×

Shocks in mixed populations. (English) Zbl 1407.62363

Rykov, Vladimir V. (ed.) et al., Mathematical and statistical models and methods in reliability. Applications to medicine, finance, and quality control. Invited papers based on the presentation at the 6th international conference (MMR 2009), Moscow, Russia, June 22–26, 2009. Boston, MA: Birkhäuser. Stat. Ind. Technol., 335-344 (2010).
Summary: We consider shocks as a method of burn-in in discrete and continuous heterogeneous populations. Burn-in is a widely used engineering method of elimination of defective items before they are shipped to customers or put into field operation. In conventional burn-in procedures, components or systems are subject to a period of simulated operation prior to actual usage and those which failed during this period are scrapped and discarded. In this paper, we assume that the ‘weak’ items are more susceptible to elimination via shocks and therefore this method can be considered as burn-in. Optimal severity levels of these shocks that minimize the defined expected costs are investigated.
For the entire collection see [Zbl 1203.60007].

MSC:

62N05 Reliability and life testing
Full Text: DOI

References:

[1] Block, H.W., Savits, T.H.: Burn-in. Statistical Science, 12, 1-19 (1997) · doi:10.1214/ss/1029963258
[2] Block, H.W., Mi, J., Savits, T.H.: Burn-in and mixed populations. Journal of Applied Probability, 30, 692-702 (1993) · Zbl 0781.60073 · doi:10.2307/3214775
[3] Block, H.W., Savits, T.H., Singh, H.: Criterion for burn-in that balances mean residual life and residual variance. Operations Research, 50 290-296 (2002) · Zbl 1163.62350 · doi:10.1287/opre.50.2.290.435
[4] Cha, J.H.: On a better burn-in procedure. Journal of Applied Probability, 37 1099-1103 (2000) · Zbl 0984.60090 · doi:10.1239/jap/1014843087
[5] Cha, J.H.: Burn-in procedures for a generalized model. Journal of Applied Probability, 38 542-553 (2001) · Zbl 0983.60085 · doi:10.1239/jap/996986761
[6] Cha, J.H.: A further extension of the generalized burn-in model. Journal of Applied Probability, 40 264-270 (2003) · Zbl 1020.60079 · doi:10.1239/jap/1044476840
[7] Cha, J.H.: A stochastic model for burn-in procedures in accelerated environment. Naval Research Logistics, 53 226-234 (2006) · Zbl 1122.90334 · doi:10.1002/nav.20135
[8] Clarotti, C.A., Spizzichino, F.: Bayes burn-in decision procedures. Probability in the Engineering and Informational Sciences, 4 437-445 (1991) · Zbl 1134.90355 · doi:10.1017/S0269964800001741
[9] Finkelstein, M.S.: Failure Rate Modelling for Reliability and Risk. Springer, London (2008) · Zbl 1194.90001
[10] Jensen, F., Petersen, N.E.: Burn-in. Wiley, New York (1982)
[11] Kuo, W., Kuo, Y.: Facing the headaches of early failures: A state-of-the-art review of burn-in decisions. Proceedings of IEEE., 71 1257-1266 (1983) · doi:10.1109/PROC.1983.12763
[12] Mi, J.: Optimal burn-in. Ph.D. Thesis, Univ. Pittsburgh, Pittsburgh (1991)
[13] Mi, J.: Burn-in and maintenance policies. Advances in Applied Probability, 26 207-221 (1994) · Zbl 0797.60075 · doi:10.2307/1427587
[14] Mi, J.: Maximization of a survival probability and its application. Journal of Applied Probability, 31 1026-1033 (1994) · Zbl 0811.60071 · doi:10.2307/3215326
[15] Mi, J.: Minimizing some cost functions related to both burn-in and field use. Operations Research, 44 497-500 (1996) · Zbl 0864.90053 · doi:10.1287/opre.44.3.497
[16] Mi, J.: Warranty policies and burn-in. Naval Research Logistics, 44 199-209 (1997) · Zbl 0891.90079 · doi:10.1002/(SICI)1520-6750(199703)44:2<199::AID-NAV4>3.0.CO;2-4
[17] Nguyen, D.G., Murthy, D.N.P.: Optimal burn-in time to minimize cost for products sold under warranty. IIE Transactions, 14 167-174 (1982) · doi:10.1080/05695558208974600
[18] Shaked, M., Shanthikumar, J.G.: Stochastic Orders. Springer, New York (2006) · Zbl 0806.62009
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.