A family of tests for trend change in failure rate function with right censored data

Abstract

In this paper we extend the family of test proposed by Majumder and Mitra [Detecting trend change in failure functions-an L-statistic approach. Stat Pap. 2019;62:31–52. doi: 10.1007/s00362-018-01074-8] for testing exponentiality against bathtub (BT) failure rate (upside down bathtub (UBT)) to randomly right censored case. We derive the asymptotic distribution of the test statistic and using Monte Carlo simulation we obtain the empirical powers for certain alternative distributions. As a special case the asymptotic distribution of the test statistic proposed by Park [Testing whether failure rate changes its trend. IEEE Trans Reliab. 1988;37(4):375–378. doi: 10.1109/24.9842] is obtained. Finally some examples of real life data are given for illustrative purpose.

Keywords:

• Bathtub shaped failure rate distribution
• upside down bathtub failure rate distribution
• replacement model
• right censoring
• Pitman's asymptotic relative efficiency

Acknowledgments

The authors would like to thank the Reviewer and Associate Editor for their insightful comments and constructive suggestions, which helped in improving the presentation.

Disclosure statement

No potential conflict of interest was reported by the author(s).