Sharp bounds for the mean of the total time on test for distributions with increasing generalized failure rate

ABSTRACT

The results of this paper are the continuation of the research presented by Bieniek [Optimal bounds for the mean of the total time on test for distributions with decreasing generalized failure rate. Statistics. 2016;50:1206–1220]. We consider the remaining total time on test after a given failure in a life test experiment. We derive sharp upper bounds on the mean of the total time on test optimal in the class of distributions with increasing generalized failure rate with respect to generalized Pareto distributions. Specific results are obtained for distributions with increasing density and increasing failure rate. We also provide exemplary numerical values of the obtained bounds and we compare them with the corresponding bounds for distributions with decreasing generalized failure rate.

KEYWORDS:

• Total time on test
• generalized failure rate
• generalized Pareto distribution
• projection method
• sharp bounds
• life testing

AMS SUBJECT CLASSIFICATIONS:

• 62G30
• 62N05

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Mariusz Bieniek http://orcid.org/0000-0002-8151-637X

Additional information

Funding

The first author was supported by Polish National Science Center [grant no. 2015/19/B/ST1/03100].