# Optimal Designs for Step-Stress Models Under Interval Censoring

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## Abstract

This article proposes new approaches for optimal planning of step-stress accelerated life testing models. The experiment considered is time constrained with the tested items not monitored continuously but inspected at particular time points instead. The inspection points are primarily the points of stress level change and the experiment’s termination point, but the inclusion of additional intermediate inspection points is possible. The underlying lifetimes in each stress level follow a general-scale family of distributions having, among others, the exponential and the Weibull as special cases. For this model, the optimal allocation of the inspection points is studied in terms of the classical *A*-, *C*-, *D*- and *E*-optimality criteria, as well as in the context of minimizing the probability of nonexistence of the maximum likelihood estimators of the model’s parameters. For the determination of the inspection intervals’ length, a deterministic and a hazard rate-based approach are introduced. Simulation study results indicate that these new approaches outperform the standard ones of equal spacing and equal probability. All the considered designs are comparatively evaluated and discussed on the basis of simulation studies.

## Keywords

Accelerated life testing*C*-optimality

*A*-optimality

*D*-optimality

*E*-optimality Equal spacing Equal probability

## Notes

### Acknowledgements

The first author was supported by the Seed Fund Project ‘*Inference and optimal planning for step-stress accelerated life testing under interval censored sampling*’ of the RWTH Aachen University, funded by the Excellence Initiative of the German Federal and State Governments. The authors thank the associate editor and the reviewer for their constructive and useful comments on an earlier version of the manuscript.

### Compliance with Ethical Standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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