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**Periodic replacement when minimal repair costs vary with time.**
*(English)*
Zbl 0538.90026

Summary: A policy of periodic replacement with minimal repair at failure is considered for a complex system. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed at any intervening system failures. The cost of a minimal repair to the system is assumed to be a nondecreasing function of its age. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the system. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited in the case where the system life distribution is strictly increasing failure rate.

### MSC:

90B25 | Reliability, availability, maintenance, inspection in operations research |

62N05 | Reliability and life testing |

### Keywords:

necessary and sufficent existence conditions; periodic replacement; minimal repair; complex system; optimal replacement interval
Full Text:
DOI

### References:

[1] | Barlow, Operations Research 8 pp 90– (1960) |

[2] | and , Mathematical Theory of Reliability (John Wiley and Sons, New York, 1965). |

[3] | Boland, Operations Research 30 pp 1183– (1982) |

[4] | and , The Theory of Stochastic Processes (Chapman and Hall, London, 1965). |

[5] | Nakagawa, Journal of Operations Research Society of Japan 24 pp 3– (1981) |

[6] | Stochastic Processes, Holden Day Series in Probability and Statistics (Holden-Day, Inc. San Francisco, CA, 1962). |

[7] | Thompson, Technometrics 23 pp 1– (1981) |

[8] | Tilquin, Journal of Statistical Computing and Simulation 4 pp 63– (1975) · Zbl 0322.90029 |

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