Periodic Replacement Policies and Comparisons with Their Extended Policies

It has been well known that minimal repairs are widely used in planning periodic replacement policies in reliability engineering. In this chapter, we begin with the standard periodic replacement policies that are planned at time T or at failure K, respectively, where the cumulative hazard function H(t) is used to count the number of minimal repairs. Next, three extensions of the above standard policies are discussed: (1) When the replacement policies of T and K are planned simultaneously, the approaches of first and last are used to make the best choice. (2) We delay replacement to be done at the first failure over T when it cannot be performed on time T. (3) We begin to plan replacement time T once the first failure or the Kth failure has occurred. We formulate the models of cost rates and give analytical discussions. In addition, comparisons are made for the above policies from point of cost. Finally, numerical examples are illustrated when the failure time has a Weibull distribution.