A distribution-free method for reliability improvement based on design of experiments

Given growing consumer expectations for enhanced product lifespans, there is a particular focus on improving product reliability. Design of Experiments (DOE) is a useful tool for identifying significant factors and determining factor levels to enhance product reliability. Current research commonly assumes that the lifetime data follows a specific distribution. This overlooks the possibility that erroneous assumptions about the data distribution may lead to imprecise factors identification. Additionally, factorial effect principles are often disregarded in factors effects identification. In this paper, a distribution-free method named Factor-Effect Bayesian Quantile Regression (FEBQR) is proposed to address the aforementioned issues. We first construct a new set of factor indicator variables, considering the principles of effect sparsity, weak effect hierarchy, and effect heredity. Then we develop a novel model that extends the Bayesian quantile regression framework by incorporating the principle of factor effects to describe the relationship between percentile lifetimes and factor effects. Unknown parameter estimates are obtained through the Gibbs sampling algorithm, and significant factors are identified based on the posterior mean of the proposed factor indicator variables. Two practical examples are illustrated using the proposed method. Compared with traditional methods, the proposed method provides more accurate factor identification results.