Reliability analysis of δ-shock models based on the Markovian arrival process

被引：1

作者：

Goyal, Dheeraj ^{[1
,2
]}

Ali, Ramjan ^{[1
]}

Hazra, Nil Kamal ^{[1
]}

机构：

[1] Indian Inst Technol Jodhpur, Dept Math, Karwar, Rajasthan, India

[2] Indian Inst Technol Jodhpur, Dept Math, Karwar 342037, Rajasthan, India

来源：

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY | 2024年 / 40卷 / 05期

关键词：

delta-shock model; Markovian arrival process; optimal replacement policy; phase-type distribution; reliability; LIFE BEHAVIOR;

D O I：

10.1002/asmb.2858

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The Markovian arrival process (MAP) is a versatile counting process with dependent and non-identically distributed inter-arrival times following the phase-type distribution. In this article, we study the classical delta-shock model and a mixed delta-shock model by assuming the MAP of shocks. We derive explicit expressions for the reliability and the mean lifetime of the system. Further, we study an optimal replacement policy based on the MAP. We illustrate the developed results through several numerical examples.

引用

页码：1291 / 1312

页数：22

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