Optimal Replacement Policies for a Multistate Degenerative System with Negligible or Nonnegligible Repair Times

Abstract In this paper, a repairable system of a monotone process model for a one-component multistate degenerative system with (k + 1) states(k-failure states and one working state) is studied. Also an alternative model, called the Negligible Or Non-Negligible (NONN) repair times introduced by Thangaraj and Rizwan (2001) is incorporated in this model to develop some new repair models. A replacement policy T is adapted by which the system will be replaced whenever the working age of the system reaches T ; another replacement policy T but with NONN repair times; the N policy, based on the number of failures of the system assuming NONN repair times and a bivariate replacement policy (T,N) under NONN repair times, where T is the working age and N is the number of failures of the system are studied. Furthermore, explicit expressions for the long-run average cost of the above policies are derived. Also the conditions for the existence of univariate optimal replacement policies are derived. Finally, we show that the optimal policy (T,N)∗ is better than the optimal policy N∗ or the optimal policy T ∗. We conclude with a conjecture that N-policy is the best replacement policy for any deteriorating system among the univariate policies.