Shocks as Burn-In in Heterogeneous Populations

Abstract

Burn-in is usually performed for items with decreasing or bathtub failure rates in order to eliminate early failures. This can be done in a “normal” or accelerated environment or with the help of high environmental stresses, which can often be referred to as “shocks”. The latter method of burn-in was not considered so far in the literature on burn-in modeling. Mixtures of distributions present a useful survival model for modeling lifetime distributions in heterogeneous populations. They often result in decreasing failure rates in some time intervals. In this article, we consider shocks that eliminate items in heterogeneous populations with probabilities that depend on the corresponding frailty parameters. We assume that the larger the failure rate of an item in a heterogeneous population is, the larger the probability of this elimination. The optimal level of severity of shocks that minimizes the corresponding total expected costs function is analyzed. Some meaningful examples are discussed.

Keywords:

• Accelerated burn-in
• Burn-in
• Heterogeneous populations
• Shocks
• Total expected cost

Mathematics Subject Classification:

• Primary 60E05
• Secondary 90B25

Acknowledgments

The authors would like to thank the referee for very helpful and careful comments and suggestions, which considerably improved the presentation of this article.

The work of the first author was supported by the Ewha Womans University Research Grant of 2008. The work of the second author was supported by the NRF (National Research Foundation of South Africa) grant FA2006040700002.