IEEE Transactions on Reliability · 1998 · 155 citations · 7 references
EngineeringLife PredictionDeterioration ModelingReliability EngineeringStep-stress TestingStressExperimental TestingBiostatisticsModeling And SimulationStatisticsStress ManagementAccelerated Life TestingReliabilityPsychiatryMathematical IntractabilityExponential Step-stress ModelReliability PredictionReliability ModellingSoftware TestingCivil EngineeringExponential Ce-mFailure Prediction
The mathematical intractability of the Weibull cumulative exposure model (CE‑M) has impeded the development of statistical procedures for step‑stress accelerated life tests. The authors propose the KH‑M model, a time‑transformed exponential CE‑M, to enable use of existing multiple‑step, multiple‑stress results for step‑stress accelerated life tests. The model derives maximum likelihood estimates for test plans with unknown shape parameters and employs chi‑square goodness‑of‑fit tests on simulated data to compare model fits. KH‑M exhibits a realistic proportional‑hazard property, matches the Weibull CE‑M in flexibility while simplifying parameter estimation, and is mathematically similar to the constant‑stress Weibull model.
The mathematical intractability of the Weibull cumulative exposure model (CE-M) has impeded the development of statistical procedures for step-stress accelerated life tests. Our new model (KH-M) is based on a time transformation of the exponential CE-M. The time-transformation enables the reliability engineer to use known results for multiple-step, multiple-stress models that have been developed for the exponential step-stress model. KH-M has a realistically appealing proportional-hazard property. It is as flexible as the Weibull CE-M for fitting data, but its mathematical form makes it easier to obtain parameter estimates and standard deviations. Maximum likelihood estimates are given for test plans with unknown shape parameter. The mathematical similarity to the constant-stress Weibull model is shown. Chi-square goodness of fit tests are performed on simulated data to compare the fit of the models.
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Statistical Models and Methods for Lifetime Data.
Brian Francis, Jerald F. Lawless · Biometrics · 1983 · 2.8K citations