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Study of Optimum Time for Repair or Replacement of Equipment Using Decreasing Failure Rate Distributions

In this paper, after introducing the renewal process, the cost function for some statistical distributions such as Weibull, mixture of Exponential and Geometric, mixture of Exponential and zero truncated Poisson are obtained. It is shown that these cost functions are decreasing functions (Figure 1). Using the failure rate and cost functions, the optimal distribution of repair for the successive repair is achieved. Also for industrial applications, the cost functions are calculated numerically and are plotted. By this method, the user could compare the presented figures and choose the best distribution.