Maximum Product of Spacings Estimator Under Type-I Censoring With an Application to a Step-Stress Model With Weibull Lifetimes

A maximum likelihood (ML) method is known to produce inconsistent estimators if the likelihood function is unbounded from above, e.g., in models with heavy-tailed distribution or unknown shift parameter. Such examples can be found in accelerated life testing (ALT) experiments, commonly applied in reliability studies on extremely durable products. In such cases, the maximum product of spacings (MPS) approach can be used as a more robust alternative that leads to asymptotically efficient estimators. Here, the MPS method is adjusted for Type-I censored samples in order to address complications that may arise in estimation. Moreover, the asymptotic theory of MPS estimators is adapted for the framework of Type-I censored simple step-stress ALT (SSALT) experiments. As an application, a failure-rate-based simple SSALT model with Weibull lifetimes, sharing a common shape parameter on both the stress levels, is considered. It is shown that the MPS estimator exists in situations where the ML fails to produce parameter estimations. Furthermore, the ML and MPS approaches are compared via a simulation study and applied to a real-life data example.