Performance of Two-Component Systems with Imperfect Repair

نویسنده

  • Mohammed Hajeeh
چکیده

Operational systems deteriorate over time and eventually fail by the failure of one or more of their components. Failed components are either replaced or repaired, and replacement is usually expensive. This article examines the behavior of repairable systems with imperfect repair, where a failed component is repaired once or more depending on factors such as repair cost, level of deterioration, and criticality of the component. When these systems are subjected to a customer use environment, their performance must endure different conditions. In imperfect repair, the performance of the system lessens after each failure. Three models of a two-component system studied are the series, parallel, and standby configurations, and the components are identical and independent. A closed form analytical expression for steady state operational probability is derived for different configurations under exponential distribution time to failure and repair time. Two examples are then discussed thoroughly. DOI: 10.4018/joris.2010040104 International Journal of Operations Research and Information Systems, 1(2), 50-63, April-June 2010 51 Copyright © 2010, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. In Wang and Sivazlian (1997), two different configurations with parallel components are compared based on their overall availability and life cycle costs under uncertainty of the system’s lifetime. The time-to-repair and the time to failure for each of the primary and parallel components are assumed to have the negative exponential distribution. The unconditional expected present worth of all expenditures during the entire life of the system is obtained using Laplace transform techniques in terms of the initial investment (P), the operating and maintenance costs (C), and the interest rate r. They derived the steady-state availability (AT(∞)), and the cost/benefit ratio, (C/B), for the two configurations and performed a comparative analysis. Vittoria and Vincnzo (1999) presented an analytical model of a parallel computing system. Since the probability of fault occurrence is non-negligible, the model takes into consideration fault–tolerance issues, by combining results obtained from a performance model with a fault/repair model. The system performance was evaluated under different configurations caused by the occurrence of faults and repairs. This requires efficient solution techniques of the performance model. They proved that the underlying Markov process has a particular structure suitable for efficient solution. To show a possible use of such a model, numerical results were presented for a particular maintenance policy, looking for the optimal trade-off between the frequency of service interruption due to repair operations and the need of avoiding excessive performance degradation. The paper by Wang and Kuo (2000) dealt with the reliability and availability characteristics of four different series system configurations with mixed standby (include cold standby and warm standby) components. The failure times of the primary and warm standby components are assumed to be exponentially distributed with parameters λ and α, respectively. The repair time distribution of each server is also exponentially distributed with parameter μ. They derived the mean time-to-failure, MTTF, and the steady-state availability, AT (∞), for the four configurations, comparisons are done for specific values of distribution parameters and for the cost of the components. Finally, the configurations are ranked based on: MTTF, AT (∞), and cost/benefit where either MTTF or AT (∞) are taken as the benefit. Oliveira et al. (2005) developed a method for reliability analysis of systems of components whose failure rates may be time-dependent. One special case of such systems is the one whose components are under aging. The hypothesis of minimum repair is adequate in many cases, especially in heavy industries, such as the nuclear industry. The method employs the technique of supplementary variables to transform the models of the non-Markovian systems into Markovian ones. The Laplace transform technique was used in order to reduce the number of equations, which are then solved by numerical methods. The inverse Laplace transforms to obtain the final solution of the set of differential equations is also utilized by using the Gauss–Legendre quadrature method which is very fast. Applications to safety systems, like the auxiliary feed water system of a typical PWR plant showed that the method is very fast and accurate as compared to other simulation methods. Dohi et al. (2003), studied a simple repair-time limit replacement problem with imperfect repair, and focused on the problem of determining the optimal repair-time limit which minimizes the expected cost per unit time in the steady-state. Applying the Lorenz transform, they developed a nonparametric method to estimate the optimal repair-time limit from the empirical repair-time data. Numerical examples are used for calculating the optimal policy and to examine the asymptotic properties of the estimator. In this paper, three two-component systems were examined i.e., series configuration, standby configuration, and parallel configuration. The article by Doyen and Gaudoin (2004) proposed two new classes of imperfect repair models. It was assumed that the conditional failure intensity before the first repair is a continuous function of time. In the first class of models, the repair effect is expressed by the reduction of failure intensity. In the second class, 12 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the publisher's webpage: www.igi-global.com/article/performance-two-componentsystems-imperfect/43016

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عنوان ژورنال:
  • IJORIS

دوره 1  شماره 

صفحات  -

تاریخ انتشار 2010