Reliability improvement through designed experiments with random effects

Design of experiment (DOE) is a useful tool to identify significant factors and choose factor levels for product reliability improvement. In practice, practitioners often ignore random effects that result from the experimental protocol in the reliability experiment. In this paper, we consider product reliability improvement with designed experiment when the test is actually not completely randomized. The Weibull distribution is used to model the lifetime, leading to a smallest extreme value distribution for the log-lifetime. Random effects are incorporated into the model through mean time to failure (MTTF). We improve the product reliability with maximizing the MTTF. The simulation study shows that ignoring random effects in modeling can result in unreliable factors identification and estimation. We also illustrate the proposed method with a real example.