Accelerated degradation-tests with tightened critical values

ALT (accelerated life tests) are widely used to provide quickly the information about life distributions of products. Life data at elevated stresses are extrapolated to estimate the life distribution at design stress. The existing estimation methods are efficient and easy to implement—given sufficient life data. However, ALT frequently results in few or no failures at low-level stress, making it difficult to estimate the life distribution. For products whose failures are defined in terms of performance characteristics exceeding their critical values, reliability assessment can be based on degradation measurements by using degradation models. The estimation, however, is usually mathematically complicated and computationally intensive. This paper presents a method for the estimation of life distribution by using life data from degradation measurements. Since the time-to-failure depends on the level of a critical value, more life data can be obtained by tightening the critical value. The relationship between life and critical value and stress is modeled and used to estimate the life distribution at a usual critical value and design stress. The model parameters are estimated by using maximum likelihood. The optimum test plans, which choose the critical values, stress levels, and proportions of sample size to each stress level, are devised by minimizing the asymptotic variance of the mean (log) life at a usual critical value and design stress. The comparison between the proposed and existing 2-level test plans shows that the proposed plans have smaller asymptotic variance and are less sensitive to the uncertainty of the pre-estimates of unknown parameters.