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

Usman Rizwan, Perumal Govindaraju, Venu Thangaraj


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.

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DOI: http://dx.doi.org/10.5539/jmr.v2n1p171

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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