Optimal planning of progressively Type-I censored step-stress accelerated life test under interval inspection

Abstract

For highly reliable products and devices, conducting the life tests at normal usage conditions demands a great deal of time and cost, which can result in missed opportunities to introduce the product to the market in a timely manner and eventually loss of the market share. By subjecting test units at higher stress levels than normal operating conditions, accelerated life tests solve this problem and quickly produce information on the lifetime parameters. The lifetime at the design stress is then estimated through extrapolation using a regression model. Due to technical limitations and/or budgetary constraints, the exact failure times of test units may not be available in practice but only the failure counts are collected at certain time points during the life test. In this work, the design optimization of a general k-level step-stress accelerated life test under progressive Type-I censoring is considered with a uniform step duration Δ when the exact failure times are not observable ($i.e.,$ interval inspection). Allowing the intermediate censoring at each stress change time point (viz., $i\Delta ,i=1,2,\dots ,k$), the optimal Δ is determined under various design criteria including D-optimality, T-optimality, C-optimality, A-optimality, and E-optimality. The existence of these optimal designs is investigated in detail for exponential lifetimes with a single stress variable, and the design efficiency is compared to the situation when the exact failure times are available ($i.e.,$ continuous inspection).

Keywords:

• Accelerated life tests
• Design of experiment
• Fisher information
• Interval inspection
• Order statistics
• Progressive Type-I censoring
• Step-stress loading

Acknowledgments

The authors are grateful to the editor and anonymous reviewers for their critical comments and valuable suggestions for improving the previous version of the manuscript.