Inference under random maintenance policies with a polynomial form as the repair alert function

Abstract

This paper deals with random sign-censoring data (RSCD) which may be observed under repair alert models (RAMs) for implementing age-dependent maintenance policies on engineering devices. A general family for lifetime distributions of devices is considered and estimates of parameters are derived on the basis of RSCD via the likelihood and the Bayesian approaches. In recent literature, the cumulative repair alert function (CRAF), denoted by $G\left(t\right)$, of the RAMs is considered proportional to the cumulative hazard rate function of the device lifetime. This paper also suggests a polynomial form for the CRAF $G\left(t\right)$ for modelling purposed. A comparison between the two kinds of CRAFs under the RAMs is given for a real data set from Mendenhall and Hader [Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data. Biometrika. 1958;45:504–520] The data are times to failure for a type of communication transmitter-receivers of a single commercial airline. Some special cases including exponential, Weibull and Pareto distributions are studied in a great detail.

Keywords:

• estimation
• lifetimes
• preventive maintenance
• random sign censoring
• repair alert models

Mathematics Subject Classification:

• 62F10
• 62N05
• 90B25

Acknowledgments

The authors are grateful to the Editor-in-Chief, the Associate Editor and anonymous referees for their many helpful comments and suggestions on an earlier version of this paper which led to this improved version.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Mahdi Doostparast http://orcid.org/0000-0002-4614-8137