The algorithms proposed utilize perturbation analysis to carry out gradient estimation and stochastic approximation to find the optimal threshold values for unreliable one- and two-machine systems. The perturbation analysis techniques initiated by Y.C. Ho and X. Cao (1991) are used to deduce a simple gradient estimate, and the stochastic optimization techniques are employed to develop iterative algorithms for approximating the optimal threshold values. The formulation for the one-machine problem is given and the iterative algorithm is also developed. An example for the one-machine case is included. The result from the numerical study is compared with existing analytical results. The extension to multimachine systems is explained.
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