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This paper considers an optimal replacement model for a system subject to two types of failure. If the failure is of type 1, the system is minimally repaired. In the case of type 2 failure, the system is minimally repaired with probability p and replaced with probability 1 qp . A modified random and age replacement model is considered in which the system is replaced at a planned time T, at a random working time Y, or at the first non repairable type 2 failure whichever occurs first. Explicit expression for the expected total cost and the optimal replacement time T, minimizing the expected total cost are derived analytically. Finally, numerical example is considered to highlight the characteristics of the policy.

In this paper, we studied some reliability characteristics of a repairable 3-out-of-4 system with three modes: normal, deterioration and failure modes. The deterioration mode could be slow or fast. Failure and repair time are assumed to be exponential. We develop the explicit expressions for steady-state availability, busy period of repair man, profit function and mean time to system failure for the system using linear first order differential equations. Various cases are analyzed graphically to investigate the impact of system parameters on MTSF and profit function.

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This study or research work considered a complex system whose components are grouped into two each with different failure type. The first group consists of components or devices that are repairable and replaceable at failure (type y) and the second group consist of components that are non-repairable but replaceable at failure (type z). We rectify the defect of first group using minimal repair with probability p and replacement with probability 1-p at some threshold number n+1, n˃1 of the minimal repair, whereas for components at second group we adopt only replacement in order to correct the failure of the components. Cost functions of the model are derived and both analytical and empirical realizations are made.