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473 – Design of Experiments and Advanced Analytics

Inference for k-Level Step-Stress Accelerated Life Tests Under Progressive Type-I Censoring with the Lifetimes from a Log-Location-Scale Family

at The University of Texas at San Antonio

In reliability engineering, the accelerated life test is not only getting increasingly popular but also absolutely necessary as it rapidly yields information about the lifetime distribution of a highly reliable product and device in a shorter period of time by conducting the life test at more extreme stress levels than normal operating conditions. Through extrapolation, the lifetime distribution at the usage stress can be estimated with an appropriate regression model. In this work, we investigate the statistical inference for a progressively Type-I censored k-level step-stress accelerated life test when the lifetime of a test unit follows a log-location-scale family of distributions. Although simple and analytical, the popular exponential distribution lacks the model flexibility demanded in practice due to its constraint of constant hazard rates. In practice, Weibull or lognormal distributions, which are members of the log-location-scale family, demonstrate more superior model fits. Therefore, our study is extended to consider the general log-location-scale family, and our inferential methods are illustrated using three popular lifetime distributions, including Weibull, lognormal, and log-logistic. Assuming that the location parameter is linearly linked to the (transformed) stress level (i.e., µi = α + βxi), an iterative algorithm is developed to estimate the regression parameters α and β along with the scale parameter σ. Allowing the intermediate censoring to take place at the end of each stress level xi (viz., Ƭi, i = 1; 2; ... ; k), the Fisher’s expected information is derived, and the interval estimation is discussed based on the results. The effect of the intermediate censoring proportion on the inferential performance is also assessed computationally.