful barrier test may demonstrate only the modes exercised by the test. It might not probe lost utilities, common-cause failure, maintenance bypass or the specific initiating condition. A useful counterfactual question is: If the expected result were wrong tomorrow, which observation would reveal it first? Identify an observable precursor and a clear escalation action. This turns an educational calculation into a disciplined evidence requirement without representing it as a plant certification.

Independent exercises

1. Boundary and mechanism: Draw one fault tree in which a common electrical supply invalidates the independent-branch estimate. Label at least one fact, one assumption and one unknown.

2. Quantitative check: Reproduce one result from Lab 11. Show units, the governing relationship and a simple limiting-case or conservation check.

3. Scenario variation: Replace one favorable assumption with an unfavorable but plausible operating condition. Explain which safeguarding claim is weakened and why.

4. Decision note: Summarize in 200–300 words whether use trees to expose logical structure, then obtain justified failure data. Specify the additional observation that could change your conclusion.

5. Critical review: Explain why multiplying dependent failure probabilities or mixing demand probabilities with annual frequencies would be misleading when a high-consequence scenario is involved.

Lesson outcome checklist

• A credible scenario chain is drawn, without conflating initiating cause, top event and outcome.
• Model assumptions and units are explicit and the numerical output is checked independently.
• Any barrier credit is tied to function, independence, availability, evidence and an owner.
• The decision specifies what remains unverified; it does not present an educational model as a safe operating limit.

Unit 4 · Lesson 3: Event trees and conditional branch outcomes

[Unit overview](../units/unit-04.html) · [Interactive lab 12](../labs/lab-12.html) · [Assessment](../assessments/unit-04.html) · [Applied project](../projects/unit-04.html)

The engineering question

An event tree begins at an initiating event and follows successful or failed protective functions. Branch frequencies are products of initiating frequency and conditional probabilities only when branch assumptions are justified. This lesson belongs to Structured Process Hazard Analysis, where the course objective is to use HAZID, HAZOP, checklists, fault trees and event trees to ask systematically how safeguards fail, including human and common-cause contributions. The governing issue is not whether one can calculate a number; it is whether that number describes the failure mechanism under study. A competent analysis separates a claim about what happens, an argument about why it would happen, and evidence that the safeguards could withstand real operation.

Specific thought experiment. An illustrative initiating frequency of 0.1/y and a 0.1 failure probability of a safeguard yield a 0.01/y branch under the model assumptions. Work from the equipment boundary outward. Name the initiating event, the operating mode, the top event, the potentially exposed people or environment, and the time over which the consequences could develop. If any one of these is unspecified, maintain the uncertainty rather than inventing a value.

Principles and analytical relationship

The working relation or structured method is f_branch = f_initiator × ∏P(branch state | prior states). It is useful because it forces an analyst to state inputs and ask whether the units, time basis and conditioning assumptions match. A rate per year cannot be multiplied by an arbitrary probability without asking what event that probability conditions upon. Similarly, an ordinary fraction is not a mass fraction until the relevant mass balance has been declared. In a causal diagram, an arrow represents a proposed physical or organizational dependency; it is not, by itself, proof of causality.

The physical interpretation for event trees and conditional branch outcomes is the following: An event tree begins at an initiating event and follows successful or failed protective functions. Branch frequencies are products of initiating frequency and conditional probabilities only when branch assumptions are justified. Thus the result needs an audit trail back to observations, design documents or a controlled estimate. There is no universal conversion from a neat calculation to safe operation. Where the relationship is qualitative, a complete answer explains the conditions for each step and which alternative cause could produce the same observed symptom. When the relation is quantitative, a complete answer supplies units, ranges and a check against a limiting case.

For the course case, a line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover. Consider three boundaries before deciding whether the model is applicable: the system under study, the observation period, and the intervention boundary. System boundaries determine which inventories and energy flows are included. Observation periods distinguish transient loss of control from a steady process average. Intervention boundaries identify where automatic protection, human response or passive containment can plausibly act. A safeguard that acts after the harm does not prevent the initiating event, although it may limit the consequence.

Worked reasoning example

Unverified numerical or qualitative illustration: An illustrative initiating frequency of 0.1/y and a 0.1 failure probability of a safeguard yield a 0.01/y branch under the model assumptions. Begin with the stated conditions only. Write the relationships that must hold, then identify at least one variable not specified in the example. If an exact arithmetic result is given, reproduce it independently and add a clear qualifier about the simplified model. If the example is qualitative, draw a two-branch argument: one where the existing barrier is available and one where it is defeated by a plausible condition. Do not fill missing branches with assumed success simply to obtain a final score.

A useful way to test the claim is to ask what change would produce the opposite conclusion. For this topic, the specific analytical trap is reporting illustrative conditional branch values as measured event frequencies. Try to construct a counterexample with the same nominal process equipment but an altered startup, maintenance, utility, human or instrument condition. A single plausible counterexample indicates that the original claim was conditional. It does not automatically establish that the process is unsafe; it establishes which fact must be investigated before any stronger judgment.

Evidence and traceability

The minimum relevant evidence set is initiating data, barrier design, maintenance, testing, bypass procedures and correlation analysis. For each item record source, revision, date, scope, owner and confidence. Separate field-measured values from vendor guarantees, industry generic estimates and deliberately fictional learning inputs. For example, two pumps sold at the same nominal capacity do not necessarily share seal arrangements, failure modes or instrument interfaces. Even an authoritative standard does not substitute for actual testing or determine whether a particular facility falls within its legal scope.

An effective review checks whether evidence is current for the operating mode. Startup differs from steady production; temporary operation after a maintenance outage may differ from both. Procedures, alarms and emergency equipment must be evaluated for those modes explicitly. A reliability assertion based on one short interval must not silently be extended to years of service. Missing evidence should generate a specific work request instead of a generic recommendation to “improve safety.”

Laboratory investigation and sensitivity

Use [Lab 12: Event-tree failed-branch frequency](../labs/lab-12.html). The printed equation is f_branch = f_i p_A p_B. Follow a hypothetical initiating frequency through two conditional failures. Start from each slider's default, record the displayed metric and vary the first parameter over five or more settings. The graph and CSV should agree with your hand calculations. Next, change one other parameter while keeping the first fixed; this distinguishes a mathematical sensitivity from a trend caused by simultaneous input changes.

Investigation target: Report the branch frequency, then state what data would justify pA and pB. The major simplification is Frequencies and probabilities are invented; assumes conditional independence and stated branch timing.. A good lab report predicts the sign of the derivative or change before observing the plot, then explains what physical process that derivative represents. If an output is nonphysical or a limiting denominator becomes zero, it should be reported as an invalid domain rather than manipulated into a finite reassuring result. Place the lesson's analytical relationship alongside the lab relation; explain whether they describe the same physical quantity or different levels of abstraction.

As a challenge, compare this model with [Lab 10: Independent OR fault-tree gate](../labs/lab-10.html). The second model's relation is P(A ∪ B) = 1−(1−p_A)(1−p_B), and its stated limitation is Independence assumed and same observation basis; shared causes require separate model.. The comparison is not an invitation to combine numbers blindly. Explain what would need to be measured so the two simplified relationships could appear in one defensible engineering argument.

Failure-first decision review

The unacceptable shortcut is reporting illustrative conditional branch values as measured event frequencies. Make a table with columns assumption, possible failure, observation that would expose it, cheapest credible check, owner, and decision consequence. For this particular topic the review should prioritize the evidence sources above rather than produce a broad list of every conceivable failure. Then ask what is the most important remaining uncertainty if all routine checks pass. Low-frequency high-consequence scenarios often cannot be validated simply by waiting for an incident.

The recommended analytical action is: Make assumptions and units explicit in every event-tree calculation. This recommendation is a learning exercise, not a control-system change or site-specific directive. Describe its boundaries. What would have to be established by independent qualified review? How would an operator learn that the intended protective measure had become unavailable? Which record would demonstrate closure after a modification? A paper action with no verification is not the same as an effective protective function.

Interpreting uncertainty and competing explanations

Uncertainty enters from input data, model structure, operating variability and human or organizational factors. Input uncertainty might be reduced by a calibrated measurement, whereas model-structure uncertainty demands a different physical model or field trial. Increasing the number of decimal places addresses neither. Separate uncertainty that could reverse the conclusion from uncertainty that changes only the reported numerical precision. The severity of a credible major-accident scenario should influence how urgently an evidence gap is reviewed, even when its probability is difficult to quantify.

For event trees and conditional branch outcomes, an apparently successful barrier test may demonstrate only the modes exercised by the test. It might not probe lost utilities, common-cause failure, maintenance bypass or the specific initiating condition. A useful counterfactual question is: If the expected result were wrong tomorrow, which observation would reveal it first? Identify an observable precursor and a clear escalation action. This turns an educational calculation into a disciplined evidence requirement without representing it as a plant certification.

Independent exercises

1. Boundary and mechanism: Compare a branch with and without a shared-cause failure and state which data are missing. Label at least one fact, one assumption and one unknown.

2. Quantitative check: Reproduce one result from Lab 12. Show units, the governing relationship and a simple limiting-case or conservation check.

3. Scenario variation: Replace one favorable assumption with an unfavorable but plausible operating condition. Explain which safeguarding claim is weakened and why.

4. Decision note: Summarize in 200–300 words whether make assumptions and units explicit in every event-tree calculation. Specify the additional observation that could change your conclusion.

5. Critical review: Explain why reporting illustrative conditional branch values as measured event frequencies would be misleading when a high-consequence scenario is involved.

Lesson outcome checklist

• A credible scenario chain is drawn, without conflating initiating cause, top event and outcome.
• Model assumptions and units are explicit and the numerical output is checked independently.
• Any barrier credit is tied to function, independence, availability, evidence and an owner.
• The decision specifies what remains unverified; it does not present an educational model as a safe operating limit.

Unit 4 · Lesson 4: FMEA, prioritization and uncertainty

[Unit overview](../units/unit-04.html) · [Interactive lab 10](../labs/lab-10.html) · [Assessment](../assessments/unit-04.html) · [Applied project](../projects/unit-04.html)

The engineering question

Failure modes and effects analysis is useful for asset-level failure identification and action ownership. A severity-occurrence-detection product is ordinal and not a substitute for quantitative risk or consequence analysis. This lesson belongs to Structured Process Hazard Analysis, where the course objective is to use HAZID, HAZOP, checklists, fault trees and event trees to ask systematically how safeguards fail, including human and common-cause contributions. The governing issue is not whether one can calculate a number; it is whether that number describes the failure mechanism under study. A competent analysis separates a claim about what happens, an argument about why it would happen, and evidence that the safeguards could withstand real operation.

Specific thought experiment. A failure mode with scores 8, 3 and 4 has an index 96; scores are internal meeting scales, not hazard probabilities. Work from the equipment boundary outward. Name the initiating event, the operating mode, the top event, the potentially exposed people or environment, and the time over which the consequences could develop. If any one of these is unspecified, maintain the uncertainty rather than inventing a value.

Principles and analytical relationship

The working relation or structured method is Illustrative priority index = S × O × D (ordinal ranking only). It is useful because it forces an analyst to state inputs and ask whether the units, time basis and conditioning assumptions match. A rate per year cannot be multiplied by an arbitrary probability without asking what event that probability conditions upon. Similarly, an ordinary fraction is not a mass fraction until the relevant mass balance has been declared. In a causal diagram, an arrow represents a proposed physical or organizational dependency; it is not, by itself, proof of causality.

The physical interpretation for fmea, prioritization and uncertainty is the following: Failure modes and effects analysis is useful for asset-level failure identification and action ownership. A severity-occurrence-detection product is ordinal and not a substitute for quantitative risk or consequence analysis. Thus the result needs an audit trail back to observations, design documents or a controlled estimate. There is no universal conversion from a neat calculation to safe operation. Where the relationship is qualitative, a complete answer explains the conditions for each step and which alternative cause could produce the same observed symptom. When the relation is quantitative, a complete answer supplies units, ranges and a check against a limiting case.

For the course case, a line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover. Consider three boundaries before deciding whether the model is applicable: the system under study, the observation period, and the intervention boundary. System boundaries determine which inventories and energy flows are included. Observation periods distinguish transient loss of control from a steady process average. Intervention boundaries identify where automatic protection, human response or passive containment can plausibly act. A safeguard that acts after the harm does not prevent the initiating event, although it may limit the consequence.

Worked reasoning example

Unverified numerical or qualitative illustration: A failure mode with scores 8, 3 and 4 has an index 96; scores are internal meeting scales, not hazard probabilities. Begin with the stated conditions only. Write the relationships that must hold, then identify at least one variable not specified in the example. If an exact arithmetic result is given, reproduce it independently and add a clear qualifier about the simplified model. If the example is qualitative, draw a two-branch argument: one where the existing barrier is available and one where it is defeated by a plausible condition. Do not fill missing branches with assumed success simply to obtain a final score.

A useful way to test the claim is to ask what change would produce the opposite conclusion. For this topic, the specific analytical trap is ranking a high-consequence mode low because a detector seems easy to use. Try to construct a counterexample with the same nominal process equipment but an altered startup, maintenance, utility, human or instrument condition. A single plausible counterexample indicates that the original claim was conditional. It does not automatically establish that the process is unsafe; it establishes which fact must be investigated before any stronger judgment.

Evidence and traceability

The minimum relevant evidence set is asset function, failure history, inspection records, assessor definitions and consequences. For each item record source, revision, date, scope, owner and confidence. Separate field-measured values from vendor guarantees, industry generic estimates and deliberately fictional learning inputs. For example, two pumps sold at the same nominal capacity do not necessarily share seal arrangements, failure modes or instrument interfaces. Even an authoritative standard does not substitute for actual testing or determine whether a particular facility falls within its legal scope.

An effective review checks whether evidence is current for the operating mode. Startup differs from steady production; temporary operation after a maintenance outage may differ from both. Procedures, alarms and emergency equipment must be evaluated for those modes explicitly. A reliability assertion based on one short interval must not silently be extended to years of service. Missing evidence should generate a specific work request instead of a generic recommendation to “improve safety.”

Laboratory investigation and sensitivity

Use [Lab 10: Independent OR fault-tree gate](../labs/lab-10.html). The printed equation is P(A ∪ B) = 1−(1−p_A)(1−p_B). Compute union of two independent basic events. Start from each slider's default, record the displayed metric and vary the first parameter over five or more settings. The graph and CSV should agree with your hand calculations. Next, change one other parameter while keeping the first fixed; this distinguishes a mathematical sensitivity from a trend caused by simultaneous input changes.

Investigation target: Check result is at least the larger component probability. The major simplification is Independence assumed and same observation basis; shared causes require separate model.. A good lab report predicts the sign of the derivative or change before observing the plot, then explains what physical process that derivative represents. If an output is nonphysical or a limiting denominator becomes zero, it should be reported as an invalid domain rather than manipulated into a finite reassuring result. Place the lesson's analytical relationship alongside the lab relation; explain whether they describe the same physical quantity or different levels of abstraction.

As a challenge, compare this model with [Lab 11: Independent AND fault-tree gate](../labs/lab-11.html). The second model's relation is P(A ∩ B) = p_A p_B, and its stated limitation is Does not model dependencies, systematic failures, repair or demand frequency.. The comparison is not an invitation to combine numbers blindly. Explain what would need to be measured so the two simplified relationships could appear in one defensible engineering argument.

Failure-first decision review

The unacceptable shortcut is ranking a high-consequence mode low because a detector seems easy to use. Make a table with columns assumption, possible failure, observation that would expose it, cheapest credible check, owner, and decision consequence. For this particular topic the review should prioritize the evidence sources above rather than produce a broad list of every conceivable failure. Then ask what is the most important remaining uncertainty if all routine checks pass. Low-frequency high-consequence scenarios often cannot be validated simply by waiting for an incident.

The recommended analytical action is: Keep severe single-point failures visible regardless of composite score. This recommendation is a learning exercise, not a control-system change or site-specific directive. Describe its boundaries. What would have to be established by independent qualified review? How would an operator learn that the intended protective measure had become unavailable? Which record would demonstrate closure after a modification? A paper action with no verification is not the same as an effective protective function.

Interpreting uncertainty and competing explanations

Uncertainty enters from input data, model structure, operating variability and human or organizational factors. Input uncertainty might be reduced by a calibrated measurement, whereas model-structure uncertainty demands a different physical model or field trial. Increasing the number of decimal places addresses neither. Separate uncertainty that could reverse the conclusion from uncertainty that changes only the reported numerical precision. The severity of a credible major-accident scenario should influence how urgently an evidence gap is reviewed, even when its probability is difficult to quantify.

For fmea, prioritization and uncertainty, an apparently successful barrier test may demonstrate only the modes exercised by the test. It might not probe lost utilities, common-cause failure, maintenance bypass or the specific initiating condition. A useful counterfactual question is: If the expected result were wrong tomorrow, which observation would reveal it first? Identify an observable precursor and a clear escalation action. This turns an educational calculation into a disciplined evidence requirement without representing it as a plant certification.

Independent exercises

1. Boundary and mechanism: Construct two score sets with equal product but different consequence severity and discuss priority. Label at least one fact, one assumption and one unknown.

2. Quantitative check: Reproduce one result from Lab 10. Show units, the governing relationship and a simple limiting-case or conservation check.

3. Scenario variation: Replace one favorable assumption with an unfavorable but plausible operating condition. Explain which safeguarding claim is weakened and why.

4. Decision note: Summarize in 200–300 words whether keep severe single-point failures visible regardless of composite score. Specify the additional observation that could change your conclusion.

5. Critical review: Explain why ranking a high-consequence mode low because a detector seems easy to use would be misleading when a high-consequence scenario is involved.

Lesson outcome checklist

• A credible scenario chain is drawn, without conflating initiating cause, top event and outcome.
• Model assumptions and units are explicit and the numerical output is checked independently.
• Any barrier credit is tied to function, independence, availability, evidence and an owner.
• The decision specifies what remains unverified; it does not present an educational model as a safe operating limit.

Applied Project 04 — Structured Process Hazard Analysis

Scenario and objective

Scenario: A line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover.

Target: Use HAZID, HAZOP, checklists, fault trees and event trees to ask systematically how safeguards fail, including human and common-cause contributions.

The task is a supervised conceptual study. It is not permission to change operating procedures, introduce hazardous chemicals, bypass protection or size relief devices. Assume that a multidisciplinary panel must decide whether to commission additional analysis, not whether this student workbook certifies a plant. Your deliverable must identify the claim being made, what evidence supports it, and what uncertainty remains. The board values clear red flags over cosmetic completion percentages.

Work package A: describe the situation

Draw a block-flow boundary showing process inventory, incoming feeds or energy, manipulated variables, utilities, protective controls and relevant maintenance interfaces. Record the operating mode, unit conventions, material identity gaps and any location- or jurisdiction-dependent regulatory questions. Write one plausible hazardous event without guessing its annual frequency. For each asserted safeguard, identify what action it takes, when it acts relative to the top event, and which elements it shares with other protective controls.

The case provides a starting point only: A line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover.. Ask how equipment failure and incorrect operating information could combine. Check a routine operation, startup, shutdown and an interrupted utility condition. Treat any missing process safety information as a question with an owner; do not silently assume that a procedure exists or a transmitter is independent. Make a compact register of at least eight assumptions grouped into physical properties, instrumentation, human response and external conditions.

Work package B: model and verify

Lab 10 — [Independent OR fault-tree gate](../labs/lab-10.html). Compute the baseline from P(A ∪ B) = 1−(1−p_A)(1−p_B) and export a one-parameter sweep. Check result is at least the larger component probability. The condition Independence assumed and same observation basis; shared causes require separate model. must appear as a red-line limitation in the report. Record at least one changed parameter set and reproduce one plotted point without JavaScript. Explain whether a favorable change in this model would genuinely improve the identified hazard or merely change one simplified quantity.

Lab 11 — [Independent AND fault-tree gate](../labs/lab-11.html). Compute the baseline from P(A ∩ B) = p_A p_B and export a one-parameter sweep. How does common power failure invalidate this product? The condition Does not model dependencies, systematic failures, repair or demand frequency. must appear as a red-line limitation in the report. Record at least one changed parameter set and reproduce one plotted point without JavaScript. Explain whether a favorable change in this model would genuinely improve the identified hazard or merely change one simplified quantity.

Lab 12 — [Event-tree failed-branch frequency](../labs/lab-12.html). Compute the baseline from f_branch = f_i p_A p_B and export a one-parameter sweep. Report the branch frequency, then state what data would justify pA and pB. The condition Frequencies and probabilities are invented; assumes conditional independence and stated branch timing. must appear as a red-line limitation in the report. Record at least one changed parameter set and reproduce one plotted point without JavaScript. Explain whether a favorable change in this model would genuinely improve the identified hazard or merely change one simplified quantity.

Work package C: argue the controls

Prepare a bow-tie-style diagram with three credible threats and two possible consequence pathways. Describe at least one prevention design measure, one operating or inspection control, one possible protective-system layer and one mitigation measure. Do not treat all of these as independent or calculate a cumulative protection factor without justified evidence. Identify a shared-cause vulnerability (for example, common power supply, blocked sensing line or maintenance isolation) and show how your recommended verification would detect it.

Create a control register with columns control purpose, covered initiating mechanism, physical element, mode of demand, availability evidence, testing method, owner, and unresolved dependency. A valid control should have a documented performance claim that can be tested in the field. If field testing would introduce danger, propose a qualified nonintrusive verification method or documentation review instead of suggesting an uncontrolled trial.

Work package D: decision, uncertainty and follow-up

Deliver a 600–900-word decision memo with a recommendation of further analysis, redesign for inherent safety, or insufficient evidence to proceed. The answer must not state that a student's simulation proves safety or regulatory compliance. Begin with the most serious potentially unmitigated scenario. Include a one-page assumptions register and a prioritized list of the five most valuable additional data items. Differentiate uncertainty in inputs from uncertainty in the basic model structure. Show how one new piece of evidence could reverse your recommendation.

The expected project artifact is: A worksheet is a prompt for multidisciplinary reasoning, not proof that the identified scenario list is exhaustive. Describe at least three acceptance tests, responsible roles and the evidence each would produce. Finish with a handover list for a qualified engineer or hazard-analysis team. A statement like “we will improve training” is insufficient without specifying which error pathway it is intended to reduce and how the effect would be checked.

Assessment criteria

• Process and time boundaries are explicit and aligned with the chosen hazardous event.
• Equations reproduce the baseline, limits are visible, and CSV data agree with an independent computation.
• Claimed safeguards have separate mechanisms and credible evidence; common-cause weaknesses are challenged.
• Unknown chemical properties, actual frequencies and code requirements are not invented.
• The conclusion is proportional to evidence and contains accountable next actions rather than a blanket approval.

Unit 04 — Assessment: Structured Process Hazard Analysis

Scenario: A line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover. This assessment contains 16 separately numbered, multi-part tasks, four per lesson. Students should complete the numerical parts independently and explicitly distinguish illustrative assumptions from measured or regulated inputs. There is no site-specific pass/fail safety conclusion.

Learning standard: A worksheet is a prompt for multidisciplinary reasoning, not proof that the identified scenario list is exhaustive.

Scoring rubric

Each task is worth ten marks: physical or causal boundary (2), correct relationship or defensible logic (2), evidence and units (2), explicit limitation (2), and transparent action or interpretation (2). A risk claim without necessary provenance receives no numerical credit regardless of apparent precision. Students may challenge an ill-posed input as part of the solution if they explain which information is missing.

Lesson 1 — HAZOP guidewords and nodes

The four problems below require different kinds of evidence; do not copy a single stock paragraph as four answers.

Q01 — Physical reconstruction (10 marks). Start from Deviation = guideword applied to a defined process parameter in the following case: For a transfer line, investigate NO FLOW with a running pump, then compare with REVERSE FLOW when downstream pressure is higher. Identify each term or causal link, the relevant units or event definition, and a reasonable limiting case. Describe at least one operational state in which the relationship would no longer be adequate. For numerical examples, reproduce the printed result with no more significant figures than the inputs justify.

Q02 — Interactive computation and falsification (10 marks). Run [Lab 10](../labs/lab-10.html), Independent OR fault-tree gate. Tabulate at least seven points for its first variable, calculate one independent output, then change its second variable. The lab asks: Check result is at least the larger component probability. Evaluate the specific restriction Independence assumed and same observation basis; shared causes require separate model.; provide a case where this restriction matters and state what additional physical model would be needed.

Q03 — Hazard and barrier chain (10 marks). Examine hazop guidewords and nodes using this hazard background: A line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover. Name an initiating mechanism, the loss-of-control top event, one possible consequence, an inherently safer alternative and an independent barrier if credible. The analysis must explicitly challenge the misleading assumption using a guideword list as a substitute for a facilitated multi-disciplinary meeting. Which shared utility, maintenance activity or human action could defeat the claimed protections?

Q04 — Evidence-led technical memo (10 marks). Prepare a 250-word memo answering: Write two complete worksheet rows; distinguish cause from safeguard and consequence. The recommendation should be record decisions and evidence for actions, including reasons for no recommendation but you must justify or challenge it. List the real-world records needed: Updated P&IDs, operating procedures, instrument and equipment descriptions, experienced team members. Separate a hypothetical mathematical statement from an engineering action and identify the competent approver and a falsifiable follow-up test.

Lesson 2 — Fault trees and dependent events

The four problems below require different kinds of evidence; do not copy a single stock paragraph as four answers.

Q05 — Physical reconstruction (10 marks). Start from P(A∨B)=P(A)+P(B)−P(A∩B) in the following case: If independent valve failure and sensor failure probabilities are 0.03 and 0.02, their OR event is 0.0494. Identify each term or causal link, the relevant units or event definition, and a reasonable limiting case. Describe at least one operational state in which the relationship would no longer be adequate. For numerical examples, reproduce the printed result with no more significant figures than the inputs justify.

Q06 — Interactive computation and falsification (10 marks). Run [Lab 11](../labs/lab-11.html), Independent AND fault-tree gate. Tabulate at least seven points for its first variable, calculate one independent output, then change its second variable. The lab asks: How does common power failure invalidate this product? Evaluate the specific restriction Does not model dependencies, systematic failures, repair or demand frequency.; provide a case where this restriction matters and state what additional physical model would be needed.

Q07 — Hazard and barrier chain (10 marks). Examine fault trees and dependent events using this hazard background: A line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover. Name an initiating mechanism, the loss-of-control top event, one possible consequence, an inherently safer alternative and an independent barrier if credible. The analysis must explicitly challenge the misleading assumption multiplying dependent failure probabilities or mixing demand probabilities with annual frequencies. Which shared utility, maintenance activity or human action could defeat the claimed protections?

Q08 — Evidence-led technical memo (10 marks). Prepare a 250-word memo answering: Draw one fault tree in which a common electrical supply invalidates the independent-branch estimate. The recommendation should be use trees to expose logical structure, then obtain justified failure data but you must justify or challenge it. List the real-world records needed: Equipment failure modes, proof test histories and common-cause mechanisms. Separate a hypothetical mathematical statement from an engineering action and identify the competent approver and a falsifiable follow-up test.

Lesson 3 — Event trees and conditional branch outcomes

The four problems below require different kinds of evidence; do not copy a single stock paragraph as four answers.

Q09 — Physical reconstruction (10 marks). Start from f_branch = f_initiator × ∏P(branch state | prior states) in the following case: An illustrative initiating frequency of 0.1/y and a 0.1 failure probability of a safeguard yield a 0.01/y branch under the model assumptions. Identify each term or causal link, the relevant units or event definition, and a reasonable limiting case. Describe at least one operational state in which the relationship would no longer be adequate. For numerical examples, reproduce the printed result with no more significant figures than the inputs justify.

Q10 — Interactive computation and falsification (10 marks). Run [Lab 12](../labs/lab-12.html), Event-tree failed-branch frequency. Tabulate at least seven points for its first variable, calculate one independent output, then change its second variable. The lab asks: Report the branch frequency, then state what data would justify pA and pB. Evaluate the specific restriction Frequencies and probabilities are invented; assumes conditional independence and stated branch timing.; provide a case where this restriction matters and state what additional physical model would be needed.

Q11 — Hazard and barrier chain (10 marks). Examine event trees and conditional branch outcomes using this hazard background: A line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover. Name an initiating mechanism, the loss-of-control top event, one possible consequence, an inherently safer alternative and an independent barrier if credible. The analysis must explicitly challenge the misleading assumption reporting illustrative conditional branch values as measured event frequencies. Which shared utility, maintenance activity or human action could defeat the claimed protections?

Q12 — Evidence-led technical memo (10 marks). Prepare a 250-word memo answering: Compare a branch with and without a shared-cause failure and state which data are missing. The recommendation should be make assumptions and units explicit in every event-tree calculation but you must justify or challenge it. List the real-world records needed: Initiating data, barrier design, maintenance, testing, bypass procedures and correlation analysis. Separate a hypothetical mathematical statement from an engineering action and identify the competent approver and a falsifiable follow-up test.

Lesson 4 — FMEA, prioritization and uncertainty

The four problems below require different kinds of evidence; do not copy a single stock paragraph as four answers.

Q13 — Physical reconstruction (10 marks). Start from Illustrative priority index = S × O × D (ordinal ranking only) in the following case: A failure mode with scores 8, 3 and 4 has an index 96; scores are internal meeting scales, not hazard probabilities. Identify each term or causal link, the relevant units or event definition, and a reasonable limiting case. Describe at least one operational state in which the relationship would no longer be adequate. For numerical examples, reproduce the printed result with no more significant figures than the inputs justify.

Q14 — Interactive computation and falsification (10 marks). Run [Lab 10](../labs/lab-10.html), Independent OR fault-tree gate. Tabulate at least seven points for its first variable, calculate one independent output, then change its second variable. The lab asks: Check result is at least the larger component probability. Evaluate the specific restriction Independence assumed and same observation basis; shared causes require separate model.; provide a case where this restriction matters and state what additional physical model would be needed.

Q15 — Hazard and barrier chain (10 marks). Examine fmea, prioritization and uncertainty using this hazard background: A line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover. Name an initiating mechanism, the loss-of-control top event, one possible consequence, an inherently safer alternative and an independent barrier if credible. The analysis must explicitly challenge the misleading assumption ranking a high-consequence mode low because a detector seems easy to use. Which shared utility, maintenance activity or human action could defeat the claimed protections?

Q16 — Evidence-led technical memo (10 marks). Prepare a 250-word memo answering: Construct two score sets with equal product but different consequence severity and discuss priority. The recommendation should be keep severe single-point failures visible regardless of composite score but you must justify or challenge it. List the real-world records needed: Asset function, failure history, inspection records, assessor definitions and consequences. Separate a hypothetical mathematical statement from an engineering action and identify the competent approver and a falsifiable follow-up test.

Synthesis: no-go evidence check

Construct an evidence table for structured process hazard analysis. Include the case A line-up error during tank transfer can be initiated by an incorrect valve state, ambiguous labeling, instrument failure or poor shift turnover.. State one safety-critical condition that cannot be closed by the calculations above. Propose a technically reasonable way to obtain missing evidence, an owner and a hold point. Explain why a numerically appealing dashboard could still hide an unacceptable unresolved scenario.