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B0778
Title: Maximum product of spacings estimator for simple step-stress model with Weibull lifetimes Authors:  Nikolay Nikolov - RWTH Aachen University (Germany) [presenting]
Maria Kateri - RWTH Aachen University (Germany)
Abstract: Accelerated life testing (ALT) experiments are widely used in reliability studies on extremely durable products having large mean times to failure. A simple step-stress ALT (SSALT) is a special class of ALT experiments that tests the units under investigation on two different conditions by changing the stress factor (e.g., temperature) at a predetermined time point of the experiment. The maximum product of spacings (MPS) technique is considered for estimating the unknown lifetime parameters of an SSALT model under censoring. The MPS estimator is defined under Type-II censoring and proved to be asymptotically equivalent to the corresponding maximum likelihood (ML) estimator. The specific case of Weibull lifetimes sharing a common shape parameter on both stress levels is studied in more detail. The MPS estimator is given as a solution of a non-linear system of equations and can be evaluated numerically, e.g., by using the Newton-Raphson algorithm. The suggested statistical procedure is applied to an illustrative data example, while the MPS and ML approaches are compared via an extensive simulation study. In particular, approximations of the estimation bias and mean squared error are presented for various combinations of the scale and shape parameter values.