Time and cost constrained design of a simple step-stress accelerated life test under progressive Type-I censoring

Abstract

With the engineering technology and manufacturing processes continuously improving, modern products and devices are becoming more sophisticated and reliable. On the other hand, conducting traditional life tests for these products at normal operating conditions has become almost impossible because of their extremely long lifespans. In this competing market, this is largely problematic as it could substantially delay introducing the newly developed products to the market, resulting in missed business opportunities and eventually loss of the market share. This problem is solved by accelerated life tests by subjecting the test units at higher stress levels than normal so that information on the desired lifetime parameters can be obtained more rapidly. The lifetime at the design condition is then estimated through extrapolation using an appropriate regression model. In this work, the design optimization of a simple step-stress accelerated life test under progressive Type-I censoring is investigated for assessing the reliability characteristics of a solar lighting device. Under the practical constraints that the test duration is pre-fixed for a scheduling purpose and the total experimental cost does not exceed a pre-specified budget, the design is formulated explicitly with non-uniform step durations. With the intermediate censoring taking place at the stress change time point, the existence of the optimal design is demonstrated for exponential lifetimes with a single stress variable under several design criteria including D-optimality, C-optimality, A-optimality, M-optimality, and E-optimality.

Keywords:

• accelerated life tests
• cost constraint
• design of experiment
• exponential lifetimes
• progressive Type-I censoring
• step-stress loading

Acknowledgments

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

Additional information

Notes on contributors

David Han

David Han is an Associate Professor at the Department of Management Science & Statistics in the University of Texas at San Antonio, Texas. He received two Honors BSc degrees, one in Biochemistry and the other in Computer Science & Statistics, both from McMaster University in Canada. Continuing his studies at McMaster, he received MSc and PhD in Statistics. His research interests include the operations research and statistical inference for accelerated life testing in reliability engineering and survival analysis, analyses of censored data, optimal censoring plans and design of experiments, competing risks analyses, and statistical quality control.