Cost Benefit Analysis of a k-out-of-n: G Type Warm Standby Series System Under Catastrophic Failure Using Copula Linguistics

Praveen Poonia,Anu Sirohi

doi:10.30699/ijrrs.3.1.4

Abstract

This paper deals with the study of reliability measures of a complex engineering system consisting three subsystems namely L, M, and N in series configuration. The subsystem-L has three units working under 1-out-of-3: G; policy, the subsystem-M has two units working under 1-out-of-2: G policy and the subsystem-N has one unit working under 1-out-of-1: G; policy. Moreover, the system may face catastrophic failure at any time t. The failure rates of units of all subsystems are constant and assumed to follow the exponential distribution however, their repair supports two types of distribution namely general distribution and Gumbel-Hougaard family copula distribution. The system is analyzed by using the supplementary variable technique, Laplace transformation and Gumbel-Hougaard family of copula to derive the differential equations and to obtain important reliability characteristics such as availability of the system, reliability of the system, MTTF, and profit analysis. The numerical results for reliability, availability, MTTF, and profit function are obtained by taking particular values of various parameters and repair cost using maple. Tables and figures demonstrate the computed results and conclude that copula repair is more effective repair policy for better performance of repairable systems. It gives a new aspect to scientific community to adopt multi-dimension repair in form of copula. Furthermore, the results of the model are beneficial for system engineers and designers, reliability and maintenance managers.

Highlights

Determining accurate reliability and availability of an existing structure or product is a crucial task in the reliability engineering
These inactive components have a zero failure rate and cannot fail while in standby state; (ii) Hot standby in which the standby unit has the same failure rate as when it is run with the operating unit; (iii) Warm standby in which the standby unit runs in the background of operating unit
In order to improve the reliability of k-out-of-n systems, numerous researches have presented their works and contributions by constructing different types of complex repairable systems under the different types of failure and repair distributions

Summary

Introduction

Determining accurate reliability and availability of an existing structure or product is a crucial task in the reliability engineering. Singh et al [15] developed a model of a complex repairable system having two subsystems in series configuration Both subsystems includes two units in parallel, and it is assumed to work till at least one unit of both the subsystems are in good operative condition. Researchers around the world have presented their research works on reliability analysis of complex repairable system they have not focused on the study of the system consisting of three subsystems connected in series configuration with catastrophic failure. Repair is being applied using Gumbel-Hougaard family copula distribution Description This is a perfect state and all units of subsystem-L, M and N are in proper working condition. The states represent that the system is in completely failure mode and the system is under repair using Gumbel-Hougaard family copula distribution. By probability of considerations and continuity arguments, we can obtain the following set of difference-differential equations associated with the present mathematical model (see Appendix-1): t

R 2 3

Conclusion