Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-25T09:22:32.089Z Has data issue: false hasContentIssue false
  • English
  • Français

Burn-in Procedure Based on a Dependent Covariate Process

Part of: Special processes Applications

Published online by Cambridge University Press:  22 February 2016

Ji Hwan Cha  and
Gianpaolo Pulcini
Ji Hwan Cha*
Affiliation:
Ewha Womans University
Gianpaolo Pulcini*
Affiliation:
Istituto Motori
*
∗ Postal address: Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea. Email address: [email protected]
∗ Postal address: Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Burn-in is a method of ‘elimination’ of initial failures (infant mortality). In the conventional burn-in procedures, to burn-in a component or a system means to subject it to a fixed time period of simulated use prior to actual operation. Then those which fail during the burn-in procedure are scrapped and only those which survived the burn-in procedure are considered to be of satisfactory quality. Thus, in this case, the only information used for the elimination procedure is the lifetime of the corresponding item. In this paper we consider a new burn-in procedure which additionally employs a dependent covariate process in the elimination procedure. Through the comparison with the conventional burn-in procedure, we show that the new burn-in procedure is preferable under commonly satisfied conditions. The problem of determining the optimal burn-in parameters is also considered and the properties of the optimal parameters are derived. A numerical example is provided to illustrate the theoretical results obtained in this paper.

Keywords

Burn-independent covariate processpositive quadrant dependentnegative quadrant dependentdegradation phenomenaheterogeneous populationcatastrophic failure

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62P30: Applications in engineering and industry
Type
Research Article
Information
Advances in Applied Probability , Volume 47 , Issue 2 , June 2015 , pp. 506 - 529
Copyright
© Applied Probability Trust 

References

Badía, F. G., Berrade, M. D. and Campos, C. A. (2003). Why do failure rates decrease? In Seventh Conference on Applied Mathematics and Statistics, University of Zaragoza, Zaragoza-Pau, pp. 97–104.Google Scholar
Bagdonavičius, V., Kruopis, J. and Nikulin, M.S. (2011). Non-Parametric Tests for Censored Data. ISTE, London.CrossRefGoogle Scholar
Bain, L. J. (1974). Analysis for the linear failure-rate life-testing distribution. Technometrics 16, 551–559.Google Scholar
Barlow, R. E. and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing: Probability Models. To Begin With, Silver Spring, MD.Google Scholar
Block, H. W. and Savits, T. H. (1997). Burn-in. Statist. Sci. 12, 1–19.CrossRefGoogle Scholar
Bocchetti, D., Giorgio, M., Guida, M. and Pulcini, G. (2009). A competing risk model for the reliability of cylinder liners in marine Diesel engines. Reliab. Eng. System Safety 94, 1299–1307.CrossRefGoogle Scholar
Cha, J. H. (2000). On a better burn-in procedure. J. Appl. Prob. 37, 1099–1103.Google Scholar
Cha, J. H. (2001). Burn-in procedures for a generalized model. J. Appl. Prob. 38, 542–553.CrossRefGoogle Scholar
Cha, J. H. and Finkelstein, M. (2011). Burn-in and the performance quality measures in heterogeneous populations. Europ. J. Operat. Res. 210, 273–280.Google Scholar
Cha, J. H. and Finkelstein, M. (2012). Shocks as burn-in in heterogeneous populations. Commun. Statist. Theory Meth. 41, 325–340.CrossRefGoogle Scholar
Çinlar, E. (1980). On a generalization of gamma processes. J. Appl. Prob. 17, 467–480, 893.CrossRefGoogle Scholar
Clarotti, C. A. and Spizzichino, F. (1990). Bayes burn-in decision procedures. Prob. Eng. Inf. Sci. 4, 437–445.CrossRefGoogle Scholar
Finkelstein, M. (2008). Failure Rate Modeling for Reliability and Risk. Springer, London.Google Scholar
Huang, W. and Askin, R. G. (2003). Reliability analysis of electronic devices with multiple competing failure modes involving performance aging degradation. Quality Reliab. Eng. Internat. 19, 241–254.Google Scholar
Jensen, F. B. and Petersen, N. E. (1982). Burn-In. John Wiley, Chichester.Google Scholar
Kececioglu, D. B. and Sun, F.-B. (1997). Burn-In Testing. Prentice Hall, Upper Saddle River, NJ.Google Scholar
Kim, K. O. and Kuo, W. (2009). Optimal burn-in for maximizing reliability of repairable non-series systems. Europ. J. Operat. Res. 193, 140–151.Google Scholar
Kuo, W. and Kuo, Y. (1983). Facing the headaches of early failures: A state-of-the-art review of burn-in decisions. Proc. IEEE 71, 1257–1266.CrossRefGoogle Scholar
Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data, 2nd edn. John Wiley, Hoboken, NJ.Google Scholar
Lehmann, E. L. (1966). Some concepts of dependence. Ann. Math. Statist. 37, 1137–1153.Google Scholar
Mi, J. (1994). Burn-in and maintenance policies. Adv. Appl. Prob. 26, 207–221.CrossRefGoogle Scholar
Mi, J. (2003). Optimal burn-in time and eventually IFR. J. Chinese Inst. Industrial Eng. 20, 533–543.Google Scholar
Nelsen, R. B. (1992). On measures of association as measures of positive dependence. Statist. Prob. Lett. 14, 269–274.CrossRefGoogle Scholar
Pan, Z. and Balakrishnan, N. (2011). Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes. Reliab. Eng. System Safety 96, 949–957.Google Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.CrossRefGoogle Scholar
Shaked, M. and Spizzichino, F. (1998). Positive dependence properties of conditionally independent random lifetimes. Math. Operat. Res. 23, 944–959.Google Scholar
Tsai, C.-C., Tseng, S.-T. and Balakrishnan, N. (2012). Optimal design for degradation tests based on gamma processes with random effects. IEEE Trans. Reliab. 61, 604–613.Google Scholar
Tseng, S.-T., Balakrishnan, N. and Tsai, C.-C. (2009). Optimal step-stress accelerated degradation test plan for gamma degradation processes. IEEE Trans. Reliab. 58, 611–618.Google Scholar
Van Noortwijk, J. M. (2009). A survey of the application of gamma processes in maintenance. Reliab. Eng. System Safety 94, 2–21.Google Scholar
Wu, Y., Xie, L., Wu, N. and Li, J. (2011). Time-dependent reliability model of components with strength degradation based-on gamma process. In Proc. 2011 9th International Conference on Reliability, Maintainability and Safety (ICRMS), IEEE, New York, pp. 363–368.Google Scholar
Xu, W. and Wang, W. (2012). An adaptive gamma process based model for residual useful life prediction. In Proc. 2012 IEEE Conference on Prognostics and System Health Management (PHM), IEEE, New York, pp. 1–4.Google Scholar