Improved method for ALT plan optimization

Abstract

Candidate test plans with 3 stress levels (L, M, H) were identified using the probability of zero failures at one or more stress levels Pr{ZFP1} as a target parameter. For a given sample size n, the allocations nL and nM are input variables. The optimization involves finding a minimum for the lower stress level, on the premise that plans with wider spread of the stress levels have smaller error of the time-to-failure (TTF) extrapolated to the use stress condition. The only constraint is equal spacing of the stress levels, in terms of the standardized stress (ξ). The proposed method does not require computation of the large sample approximate variance (Avar). The optimization can be conveniently done using a spreadsheet and is quite flexible, enabling different censor times to be used for each stress level and can be readily extended to 4 or more stress levels. Monte Carlo simulation of the candidate test plans was used to verify the assumption that the variance of the extrapolated TTF is proportional to the lower stress ξL, for a given allocation. The optimized test plans and variance of the estimated time to 10% failure are similar to those previously published, using the same planning values. Although the optimization method identifies acceptable candidate test plans, there may be other allocations (with slightly higher ξL) that give lower variance of the estimated TTF. However, the difference is typically within the resolution of the stress factor (e.g. ∆T <1 °C) and the uncertainty of the estimated parameter. Monte Carlo simulation can be used to fine tune candidate test plans found by the optimization method.