Reliability Analysis of an Extended Shock Model and Its Optimization Application in a Production Line

Renbin Liu

doi:10.1155/2014/730264

Abstract

Firstly, a two-unit cold standby shock model with multiple adaptive vacations is introduced, in which the startup and replacement of repair facility are also considered. Secondly, using supplementary variable method and Laplace transform, some important reliability indices are derived, such as availability, failure frequency, mean vacation period, mean renewal cycle, mean startup period, and replacement frequency. Finally, a production line controlled by two cold-standby computers is modeled to present numerical illustration and its optimal part-time job policy at a maximum profit.

Highlights

It is well known that the shock model is used to study the external causes which may make a system fail
Esary et al [1], Barlow and Proschan [2], Ross [3], and Fagiuoli and Pellerey [4] dealt with Poisson shock models
The multiple adaptive vacation policy (MAVP) first proposed by Tian and Zhang [17] is more general than single vacation, multiple vacations and variant vacations, which is useful for high availability and profit optimization of the system; (iii) some new reliability indices are derived, such as mean renewal cycle, mean vacation period, mean startup period, mean idle period, and mean busy period; (iv) as an application of our model, a production line controlled by two identical cold-standby computers is modeled to analyze its optimal part-time job policy

Summary

Introduction

It is well known that the shock model is used to study the external causes which may make a system fail. Based on the above facts, in this paper we present an extended shock model for two identical unit cold-standby systems. The MAVP first proposed by Tian and Zhang [17] is more general than single vacation, multiple vacations and variant vacations, which is useful for high availability and profit optimization of the system (see Section 5); (iii) some new reliability indices are derived, such as mean renewal cycle, mean vacation period, mean startup period, mean idle period, and mean busy period; (iv) as an application of our model, a production line controlled by two identical cold-standby computers is modeled to analyze its optimal part-time job policy.

Assumptions

The State Probability Equations and Solutions

Reliability Indices

Numerical Illustration and Optimal

Conclusions