Mean Inactivity Time Function, Associated Orderings, and Classes of Life Distributions

Author

Kayid, M. ; Izadkhah, S.

Author_Institution

Dept. of Stat. & Oper. Res., King Saud Univ., Riyadh, Saudi Arabia

Volume

63

Issue

2

fYear

2014

fDate

Jun-14

Firstpage

593

Lastpage

602

Abstract

The concept of mean inactivity time plays an important role in reliability and life testing. In this investigation, based on the comparison of mean inactivity times of a certain function of two lifetime random variables, we introduce and study a new stochastic order. This new order lies between the reversed hazard rate and the mean inactivity time orders. Several characterizations and preservation properties of the new order under reliability operations of monotone transformation, mixture, and shock models are discussed. In addition, a new class of life distributions called strong increasing mean inactivity time is proposed, and some of its reliability properties are investigated. Finally, to illustrate the concepts, some applications in the context of reliability theory are included.

Keywords

life testing; reliability theory; stochastic processes; life distribution classes; life testing; lifetime random variables; mean inactivity time function; mean inactivity time orders; mixture model; monotone transformation model; reliability operations; reliability theory; reversed hazard rate; shock model; stochastic order; Context; Distribution functions; Electric shock; Hazards; Random variables; Reliability theory; Mean inactivity time order; mixture; preservation; reversed hazard rate order; shock models; strong increasing mean inactivity time class;

fLanguage

English

Journal_Title

Reliability, IEEE Transactions on

Publisher

ieee

ISSN

0018-9529

Type

jour

DOI

10.1109/TR.2014.2315954

Filename

6787061