Optimal bounds for the mean of the total time on test for distributions with decreasing generalized failure rate

ABSTRACT

During any life test experiment it is of interest to study potential costs (or profits) of performing the test to the very end. Assuming that these costs are proportional to lifetimes of analysed items the experimenter needs to know the remaining total time on test, having just observed successive failure in the test. We derive sharp upper bounds on the expectation of the remaining total time on test statistic when the underlying distributions have decreasing generalized failure rate with respect to generalized Pareto distributions. In particular we obtain the bounds valid for distributions with decreasing density or failure rate. The results are illustrated with numerical examples.

KEYWORDS:

• total time on test
• generalized failure rate
• generalized Pareto distribution
• projectionmethod
• sharp bounds
• life testing

AMS SUBJECT CLASSIFICATION:

• 62G30
• 62N05

Acknowledgements

The author wishes to thank the anonymous referees for very valuable comments and remarks which significantly helped in the preparation of the final version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author.