The step-stress tampered failure rate model under interval monitoring

A step-stress accelerated life testing model is constructed that deals with type-I censored experiments for which a continuous monitoring of the tested items is infeasible and only their inspection at particular time points is possible, producing thus grouped data. A general scale family of distributions is considered for the underlying lifetimes, which allows for flexible modeling by permitting different lifetime distributions for different stress levels. The maximum likelihood estimators of its parameters and their density functions are derived explicitly only when the inspection points coincide with the points of stress-level change. In case of additional inspection points, the estimates are obtained numerically. Asymptotic, exact (whenever possible) and bootstrap confidence intervals (CIs) are considered. For the bootstrap CIs a smoothing-modification is introduced, accounting for the categorical nature of the data.