Optimum Degradation Tests for Comparison of Products

Abstract

Life tests are often conducted to compare products, designs, or processes to select the one that has the highest reliability. To make a sound decision, engineers may require the tests to continue until all or most of the test units fail. As such, the test time is often excessive, especially when we test high-reliability products. For some products, a failure is said to have occurred when a performance characteristic reaches a specified threshold. For these products, reliability is defined by the performance characteristic. Then comparing the reliabilities of two products can be turned into comparison of their performance characteristics. During testing, it is possible to measure the performance characteristics at different times. Measurement data can be employed to predict whether or not the performance characteristics of the two products will be significantly different at the time of interest, e.g., design life, warranty time, or specified test time. When there are sufficient data to make such a prediction with a high degree of confidence, the test can be terminated. As a result, the test time is reduced. This paper presents a method for comparing the performance characteristics of two products with a reduced test time, where the log performance characteristics are -normally distributed with a mean as a (transformed) linear function of time, and a constant standard deviation. In particular, the paper describes a test method, test termination rules, and degradation modeling. Then we develop an overlap probability as a metric to measure the difference between two products. The confidence interval for the overlap probability is calculated. The reliability and its confidence interval are computed from the degradation data. The paper also delineates optimum test plans which choose sample size and test time to minimize the variance of an estimate related to the overlap probability, and simultaneously satisfy the constraints on test budget and available sample size. The test plans are robust against the pre-estimates of model parameters. The proposed method is illustrated with a practical example. The application shows that the method is effective at reducing test time.