L.R. Goel

Profit analysis of a two-unit redundant system with provision for rest and correlated failures and repairs

Abstract This paper analyses a two-unit cold standby system with the provision of rest for the operating unit. Also, the failure and repair times of each unit are assumed to be correlated by taking their joint density as bivariate exponential. The system is observed at suitable regenerative epochs to obtain various reliability characteristics of interest, such as the distribution of time to system failure (TSF) and its mean (MTSF), and steady-state probabilities of the system being in up or down states or under repair. Earlier results are verified as particular cases.

Profit analysis of two-unit priority standby system with administrative delay in repair

The profit analysis of a single server two-unit (one priority and the other ordinary) cold standby system with two modes normal and total failure is examined. The priority unit gets preference both for operation and repair. Whenever an operative unit fails, a delay occurs in locating the repairman and getting him to the system location due to certain administrative actions with known probability p. The system is observed at suitable regenerative epochs in order to obtain several economics-related reliability characteristics. Explicit results are obtained in a few particular cases.

Two unit cold standby system with correlated failures and repairs

Abstract A two unit cold standby system with correlated failure and repair processes is studied. Such a system has not been studied so far in the context of reliability. We obtain the reliability characteristics of interest to system designers such as the mean time to system failure, pointwise and steady state availablity of the system, expected up time and down time of the system in a finite interval, etc. In fact the joint distribution of failure and repair times is taken as bivariate exponential. Earlier results with independent failure and repair times are verified.

Cost analysis of a two unit priority standby system with imperfect switch and arbitrary distributions

Abstract This paper deals with cost analysis of a single server two-unit (one priority and the other ordinary) cold standby system with two modes—normal and total failure. A switch is used to operate the standby unit (ordinary) and it works successfully with known probability p( = 1 − q). Priority unit gets preference both for operation and repair. Failure and repair time distributions are arbitrary. System fails when switch or both the units fail totally. The system is observed at suitable regenerative epochs in order to obtain reliability characteristics of interest to system designers and operations managers. Explicit results for the exponential time distributions have been obtained in particular cases.

Cost analysis of a two unit cold standby system under different weather conditions

Abstract This paper deals with the cost analysis of a two unit cold standby system under two different weather conditions—normal and abnormal. Failure rates of units and rates of change of weather conditions are constant, whereas repair rates are general. The system is analysed in detail using regenerative point technique and results are obtained for mean time to system failure, steady state availability, busy period analysis, expected number of visits by repairman and expected profit earned by the system.

Cost analysis of a two-unit cold standby system with two types of operation and repair

Abstract This paper deals with the cost analysis of a single-server two-identical unit cold standby system and two types of repair—minor and major. The unit requires minor repair if it fails for the first time. The major repair is required only when the unit fails after the minor repair. Upon minor repair the unit does not work as a normal unit but as a quasi-normal unit which has a different (increased) failure rate from that of a new one. Upon major repair the unit works as good as new (normal unit). Failure time distributions are negative exponential whereas repair time distributions are general. Using regeneration point technique the system characteristics of interest to system designers and operations managers have been obtained.

A multistate system with two repair distributions

Abstract This paper investigates the mathematical model of a reparable system with three possible states—normal, degraded and failed. We consider two types of repair facilities—overhaul and minor repair—having arbitrary pdf. Other transitions have constant rates.

Reliability analysis of a system with preventive maintenance, inspection and two types of repair

Abstract This paper considers a two-unit (identical) parallel system with facilities of preventive maintenance, inspection and two types of repair, type I and type II. These two types of repair facilities have a considerable difference in their costs. Both the units of the system can fail simultaneously due to some common-cause or they can fail one by one. The time of failure of a unit and system, the commencement of maintenance and inspection are assumed to be constant while repair and maintenance times are arbitrarily distributed. Various measures of system effectiveness are evaluated using regenerative point technique.

Stochastic analysis of a parallel system with common cause failure, preventive maintenance and two types of repair

Abstract This paper studies a two-unit (identical) parallel system with facilities of preventive maintenance and two types of repair, i.e. regular and occasional. When the regular repairman is unable to repair the unit/system, the occasional (expert) repairman is called for. The system can also fail due to common cause. The time of the failure of a unit and the system, the commencement of maintenance and to call the occasional repairman are assumed to be constant while the repair and maintenance times are arbitrarily distributed. The system is analysed by using regenerative point technique to obtain various economics related measures, such as mean time to system failure, steady state availability, probability that the repairman is busy, expected number of visits by the occasional repairman and the expected profit earned by the system.

Profit analysis of a cold standby system with two repair distributions

Abstract A single server two-identical unit cold standby system is analysed. Each unit has two operative modes—normal and quasi-normal. When a normal unit fails, it undergoes minor repair with probability p 1 and p 2 respectively. Upon minor repair unit works with reduced efficiency and is known as quasi-normal unit while upon major repair unit works as good as new (normal unit). When a quasi-normal unit fails, it undergoes minor or major repair with probability q 1 and q 2 respectively. Failure rates of normal and quasi-normal units are different. Failure time distributions are negative exponential whereas repair time distributions are general. Using regeneration point technique in MRP the system characteristics of interest to system designers and operations managers have been obtained.