On planned time replacement of series-parallel system

Document Type : Original Article


1 School of Continuing Education, Bayero University Kano, Nigeria

2 Department of Mathematical Sciences, Bayero University, Kano, Nigeria

3 School of Continuing Education, Bayero University, Kano, Nigeria


This paper investigate some characteristics of the age replacement model with minimal repair, of series-parallel system with non-uniform failure rates and are subjected to two different types of failures, which are Type I and Type II failures. The six units of the system formed three subsystems, which are subsystems A, B and C. Subsystem A is having three parallel units, subsystem B is having a single unit and subsystem C is having two parallel units. We constructed age replacement model with minimal repair that will determine the optimal replacement time of the series-parallel system. Furthermore, we also considered some modifications of the age replacement model with minimal repair constructed. Finally, some numerical examples are given to illustrate the characteristics of the age replacement models with minimal repair constructed. From the results obtained, it was observed that the optimal replacement time of the system when the three units of A are in parallel is higher than when the three units of A are in series. It was also observed that, the optimal replacement time obtained from the standard age replacement model is higher than the optimal replacement time obtained from standard age replacement model with minimal repair.


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