Identification of Unit Replacement Based on Long-Run Repair Average Cost Rate (Acr) Based on Truncated Exponential Failure Model

Abstract

Earlier, authors presented [1] and published [2] investigated failure nature, repair pattern and reliabilities of hydro power generators, using simple statistical tools and simulation techniques respectively. It is identified that analysis of hydro power generators require a special approach by dividing the repair into two categories based on the repair duration. That is i) Minor repairs (Repair hours less than or equal a threshold value T) and ii) Major Repairs (Repair hours greater than a threshold value T).This approach is specially introduced by authors [1, 2] and obtained good fit of “truncated exponential failure model”. Through this proposed model reliabilities are estimated and conclusions were drawn. In the above work, we have assumed that the system after repair is ‘as good as new’. On the basic assumption that the system after repair is not ‘as good as new’ and also the successive working times are stochastically decreasing while, the successive repair time's are stochastically increasing and are exposing to exponential truncated failure law. Under these assumptions, an optimal replacement policy T in which we replace the system when the repair time (working time) reaches T. It can be determined that an optimal repair replacement policy T* such that the long run average cost per unit time is minimized. It can also be derived an explicit expression of the long-run average cost and the corresponding optimal replacement policy T* can be determined analytically. Numerical results are provided to support the theoretical results.