Burn-in and covariates. (English. English summary) Zbl 1060.62114
Summary: Burn-in is a widely used engineering procedure useful for eliminating ‘weak’ items and consequently improving the quality of remaining items. The quality of items can be measured via various performance characteristics. In the present paper we develop new performance criteria for the burn-in method. Our criteria not only take into account the reliability of an item, they also incorporate covariates.
MSC:
| 62N05 | Reliability and life testing |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
| 60G15 | Gaussian processes |
Keywords:
compound Poisson process; homogeneous Poisson process; geometric Brownian motion; standard Brownian motionReferences:
| [1] | Block, H. W. and Savits, T. H. (1997). Burn-in. Statist. Sci. 12 , 1–19. |
| [2] | Cha, J. H. (2000). On a better burn-in procedure. J. Appl. Prob. 37 , 1099–1103. · Zbl 0984.60090 · doi:10.1239/jap/1014843087 |
| [3] | Cha, J. H. (2001). Burn in procedures for a generalized model. J. Appl. Prob. 38 , 542–553. · Zbl 0983.60085 · doi:10.1239/jap/996986761 |
| [4] | Clarotti, C. A. and Spizzichino, F. (1990). Bayes burn-in decision procedures. Prob. Eng. Inf. Sci. 4 , 437–445. · Zbl 1134.90355 · doi:10.1017/S0269964800001741 |
| [5] | Jensen, F. and Peterson, N. E. (1982). Burn-In. John Wiley, New York. |
| [6] | Karlin, S. and Taylor, H. (1975). A First Course in Stochastic Processes. Academic Press, New York. · Zbl 0315.60016 |
| [7] | Karlin, S. and Taylor, H. (1981). A Second Course in Stochastic Processes. Academic Press, New York. · Zbl 0469.60001 |
| [8] | Kim, K. and Kuo, W. (2003). A general model of heterogeneous system lifetimes and conditions for system burn-in. Naval Res. Logistics 50 , 364–380. · Zbl 1043.90017 · doi:10.1002/nav.10067 |
| [9] | Lai, C. D., Xie, M. and Murthy, D. N. P. (2001). Bathtub-shaped failure rate life distributions. In Handbook of Statistics , Vol. 20, Advances in Reliability , eds N. Balakrishnan and C. R. Rao, North-Holland, Amsterdam,pp. 69–105. |
| [10] | Mi, J. (1994). Maximization of survival probability and its application. J. Appl. Prob. 31 , 1026–1033. JSTOR: · Zbl 0811.60071 · doi:10.2307/3215326 |
| [11] | Siegmund, S. (1986). Boundary crossing probabilities and statistical applications. Ann. Statist. 14 , 361–404. · Zbl 0632.62077 · doi:10.1214/aos/1176349928 |
| [12] | Tseng, S. T., Tang, J. and Ku, I. H. (2003). Determination of burn-in parameters and residual life of highly reliable products. Naval Res. Logistics 50 , 1–14. · Zbl 1044.90022 · doi:10.1002/nav.10042 |
| [13] | Watson, G. S. and Wells, W. T. (1961). On the possibility of improving mean useful life of items by eliminating those with short lives. Technometrics 3 , 281–298. · Zbl 0104.12203 · doi:10.2307/1266118 |
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.
