Burn-in by environmental shocks for two ordered subpopulations. (English) Zbl 1188.90075
Summary: 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. Then those which failed during this period are scrapped and discarded. In this paper, we assume that the population of items is composed of two ordered subpopulations and the elimination of weak items by using environmental shocks is considered. Optimal severity levels of these shocks that minimize the defined expected costs are investigated. Some illustrative examples are discussed.
MSC:
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
| 91B76 | Environmental economics (natural resource models, harvesting, pollution, etc.) |
References:
| [1] | Block, H. W.; Savits, T. H., Burn-in, Statistical Science, 12, 1-19 (1997) |
| [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 |
| [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 |
| [4] | Cha, J. H., On a better burn-in procedure, Journal of Applied Probability, 37, 1099-1103 (2000) · Zbl 0984.60090 |
| [5] | Cha, J. H., Burn-in procedures for a generalized model, Journal of Applied Probability, 38, 542-553 (2001) · Zbl 0983.60085 |
| [6] | Cha, J. H., A further extension of the generalized burn-in model, Journal of Applied Probability, 40, 264-270 (2003) · Zbl 1020.60079 |
| [7] | Cha, J. H., A stochastic model for burn-in procedures in accelerated environment, Naval Research Logistics, 53, 226-234 (2006) · Zbl 1122.90334 |
| [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 |
| [9] | Finkelstein, M. S., Failure Rate Modelling for Reliability and Risk (2008), Springer: Springer London · Zbl 1194.90001 |
| [10] | Jensen, F.; Petersen, N. E., Burn-in (1982), John Wiley: John Wiley New York |
| [11] | Kim, K. O.; Kuo, W., Optimal burn-in for maximizing reliability of repairable non-series systems, European Journal of Operational Research, 193, 140-151 (2009) · Zbl 1152.90405 |
| [12] | 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) |
| [13] | Mi, J., 1991. Optimal burn-in. Ph.D. Thesis, Dept. Statistics, Univ. Pittsburgh.; Mi, J., 1991. Optimal burn-in. Ph.D. Thesis, Dept. Statistics, Univ. Pittsburgh. |
| [14] | Mi, J., Burn-in and maintenance policies, Advances in Applied Probability, 26, 207-221 (1994) · Zbl 0797.60075 |
| [15] | Mi, J., Maximization of a survival probability and its application, Journal of Applied Probability, 31, 1026-1033 (1994) · Zbl 0811.60071 |
| [16] | Mi, J., Minimizing some cost functions related to both burn-in and field use, Operations Research, 44, 497-500 (1996) · Zbl 0864.90053 |
| [17] | Mi, J., Warranty policies and burn-in, Naval Research Logistics, 44, 199-209 (1997) · Zbl 0891.90079 |
| [18] | 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) |
| [19] | Reddy, R. K.; Dietrich, D. L., A 2-level environmental-stress-screening (ESS) model: A mixed-distribution approach, IEEE Transactions on Reliability, 43, 85-90 (1994) |
| [20] | Shaked, M.; Shanthikumar, J. G., Stochastic Orders (2006), Springer: Springer New York |
| [21] | Sheu, S.; Chien, Y., Optimal burn-in time to minimize the cost for general repairable products sold under warranty, European Journal of Operational Research, 163, 445-461 (2005) · Zbl 1071.90522 |
| [22] | Wu, S.; Xie, M., Classifying weak, and strong components using ROC analysis with application to burn-in, IEEE Transactions on Reliability, 56, 552-561 (2007) |
| [23] | Yan, L.; English, J. R., Economic cost modeling of environmental-stress-screening and burn-in, IEEE Transactions on Reliability, 46, 275-282 (1997) |
| [24] | Yang, G., Environmental-stress-screening using degradation measurements, IEEE Transactions on Reliability, 51, 288-293 (2002) |
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.
