Ageing and Life-Extension Screening

Use this skill when a maintenance history has to answer a life-extension question: is this equipment getting worse, and will it still do its job in year N? It turns a list of corrective-failure dates into a trend verdict, a fitted failure-intensity model, a projection to a target year, and a maintain-versus-replace crossover.

When to Use

• A life-extension or lifetime-programme decision must be justified from failure history.
• A user asks whether failures are becoming more frequent (ageing) or less frequent (reliability growth).
• A projection is needed of how many failures to expect between today and a required end-of-life year.
• A maintain-versus-replace comparison is needed at screening level.
• A recurring failure has to be characterised across many years of records.

Do NOT Use For

• A single non-repairable item's time-to-failure distribution — that is a lifetime (Weibull) problem, not a point-process problem.
• Structural fatigue or corrosion remaining-life — those need a damage model, not a failure-count trend.
• A qualified life-extension assessment or regulatory submission. This is screening input to one.

The Modelling Trap This Skill Exists to Prevent

A population that is repaired and returned to service is a stochastic point process, not a lifetime distribution. Fitting a two-parameter Weibull to the inter-arrival times of a repairable system and reporting the shape parameter as "the ageing parameter" is a standard and consequential error: it assumes every repair restores the item to as-good-as-new, which is exactly the assumption a life-extension study must not make.

The correct screening statistic is the trend in the rate of occurrence of failures (ROCOF). This skill uses two independent, complementary tests of that trend so a single statistic cannot carry the conclusion alone.

Inputs

• failure_times_years: corrective-failure times in years measured from the start of the observation window, each in (0, observation_years].
• observation_years: length of the observation window in years (time-truncated).
• target_year_offset: years from the end of the window to the required end-of-life. Observed to 2026, required to 2037 ⇒ 11.0.
• population_size: number of items, used to normalise reported rates (default 1).
• replacement_cost, corrective_cost_per_failure, annual_cost_of_ownership, discount_rate: optional economics in one consistent currency unit.

Outputs

• laplace_u, laplace_verdict: deteriorating / improving / no-significant-trend / insufficient-data.
• crow_amsaa_beta, crow_amsaa_lambda, beta_confidence_low, beta_confidence_high.
• rate_now_per_year, rate_at_target_per_year, rate_ratio_target_over_now.
• expected_failures_to_target, expected_failures_if_no_ageing, excess_failures_from_ageing.
• ageing_verdict: significant-ageing / ageing-suspected / no-ageing-detected / improving / insufficient-data.
• life_extension_verdict: replace / extend-with-measures / extend / insufficient-data-for-decision.
• replacement_crossover_year: first year in which cumulative discounted keep-cost exceeds replacement cost, or None.
• assumptions: the public assumptions actually applied.

Engineering Method

Laplace centroid trend test. For a time-truncated process observed over $T$ with failures at $t_i$,

$$ U = \frac{\bar t - T/2}{T \big/ \sqrt{12 n}}, \qquad \bar t = \frac{1}{n}\sum_{i=1}^{n} t_i $$

$U$ is approximately standard normal under the no-trend (homogeneous Poisson) null. $U > 1.96$ means failures cluster late in the window — deterioration. $U < -1.96$ means they cluster early — improvement. The statistic is scale-invariant, so the choice of time unit cannot change the verdict.

Crow-AMSAA / NHPP power-law intensity. The mean cumulative function is modelled as

$$ N(t) = \lambda t^{\beta}, \qquad \rho(t) = \frac{\mathrm{d}N}{\mathrm{d}t} = \lambda \beta t^{\beta - 1} $$

with the time-truncated maximum-likelihood estimates

$$ \hat\beta = \frac{n}{\sum_{i=1}^{n} \ln!\left(T / t_i\right)}, \qquad \hat\lambda = \frac{n}{T^{\hat\beta}} $$

$\beta > 1$ is an increasing ROCOF (system-level wear-out), $\beta = 1$ is a homogeneous Poisson process, $\beta < 1$ is reliability growth. The asymptotic standard error of $\hat\beta$ is $\hat\beta/\sqrt{n}$, which gives the reported confidence band. Ageing is only called significant-ageing when the lower confidence bound on $\beta$ exceeds 1 — a point estimate above 1 on a short record is not evidence.

Projection to the target year. Expected failures between the end of the window $T$ and the target $T + \Delta$ are $\lambda\big[(T+\Delta)^{\beta} - T^{\beta}\big]$, compared against the no-ageing baseline $\bar\rho \Delta$. The difference is reported as excess_failures_from_ageing so the ageing penalty is separated from the base load.

Maintain-versus-replace crossover. Year-by-year the projected failure count is costed, an annual ownership cost is added, the stream is discounted, and the first year where the cumulative keep-cost exceeds the replacement cost is reported.

The Data-Quality Gate (read before trusting any verdict)

The trend statistics assume a stationary reporting regime. Every real CMMS record set violates that somewhere, and each violation biases the trend in a predictable direction:

The last row is the strongest defence: always compute the same trend on a control population from the same plant and report both. A rising rate that matches the plant-wide rise is a reporting change, not ageing.

Python Usage Pattern

from ageing_life_extension_screening import AgeingLifeExtensionModel

model = AgeingLifeExtensionModel()
result = model.evaluate(
    failure_times_years=[2.1, 5.4, 8.8, 11.2, 12.9, 14.1, 15.6, 16.4, 17.2, 17.9],
    observation_years=18.0,      # 2008 -> 2026
    target_year_offset=11.0,     # required to 2037
    population_size=168,
    replacement_cost=1.0e7,
    corrective_cost_per_failure=1.2e5,
    discount_rate=0.07,
)

print(result.laplace_verdict, result.crow_amsaa_beta)
print(result.expected_failures_to_target, result.excess_failures_from_ageing)
print(result.ageing_verdict, result.life_extension_verdict)

Interpreting the Verdicts

A replace verdict is a screening signal. It has to be combined with the consequence side — for a safety-critical element, a barrier-performance and regulatory assessment governs, not the economics.

Validation Checklist

• At least four usable corrective failure records, otherwise the verdict is insufficient-data-for-decision and no rate is reported.
• The data-quality gate above has been walked: migration date, mid-window tag creation, yard stays, and campaign inspections all screened out.
• The same trend has been computed on a plant-wide control population and both are reported.
• observation_years covers operating time only, with non-operating periods subtracted.
• Costs are on one basis (same currency, same year) and the discount rate is stated.
• The verdict is presented as screening, with the consequence side handled separately for safety-critical elements.

Common Mistakes

Related Skills and Agents

• neqsim-reliability-data-screening — MTBF / availability once a failure rate is agreed. Use this skill first to establish whether that rate is constant; use that skill second to turn it into availability.
• neqsim-safety-function-coverage-screening — when the item is a protective function.
• enterprise-life-extension-assessment — the governed enterprise wrapper: regulatory framing, SAP/STID evidence requirements, safety-critical-element gating, and review handoff.
• enterprise-maintenance-api — pulls the corrective-failure history that feeds failure_times_years.
• enterprise-ram-availability — company acceptance policy on the resulting availability.

Limitations

• Screening only. Not a qualified life-extension assessment, technical-condition survey, or regulatory submission.
• The NHPP assumes minimal repair; a genuinely as-good-as-new renewal is not represented.
• Verdicts are driven by open thresholds, not by any operator's acceptance criteria.
• No failure-mode resolution: the projection covers all corrective failures together. Split the series by failure mode when one mode dominates.

References

• ISO 14224, Collection and Exchange of Reliability and Maintenance Data for Equipment.
• NORSOK Z-008, Risk Based Maintenance and Consequence Classification.
• Crow, L. H., Reliability Analysis for Complex, Repairable Systems, in Reliability and Biometry, SIAM, 1974 — the Crow-AMSAA / NHPP power-law model.
• Ascher, H., and Feingold, H., Repairable Systems Reliability, Marcel Dekker, 1984 — the Laplace trend test and the minimal-repair assumption.
• NeqSim repository: https://github.com/equinor/neqsim