Journal of Statistical Theory and Applications

Volume 20, Issue 2, June 2021, Pages 180 - 192

A Repairable System Supported by Two Spare Units and Serviced by Two Types of Repairers

Authors
Vahid Andalib1, *, Jyotirmoy Sarkar2
1 Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA
2 Department of Mathematical Sciences, Indiana Universiry-Purdue University Indianapolis, Indianapolis, IN 46202, USA
*Corresponding author. Email: vandalib1@umbc.edu
Corresponding Author
Vahid Andalib
Received 18 September 2019, Accepted 31 January 2021, Available Online 10 July 2021.
DOI
https://doi.org/10.2991/jsta.d.210611.001How to use a DOI?
Keywords
Cold standby, Perfect repair, Patience time, Semi-Markov process, Sojourn time, Busy time
Abstract

We study a one-unit repairable system, supported by two identical spare units on cold standby, and serviced by two types of repairers. The model applies, for instance, to ANSI (American National Standard Institute) centrifugal pumps in a chemical plant, and hydraulic systems in aviation industry. The failed unit undergoes repair either by an in-house repairer within a random or deterministic patience time, or else by a visiting expert repairer. The expert repairs one or all failed units before leaving, and does so faster but at a higher cost rate than the regular repairer. Four models arise depending on the number of repairs done by the expert and the nature of the patience time. We compare these models based on the limiting availability A, and the limiting profit per unit time ω, using semi-Markov processes, when all distributions are exponential. As anticipated, to maximize A, the expert should repair all failed units. To maximize ω, a suitably chosen deterministic patience time is better than a random patience time. Furthermore, given all cost parameters, we determine the optimum number of repairs the expert should complete, and the optimum patience time given to the regular repairer in order to maximize ω.

Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)
View full text (HTML)

Journal
Journal of Statistical Theory and Applications
Volume-Issue
20 - 2
Pages
180 - 192
Publication Date
2021/07/10
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.d.210611.001How to use a DOI?
Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Vahid Andalib
AU  - Jyotirmoy Sarkar
PY  - 2021
DA  - 2021/07/10
TI  - A Repairable System Supported by Two Spare Units and Serviced by Two Types of Repairers
JO  - Journal of Statistical Theory and Applications
SP  - 180
EP  - 192
VL  - 20
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.210611.001
DO  - https://doi.org/10.2991/jsta.d.210611.001
ID  - Andalib2021
ER  -