Product of Spacings Estimation in Step-Stress Accelerated Life Testing: An Alternative to Maximum Likelihood

Abstract

Accelerated life testing (ALT) experiments are widely used in reliability studies on extremely durable products having large mean times to failure. Simple step-stress ALT (SSALT) is a special class of ALT that tests the units under investigation on two different conditions by changing the stress factor (e.g., temperature, voltage, or pressure) at a predetermined time point of the experiment. In this study, we propose the maximum product of spacings (MPS) technique for estimating the unknown lifetime parameters as an alternative to the maximum likelihood (ML), which in some cases is not possible to be used. The MPS estimator is defined for a simple SSALT model under Type-II censoring and proved to be asymptotically equivalent to the corresponding ML estimator. The specific case of Weibull lifetimes sharing a common shape parameter on both stress levels under the tampered failure rate assumption is considered in more detail. Existence and uniqueness results are shown for the point estimators of both methods and an adjusted bootstrap algorithm is suggested for constructing interval inference procedures. Further, the ML and MPS approaches are compared via a simulation study and applied to two real lifetime data examples.