Determination of Optimum Burn-In Time: A Composite Criterion

The object of this paper is to present a mathematical model capable of determining the optimum amount of time that semiconductor devices, which have specified life characteristics, must be placed on burn-in to obtain maximum performance versus total cost. To make the model operational and realistic, the traditional assumption of an exponential (more recently, Weibull) distribution of life is omitted in favor of the generalized gamma distribution (GGD). This is done because the GGD includes, as special cases, such distributions as the normal, Rayleigh, Maxwell, chi, chi2, Weibull, exponential, ordinary gamma, etc. The use of the greater representational capability of the GGD is justified in the results of the studies showing that (other things being equal) small changes in parametric values of life characteristics can cause vast differences in the optimum burn-in time and maximum system effectiveness. The physical performance sector of the model incorporates system effectiveness that includes such factors as availability, expected time to repair, mission reliability, system use coefficient, storage survival probability, and operational readiness. The costs considered are those due to burn-in operation, production, and sales. The model has been studied by use of computer runs from the standpoint of critical analysis and parametric sensitivity analysis.