Sequential estimation of optimal age replacement policies when distribution of lifetimes is phase type.
Whitaker, Lyn R.
Bailey, Michael P.
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Optimal age replacement policies are designed to cut down system failures and minimize maintenance cost. By scheduling planned replacements, a system is replaced at age <f>* or at failure, whichever comes first, and the cost of replacement before failure (planned) is less than the cost after failure (unplanned). In this thesis, the distribution of lifetimes is a known, increasing failure rate phase type distribution. To find the optimal age of replacement, the parameters of the underlying phase type distribution must be estimated. An optimal age sequential estimation procedure is developed. In particular, the phase type distributions parameters are estimated using a matching moments nonlinear programming approach. Since there are many parameters associated with phase type distributions and the distributions include matrix exponential terms, the parameters are in general difficult to estimate. A specific case where the phase type distribution has initial probability vector a=(1,0,0) is studied for different sample sizes and compared with a similar nonparametric procedure.
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