Failure Mechanisms and Root-Cause Methods

Problem Statement: **Primary relation:** `Common screening index RPN=S×O×D uses ordinal ranks; do not interpret RPN/1000 as a failure probability.` The relation should first be read in words and translated into a dimensional statement. Identify which quantities are probabilities, time or cycle measures, rates, costs, loads, engineering scores or empirical indicators. If an input is a probability, its feasible interval is from zero to one; if it is an event intensity, it must be nonnegative and accompanied by a unit such as failures per operating hour. The output should be interpreted at the same stated boundary and over the same mission or reporting period as its inputs. **Reasoning sequence.** (i) Define the asset and the function; (ii) write all inputs and their units; (iii) choose the simplest physically defensible model; (iv) perform the computation using an independent check; (v) compare the result with limiting cases; (vi) state uncertainty and model boundaries before recommending maintenance. For example, the limit of a no-failure event probability as an assumed event rate approaches zero should be consistent with ordinary experience. A result outside its physically possible range suggests either an arithmetic fault, incompatible units or a model used outside its assumptions. **Worked engineering example.** A miscalibrated temperature sensor may score modest occurrence but very high severity if it can defeat thermal protection. A cracked bracket can be visible yet have serious falling-object consequences. After evaluating the arithmetic, report what the result means and—equally important—what it does not mean. Distinguish a hypothetical prediction from a measured population statistic. If a numerical example uses a notional fleet or synthetic data, it must not appear in an operator's work package as a measured site result. For any policy comparison, repeat the calculation using at least two plausible ranges for its most uncertain input and report whether the choice changes. ### Separate requirement from measurement An engineer should be able to state the acceptance requirement before seeing the measurement. Otherwise thresholds tend to move after results are known. Preserve the original requirement, report any exception and obtain authorized approval for changes. ## 3. Where the model can fail Changing a detection score after adding an alarm does not prove risk reduction if false negatives, sensor power loss and operator response are untested. An important diagnostic practice is to seek evidence against the simplest explanation. A repair which temporarily restores output can disguise an uncorrected design, installation or operating error. If the apparent rate improves after a maintenance change, normalize against exposure and examine whether production load, weather, equipment population or reporting conventions changed in the same period. Correlation between a signal and a failure does not establish that intervening on the signal will prevent the failure.

Problem Statement: **Primary relation:** `If P-F interval has a conservative estimate of 12 days, a proposed 30-day inspection cannot reliably find the warning in that window.` The relation should first be read in words and translated into a dimensional statement. Identify which quantities are probabilities, time or cycle measures, rates, costs, loads, engineering scores or empirical indicators. If an input is a probability, its feasible interval is from zero to one; if it is an event intensity, it must be nonnegative and accompanied by a unit such as failures per operating hour. The output should be interpreted at the same stated boundary and over the same mission or reporting period as its inputs. **Reasoning sequence.** (i) Define the asset and the function; (ii) write all inputs and their units; (iii) choose the simplest physically defensible model; (iv) perform the computation using an independent check; (v) compare the result with limiting cases; (vi) state uncertainty and model boundaries before recommending maintenance. For example, the limit of a no-failure event probability as an assumed event rate approaches zero should be consistent with ordinary experience. A result outside its physically possible range suggests either an arithmetic fault, incompatible units or a model used outside its assumptions. **Worked engineering example.** An oil-contamination trend may give weeks of warning for a gearbox; an electronic switch can fail randomly without a measurable P-F precursor. Different policies are justified. After evaluating the arithmetic, report what the result means and—equally important—what it does not mean. Distinguish a hypothetical prediction from a measured population statistic. If a numerical example uses a notional fleet or synthetic data, it must not appear in an operator's work package as a measured site result. For any policy comparison, repeat the calculation using at least two plausible ranges for its most uncertain input and report whether the choice changes. ### Distinguish data from decisions A probability is an input to a decision rather than a decision by itself. Two alternatives with equal failure probability can lead to different responses when consequences, restoration time and regulatory obligations are different. ## 3. Where the model can fail A theoretically effective task may be impractical due to unsafe access, inability to isolate equipment, or inadequate measurement repeatability. An important diagnostic practice is to seek evidence against the simplest explanation. A repair which temporarily restores output can disguise an uncorrected design, installation or operating error. If the apparent rate improves after a maintenance change, normalize against exposure and examine whether production load, weather, equipment population or reporting conventions changed in the same period. Correlation between a signal and a failure does not establish that intervening on the signal will prevent the failure.

Problem Statement: **Primary relation:** `Recurrence proportion after a corrective-action date = repeated qualifying events / exposure in the defined follow-up window; comparisons require comparable exposure.` The relation should first be read in words and translated into a dimensional statement. Identify which quantities are probabilities, time or cycle measures, rates, costs, loads, engineering scores or empirical indicators. If an input is a probability, its feasible interval is from zero to one; if it is an event intensity, it must be nonnegative and accompanied by a unit such as failures per operating hour. The output should be interpreted at the same stated boundary and over the same mission or reporting period as its inputs. **Reasoning sequence.** (i) Define the asset and the function; (ii) write all inputs and their units; (iii) choose the simplest physically defensible model; (iv) perform the computation using an independent check; (v) compare the result with limiting cases; (vi) state uncertainty and model boundaries before recommending maintenance. For example, the limit of a no-failure event probability as an assumed event rate approaches zero should be consistent with ordinary experience. A result outside its physically possible range suggests either an arithmetic fault, incompatible units or a model used outside its assumptions. **Worked engineering example.** Three motor failures occur after a cooling fan redesign. Investigators should compare load, ambient temperature, ventilation blockage and repair history before judging whether the redesign worked. After evaluating the arithmetic, report what the result means and—equally important—what it does not mean. Distinguish a hypothetical prediction from a measured population statistic. If a numerical example uses a notional fleet or synthetic data, it must not appear in an operator's work package as a measured site result. For any policy comparison, repeat the calculation using at least two plausible ranges for its most uncertain input and report whether the choice changes. ### Audit model assumptions Every model has a region in which its assumptions make sense. Before using an equation in a recommendation, check units, boundary, independence assumptions, the way failures are counted, and whether repair changes the modeled population. ## 3. Where the model can fail A reduction in failure count after an upgrade may simply reflect a shorter operating period or production slowdown; normalize by exposure. An important diagnostic practice is to seek evidence against the simplest explanation. A repair which temporarily restores output can disguise an uncorrected design, installation or operating error. If the apparent rate improves after a maintenance change, normalize against exposure and examine whether production load, weather, equipment population or reporting conventions changed in the same period. Correlation between a signal and a failure does not establish that intervening on the signal will prevent the failure.

Problem Statement: **Primary relation:** `For high-cycle fatigue an illustrative Basquin relation may take σ_a=C N^b with b<0 within its applicable material regime.` The relation should first be read in words and translated into a dimensional statement. Identify which quantities are probabilities, time or cycle measures, rates, costs, loads, engineering scores or empirical indicators. If an input is a probability, its feasible interval is from zero to one; if it is an event intensity, it must be nonnegative and accompanied by a unit such as failures per operating hour. The output should be interpreted at the same stated boundary and over the same mission or reporting period as its inputs. **Reasoning sequence.** (i) Define the asset and the function; (ii) write all inputs and their units; (iii) choose the simplest physically defensible model; (iv) perform the computation using an independent check; (v) compare the result with limiting cases; (vi) state uncertainty and model boundaries before recommending maintenance. For example, the limit of a no-failure event probability as an assumed event rate approaches zero should be consistent with ordinary experience. A result outside its physically possible range suggests either an arithmetic fault, incompatible units or a model used outside its assumptions. **Worked engineering example.** A shaft suffering reversed bending near a keyway may fail after many cycles although static stress remains below yield. Inspections must consider crack accessibility and detectable size. After evaluating the arithmetic, report what the result means and—equally important—what it does not mean. Distinguish a hypothetical prediction from a measured population statistic. If a numerical example uses a notional fleet or synthetic data, it must not appear in an operator's work package as a measured site result. For any policy comparison, repeat the calculation using at least two plausible ranges for its most uncertain input and report whether the choice changes. ### Keep the operational objective in view A metric is useful when it changes a decision that helps deliver service. Additional data collection should therefore answer a concrete question: whether to inspect, redesign, change stocking policy, add monitoring or accept an explicitly bounded residual risk. ## 3. Where the model can fail An S–N fit from laboratory specimens should not be used without correction for surface condition, size, temperature, mean stress and scatter. An important diagnostic practice is to seek evidence against the simplest explanation. A repair which temporarily restores output can disguise an uncorrected design, installation or operating error. If the apparent rate improves after a maintenance change, normalize against exposure and examine whether production load, weather, equipment population or reporting conventions changed in the same period. Correlation between a signal and a failure does not establish that intervening on the signal will prevent the failure.

Problem Statement: **Primary relation:** `A diagnostic test has false-positive and false-negative rates; predictive value also depends on prevalence.` The relation should first be read in words and translated into a dimensional statement. Identify which quantities are probabilities, time or cycle measures, rates, costs, loads, engineering scores or empirical indicators. If an input is a probability, its feasible interval is from zero to one; if it is an event intensity, it must be nonnegative and accompanied by a unit such as failures per operating hour. The output should be interpreted at the same stated boundary and over the same mission or reporting period as its inputs. **Reasoning sequence.** (i) Define the asset and the function; (ii) write all inputs and their units; (iii) choose the simplest physically defensible model; (iv) perform the computation using an independent check; (v) compare the result with limiting cases; (vi) state uncertainty and model boundaries before recommending maintenance. For example, the limit of a no-failure event probability as an assumed event rate approaches zero should be consistent with ordinary experience. A result outside its physically possible range suggests either an arithmetic fault, incompatible units or a model used outside its assumptions.