Availability of Large Scale Repairable Systems with Imperfect Repair

Availability of Large Scale Repairable Systems with Imperfect Repair

Mohammed A. Hajeeh
DOI: 10.4018/ijoris.2014100105
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Operational systems consist of components that deteriorate and eventually fail. Upon failure, components are either repaired or replaced. Cheap and critical components are usually replaced, while expensive and non-critical ones are repaired before replacement. In this research work, repairable systems undergoing imperfect repair are examined where upon failure each component is repaired several times before being replaced. The main objective is to assess systems' performance by measuring the asymptotic availability. Closed forms analytical expressions are derived for the availability of some non-complicated systems while simulation is used to asses and analyze the performance of complex systems.
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1. Introduction

Components within a system that has just been installed and is performing perfectly are subject to many events such as deterioration, wear, fatigue, crack, corrosion, leakage, break down and repairs. Overtime, and in the presence of these and other factors the system ages and the frequency of its failure increases and eventually it becomes economically unjustified to keep such a component. Maintenance actions are usually applied to maintain systems in order to avoid or defer failures. Maintenance is either preventive or corrective; preventive maintenance is used to maintain the reliability of the system (age replacement, block replacement). Corrective maintenance is taking actions that are necessary to restore the system to its operational state after failure. Failure is categorized into three types: perfect repair, minimal repair, and imperfect repair. Perfect repair brings the system to the state of as good as new, minimal repair moves the system to its state just before failure (as good as old), while after each imperfect repair the system becomes inferior and its failure rate increases. Perfect repair is used with inexpensive or very critical component/systems, while imperfect repair is carried out for expensive and non critical systems. Imperfect repair has many practical applications in areas of machine shops, software/hardware distributed system, oil industry, desalinated plants, and ATM machines in banking among others.

The performance of systems with imperfect repair has been investigated thoroughly in the literature. Intensive review of imperfect repair models was provided by Pham & Wang (1996). Proschan (1982) considered a model where the cost of any new minimal repair performed is dependent on the number of minimal repairs previously done on the system. Brouwers (1986) derived mathematical expressions for the probability distributions in addition to providing several statistical parameters including mean value and standard deviation of system downtime and associated loss of production caused by irregular equipment failure and repair. All the expressions were derived on the basis of exponential failure and repair distributions for the different pieces of equipment and assuming a mean-time-to-failure to be much larger than the mean time for repair.

Nicola et al. (1993) used sampling techniques coupled with simulation to examine the reliability and availability of a system. A heuristic was developed to carry out the sampling process to non-Markovian models.

Simulation was utilized to inspect the effect of maintenance on systems with increasing and decreasing failure rates, while using component’s lifetime distribution on systems performance. Zaho (1994) investigated the failure patterns of a system with repairable components that was either perfectly or imperfectly repaired. Vanderperre (1995) examined a system composed of several operating and standby components with a single repair station assuming a constant failure rate and an arbitrary repair time distribution. Applying the Lorenz transform, a non-parametric method was developed to estimate the optimal repair-time limit from the empirical repair-time data. For illustration, numerical examples were presented for determining the optimal policy in order to study the asymptotic properties of the estimator. Three two-component configurations were investigated, namely series, standby, and parallel.

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