Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T13:32:38.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Burn-in procedures for a generalized model

Part of: Special processes Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Ji Hwan Cha
Ji Hwan Cha*
Affiliation:
Seoul National University
*
∗ Postal address: Department of Statistics, Seoul National University, San 56-1, Shinrim-Dong, Kwanak-Ku, Seoul, 151–742, Korea. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper two burn-in procedures for a general failure model are considered. There are two types of failure in the general failure model. One is Type I failure (minor failure) which can be removed by a minimal repair or a complete repair and the other is Type II failure (catastrophic failure) which can be removed only by a complete repair. During a burn-in process, with burn-in Procedure I, the failed component is repaired completely regardless of the type of failure, whereas, with burn-in Procedure II, only minimal repair is done for the Type I failure and a complete repair is performed for the Type II failure. In field use, the component is replaced by a new burned-in component at the ‘field use age’ T or at the time of the first Type II failure, whichever occurs first. Under the model, the problems of determining optimal burn-in time and optimal replacement policy are considered. The two burn-in procedures are compared in cases when both the procedures are applicable.

Keywords

general failure modelburn-inbathtub-shaped failure rateoptimal burn-inreplacement policy

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 2 , June 2001 , pp. 542 - 553
Copyright
Copyright © Applied Probability Trust 2001 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beichelt, F., and Fischer, K. (1980). General failure model applied to preventive maintenance policies. IEEE Trans. Rel. 29, 39–41.Google Scholar
Block, H. W., and Savits, T. H. (1997). Burn-in. Statist. Sci. 12, 1–19.Google Scholar
Cha, J. H. (2000). On a better burn-in procedure. J. Appl. Prob. 37, 1099–1103.Google Scholar
Clarotti, C. A., and Spizzichino, F. (1991). Bayes burn-in decision procedures. Prob. Eng. Inf. Sci. 4, 437–445.Google Scholar
Jensen, F., and Petersen, N. E. (1982). Burn-in. John Wiley, New York.Google Scholar
Mi, J. (1991). Optimal burn-in. Doctoral Thesis, Department of Statistics, University of Pittsburgh.Google Scholar
Mi, J. (1994). Burn-in and maintenance policies. Adv. Appl. Prob. 26, 207–221.CrossRefGoogle Scholar
Mi, J. (1996). Minimizing some cost functions related to both burn-in and field use. Operat. Res. 44, 497–500.Google Scholar
Nakagawa, T. (1981). Generalized models for determining optimal number of minimal repairs before replacement. J. Operat. Res. Soc. Japan 24, 325–357.Google Scholar
Nguyen, D. G., and Murthy, D. N. P. (1982). Optimal burn-in time to minimize cost for products sold under warranty. IIE Trans. 14, 167–174.Google Scholar
Sheu, S. H. (1998). A generalized age and block replacement of a system subject to shocks. Eur. J. Operat. Res. 108, 345–362.Google Scholar
Sheu, S. H., and Griffith, W. S. (1996). Optimal number of minimal repairs before replacement of a system subject to shocks. Naval Res. Logist. 43, 319–333.Google Scholar