Minimizing cost-functions related to both burn-in and field-operation under a generalized model

Summary and Conclusions-Burn-in is a method used to improve the quality of products. In field operation, only those units which survived the burn-in procedure will be used. This paper considers various additive cost structures related to both burn-in procedure and field operation under a general failure model. The general failure model includes two types of failures. Type I (minor) failure is removed by a minimal repair, whereas type II failure (catastrophic failure) is removed only by a complete repair (replacement). We introduce the following cost structures: (i) the expenses incurred until the first unit surviving burn-in is obtained; (ii) the minimal repair costs incurred over the life of the unit during field use; and (iii) either the gain proportional to the mean life of the unit in field operation or the expenditure due to replacement at a catastrophic failure during field operation. We also assume that, before undergoing the burn-in procedure, the unit has a bathtub-shaped failure rate function with change points t₁ & t₂. The optimal burn-in time b^* for minimizing the cost function is demonstrated to be always less than t₁. Furthermore, a large initial failure rate is shown to justify burn-in, i.e. b^*>0. A numerical example is presented.