A general model for accelerated life testing with time‐dependent covariates

This paper introduces a general or “distribution-free” model to analyze the lifetime of components under accelerated life testing. Unlike the accelerated failure time (AFT) models, the proposed model shares the advantage of being “distribution-free” with the proportional hazard (PH) model and overcomes the deficiency of the PH model not allowing survival curves corresponding to different values of a covariate to cross. In this research, we extend and modify the extended hazard regression (EHR) model using the partial likelihood function to analyze failure data with time-dependent covariates. The new model can be easily adopted to create an accelerated life testing model with different types of stress loading. For example, stress loading in accelerated life testing can be a step function, cyclic, or linear function with time. These types of stress loadings reduce the testing time and increase the number of failures of components under test. The proposed EHR model with time-dependent covariates which incorporates multiple stress loadings requires further verification. Therefore, we conduct an accelerated life test in the laboratory by subjecting components to time-dependent stresses, and we compare the reliability estimation based on the developed model with that obtained from experimental results. The combination of the theoretical development of the accelerated life testing model verified by laboratory experiments offers a unique perspective to reliability model building and verification. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 303–321, 1999

[1]  Thomas A. Louis,et al.  Nonparametric analysis of an accelerated failure time model , 1981 .

[2]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[3]  R. Prentice.  Linear rank tests with right censored data , 1978 .

[4]  W. Meeker,et al.  An Accelerated Life Test Model Based on Reliability Kinetics , 1995 .

[5]  A. Ciampi,et al.  A general model for testing the proportional hazards and the accelerated failure time hypotheses in the analysis of censored survival data with covariates , 1985 .

[6]  W. Nelson.  Accelerated Life Testing - Step-Stress Models and Data Analyses , 1980, IEEE Transactions on Reliability.

[7]  M. Fukuda,et al.  Failure Modes of InGaAsP/InP Lasers Due to Adhesives , 1984 .

[8]  W. Meeker.  Accelerated Testing: Statistical Models, Test Plans, and Data Analyses , 1991 .

[9]  James M. Robins,et al.  Semiparametric estimation of an accelerated failure time model with time-dependent covariates , 1992 .

[10]  M. Fukuda.  Laser and LED reliability update , 1988 .

[11]  Jerald F. Lawless,et al.  A note on lifetime regression models , 1986 .

[12]  N. Singpurwalla,et al.  Methods for Statistical Analysis of Reliability and Life Data. , 1975 .

[13]  Antonio Ciampi,et al.  Extended hazard regression for censored survival data with covariates : a spline approximation for the baseline hazard function , 1987 .

[14]  Mitsuo Fukuda,et al.  Dark defects in InGaAsP/InP double heterostructure lasers under accelerated aging , 1983 .

[15]  Martin Newby.  Perspective on Weibull proportional-hazards models , 1994 .

[16]  Moshe Shaked,et al.  INFERENCE FOR STEP-STRESS ACCELERATED LIFE TESTS , 1983 .

[17]  Richard D. Gill,et al.  Understanding Cox's regression model: a martingale approach : (preprint) , 1984 .

[18]  C. J. Dale,et al.  Application of the proportional hazards model in the reliability field , 1985 .

[19]  Z. Lin,et al.  A nonparametric approach to progressive stress accelerated life testing , 1991 .

[20]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[21]  Leon S. Lasdon,et al.  Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming , 1978, TOMS.