Profit analysis of a warm standby non-identical unit system with single server performing in normal/abnormal environment

Abstract This paper deals with a reliability model developed for a single-unit system which goes for preventive maintenance after a pre-specific time ‘t’ up to which no failure occurs. There is a single server who takes some time to arrive at the system for doing repair activities. The unit does not work as new after repair at complete failure and so called the degraded unit. The degraded unit is replaced by new one after its failure with some replacement time. The failure time, preventive maintenance time, replacement time and repair time of the unit are taken as Weibull distributed with common shape parameter and different scale parameters. The switching devices are perfect. The system is observed at suitable regenerative epochs to obtain various measures of system effectiveness of interest to system designers and operation managers.

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Two-non-identical unit-system with priority-based repair and inspection

Microelectronics Reliability ◽

10.1016/0026-2714(95)00008-p ◽

1996 ◽

Vol 36 (2) ◽

pp. 279-282 ◽

Cited By ~ 3

Author(s):

R.K. Agnihotri ◽

S.K. Satsangi

Keyword(s):

Unit System ◽

Identical Unit

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Optimal Profit Analysis of Machine Repair Problem with Repair in Phases and Organizational Delay

International Journal of Mathematical Engineering and Management Sciences ◽

10.33889/ijmems.2021.6.1.027 ◽

2020 ◽

Vol 6 (1) ◽

pp. 442-468

Author(s):

Chandra Shekhar ◽

Praveen Deora ◽

Shreekant Varshney ◽

Kunwar Pal Singh ◽

Dinesh Chandra Sharma

Keyword(s):

Finite Number ◽

Size Distribution ◽

Design Parameters ◽

Queue Size ◽

Machine Repair ◽

Critical Design ◽

Server Breakdown ◽

Profit Analysis ◽

Recursive Matrix ◽

Warm Standby

In this article, we study machine repair problems (MRP) consisting of the finite number of operating machines with the provisioning of the finite number of warm standby machines under the care of a single unreliable server. For the machining system’s uninterrupted functioning, an operating machine is immediately replaced with the available warm standby machine in negligible switchover time whenever it fails. The concept of threshold vacation policy: N-policy is also considered. Under this vacation policy, the server starts to serve the failed machines on the accumulation of a pre-specified number of failed machines in the system. The server continues until the system is empty from the failed machines; after that, the server goes for vacation. The notion of an organizational delay, server breakdown, and repair in multiple phases is also conceptualized to build the studied model more realistic. The recursive matrix method is used to find steady-state queue size distribution, and subsequently, various system performance measures are also developed to validate the studied model. The optimal analysis has been performed to identify the critical design parameters for the governing model. The state-of-the-art of the present study is its mathematical modeling of the multi-machine stochastic problem with varied limitations and strategies. The methodology to obtain queue size distribution, optimal design parameters, is beneficial for dealing with other complex and sophisticated real-time machining problems in the service system, computer and communication system, manufacturing and production system, etc. The present problem is limited to fewer machines, which can be extended to more machines with different topologies with high computational facilities.

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