×

Optimal replacement policy based on the number of down times with priority in use. (English) Zbl 1247.90122

Summary: This paper is an extension of a paper of the authors [ibid. 25, No. 1, 3–12 (2010; Zbl 1247.90123)]. While the former investigated a cold standby system consisting of two identical components, the present one considers the same situation, however, with two unequal components. The first component is very reliable while the second one is less reliable. Just as in the previous paper, a replacement policy based on the number of down times in a renewal cycle is determined that maximizes the long run expected reward per unit time. The explicit expression of the long run expected reward per unit time is derived and a numerical example is given for illustration.

MSC:

90B25 Reliability, availability, maintenance, inspection in operations research
62N05 Reliability and life testing
62P30 Applications of statistics in engineering and industry; control charts

Citations:

Zbl 1247.90123
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Barlow R. E., Journal of Operation Research 8 pp 90– (1960) · Zbl 0095.34304 · doi:10.1287/opre.8.1.90
[2] Block H. W., Journal of Applied Probability 22 pp 370– (1985) · Zbl 0564.60084 · doi:10.2307/3213780
[3] Brown M., Journal of Applied Probability 20 pp 851– (1983) · Zbl 0526.60080 · doi:10.2307/3213596
[4] Buzacott J. A, IEEE Transactions of Reliability 20 pp 60– (1971) · Zbl 0266.90030 · doi:10.1109/TR.1971.5216085
[5] Freund J. E, Journal of the American Statistical Association 56 pp 971– (1961) · Zbl 0106.13304 · doi:10.2307/2282007
[6] DOI: 10.1515/EQC.2010.001 · Zbl 1247.90123 · doi:10.1515/EQC.2010.001
[7] Kijima M, Journal of Applied Probability 26 pp 89– (1989) · Zbl 0671.60080 · doi:10.2307/3214319
[8] Lam Y. A, Advances in Applied Probability 20 pp 479– (1988) · Zbl 0642.60071 · doi:10.2307/1427402
[9] Lam Y. A, Microelectronics Reliabilty 37 (3) pp 497– (1997) · doi:10.1016/0026-2714(95)00184-0
[10] Nakagawa T., Microelectronics Reliabilty 14 (3) pp 309– (1975) · doi:10.1016/0026-2714(75)90708-8
[11] Osaki S, Canadian Journal of Operations Research Society 8 pp 60– (1970)
[12] DOI: 10.1515/EQC.2009.207 · Zbl 1247.90143 · doi:10.1515/EQC.2009.207
[13] Zhang Y. L., Engineering Optimization 38 pp 609– (2006) · doi:10.1080/16066350600608877
[14] Zhang Y. L., European Journal of Operational Research 183 pp 278– (2007) · Zbl 1127.90334 · doi:10.1016/j.ejor.2006.09.075
[15] Zhang Y. L., Reliability Engineering and System Safety 92 pp 535– (2007) · doi:10.1016/j.ress.2006.01.018
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.