Sheu, Shey-Huei A generalized model for determining optimal number of minimal repairs before replacement. (English) Zbl 0795.90029 Eur. J. Oper. Res. 69, No. 1, 38-49 (1993). Summary: A generalized model for determining the optimal number of minimal repairs before replacement is introduced which incorporates minimal repair, replacement, and general random repair cost. The expected cost rate is obtained. It is shown that the optimal number \(n^*\) which minimizes the cost rate is given by a unique solution of the equation under certain conditions. Various special cases are considered. Cited in 9 Documents MSC: 90B25 Reliability, availability, maintenance, inspection in operations research Keywords:reliability; optimal number of minimal repairs; replacement; random repair cost PDF BibTeX XML Cite \textit{S.-H. Sheu}, Eur. J. Oper. Res. 69, No. 1, 38--49 (1993; Zbl 0795.90029) Full Text: DOI OpenURL References: [1] Barlow, R. E.; Hunter, L. C., Optimum preventive maintenance policies, Operations Research, 8, 90-100 (1960) · Zbl 0095.34304 [2] Barlow, R. E.; Proschan, F., Mathematical Theory of Reliability (1965), Wiley: Wiley New York · Zbl 0132.39302 [3] Beichelt, F.; Fisher, K., General failure model applied to preventive maintenance policies, IEEE Transactions on Reliability, 29, 39-41 (1980) · Zbl 0426.60081 [4] Block, H. W.; Borges, W. S.; Savits, T. H., Age-dependent minimal repair, Journal of Applied Probability, 22, 370-385 (1985) · Zbl 0564.60084 [5] Block, H. W.; Borges, W. S.; Savits, T. H., A general age replacement model with minimal repair, Naval Research Logistics, 35, 365-372 (1988) · Zbl 0654.90029 [6] Makabe, H.; Morimura, H., A new policy for preventive maintenance, Journal of the Operations Research Society of Japan, 5/3, 110-124 (1963) [7] Makabe, H.; Morimura, H., On some preventive maintenance policies, Journal of the Operations Research Society of Japan, 6/1, 17-47 (1963) [8] Makabe, H.; Morimura, H., Some considerations on preventive maintenance policies with numerical analysis, Journal of the Operations Research Society of Japan, 7/4, 154-171 (1965) [9] Morimura, H., On some preventive maintenance policies for IFR, Journal of the Operations Research Society of Japan, 12/3, 94-124 (1970) · Zbl 0205.48401 [10] Nakagawa, T., Generalized models for determining optimal number of minimal repairs before replacement, Journal of the Operations Research Society of Japan, 24/4, 325-337 (1981) · Zbl 0475.90038 [11] Nakagawa, T.; Kowada, M., Analysis of a system with minimal repair and its application to replacement policy, European Journal of Operational Research, 12, 176-182 (1983) · Zbl 0499.90034 [12] Park, K. S., Optimal number of minimal repairs before replacement, IEEE Transactions on Reliability, 28/2, 137-140 (1979) · Zbl 0423.90021 [13] Park, K. S., Optimal number of minor failures before replacement, International Journal Systems Science, 18/2, 333-337 (1987) · Zbl 0614.62129 [14] Ross, S. M., Applied Probability Models with Optimization Applications (1970), Holden-Day: Holden-Day San Francisco, CA · Zbl 0213.19101 [15] Savits, T. H., Some multivariate distributions derived from a non-fatal shock model, Journal of Applied Probability, 25, 383-390 (1988) · Zbl 0646.60092 [16] Sheu, S. H., A generalized block replacement policy with minimal repair and general random repair costs for a multi-unit system, Journal of the Operations Research Society, 42/4, 331-341 (1991) · Zbl 0737.90031 [17] Sheu, S. H.; Griffith, W. S., Multivariate age-dependent imperfect repair, Naval Research Logistics, 38, 839-850 (1991) · Zbl 0748.62056 [18] Sheu, S. H., Optimal block replacement policies with multiple choice at failure, Journal of Applied Probability, 29, 129-141 (1992) · Zbl 0776.90028 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.