Semiparametric Analysis of Designed Reliability Improvement Experiments: Termination and Identification

ABSTRACT Reliability practitioners are very interested in which factors affect product reliability. Constrained by time and cost, they hope to terminate the experiment early without affecting the identification results of important factors. In design of experiments (DOE), practitioners usually construct the relationship between parameter and factor effects. However, the true model is usually complicated. Parametric models are often mis‐specified. In this article, we proposed a semiparametric framework to terminate the experiment and identify important factors. First, we introduce a loss function to describe the total loss of the manufacturers and the customers, then the response is the type of smaller‐the‐better. Second, we assume the lifetime data follow a Weibull distribution and get the estimates of parameters using the Bayesian method, then we compute the total loss. Next, we calculate the sum of squares (SS) gotten from different experimental levels and terminate the experiment if all the weighted relative rates of changes of SS are less than a threshold value. Finally, the classification and regression tree (CART) method is introduced to drop some unimportant factors and identify important factors through the analysis of variance (ANOVA). Additionally, we confirm the proposed method through a real example and find that the important factors obtained from the proposed terminated experiment are the same as those found from the original terminated experiment.