Likelihood Inference Under Proportional Hazards Model for One-Shot Device Testing

For devices with long lifetimes, accelerated life-tests are commonly used to induce quick failures. A link function relating stress levels and lifetime is then applied to extrapolate the lifetimes of units from accelerated conditions to normal operating conditions. Because data from one-shot devices do not contain any lifetimes, a standard reliability analysis with a parametric distributional assumption on lifetimes may be sensitive to violations of the model assumption. For this reason, we have proposed here a proportional hazards model for analyzing one-shot device testing data collected from constant-stress accelerated life-tests. The maximum likelihood estimates of the parameters of this semi-parametric model are developed. Confidence intervals for the reliability at an inspection time are constructed through asymptotic and transformation approaches. A Monte Carlo simulation study is then carried out to compare these confidence intervals in terms of coverage probabilities, and average widths. The obtained results show that the proposed flexible semi-parametric model provides a good insight into the estimation of reliability under normal (typical) operating conditions. A distance-based test statistic is also proposed for testing the proportional hazards model, and the exact calculation of its p-value is discussed. Finally, the proposed proportional hazards model is illustrated with real data from a toxicological study.