Abstract
In this paper a two unit standby system with single repair facility has been considered. When a working unit fails, it is immediately taken over by standby unit and repair on the failed unit is started immediately. Taking two types of distribution, namely, Weibull and Erlangian, various system effectiveness measures such as MTSF, Availability and Busy Periods are compared and results are interpreted numerically. Regenerative Point Technique and Semi-Markov process have been employed in this paper to find the results. Results are supported with numerical data also. Failure time distributions are taken to be exponential whereas the repair times are particular. The result obtained from this can be applied to study complex system where small change in the value of one variable affects the system measures to a great extent. Key words: MTSF, availability, busy period, regenerative point technique, Semi-Markov process.
Highlights
Reliability measures of a component for a two-component system with repair facility were obtained by several authors under different assumptions
Osaki (1980) extended the analysis to obtain the availability of the system by using a variant of Semi-Markov process with non-regeneration point technique
(g) The failure rates of all the units are taken to be exponential whereas the repair time distributions are particular
Summary
Reliability measures of a component for a two-component system with repair facility were obtained by several authors under different assumptions. Harris (1968), considered a two-unit parallel redundant system in which failure times of the components are dependent and distributed as bivariate exponential of Marshall and Olkin (1967), to derive the mean time to system failure using the supplementary variable technique for an arbitrary repair time distribution. Osaki (1980) extended the analysis to obtain the availability of the system by using a variant of Semi-Markov process with non-regeneration point technique. Jye-Chyi (1992) studied the effects of dependence on modeling system reliability via multivariate Weibull distribution. We have taken two different types of distributions namely Weibull and Erlangian to study the reliability measures such as mean time to system failure, steady-state availability, busy period of the repairman in repairing the failed units and profit analysis and compare them. (g) The failure rates of all the units are taken to be exponential whereas the repair time distributions are particular.
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