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This paper deals with the reliability analysis of a complex system consisting of a two dissimilar unit' in a parallel configuration with correlated lifetime distribution. The system stops functioning when both units stop working. Both units are inspected periodically as well as being examined before assigning to repair facility. Under consideration of the system have two states: Normal and failed. Regenerative point technique has been used for the mathematical formulation of the model. The system is analyzed using Laplace transforms to solve the mathematical equations. Reliability, Availability, MTSF, Busy Period of repairmen and Cost-effectiveness of the system has been computed. The computed results have been demonstrated by tables and graphs. The repair time of both the units follows the negative exponential distribution with different parameters in a joint probability density function. The inspection times are assumed to follow the general distribution. Some particular cases of the system have also been derived from seeing the practical importance of the model.

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The advent of copula distribution by Gumhel-Hougaard family spurred a new direction of research in multi-state complex engineering systems and is widely applied in various series-parallel systems. Considering this aspect, in this paper we study various reliability measures of a complex system consisting of eight identical computer labs as star topology working under 5-out-of-8: G policy, two different centralized data base servers working under 1-out-of-2: G policy, and a switch in series configuration. Failure rates of all the units are assumed to be constant and follow exponential distribution, while repair supports general distribution and copula distribution. The objective of this paper is to evaluate availability of the system, reliability of the system, mean time to failure and expected profit analysis by choosing arbitrary values of the parameters in a way that numerical solutions can be obtained systematically in a reasonable computational time. The problem is modelled using supplementary variable technique, Laplace transform and copula repair. We highlight the use of copula repair, while identifying the factors for improvement and future directions of work.