A simple test to determine the contributors of fraction nonconforming shifts in a multivariate binomial process

Abstract

Abstract The fraction nonconforming, which follows a binomial distribution, is one of the most critical quality characteristics of attribute processes. In addition, the multivariate binomial process plays an important role in industries due to the enormous diversity of quality characteristics. A multivariate binomial process is deemed out of control when it triggers a signal in a multivariate statistical process control chart. However, it is difficult to determine which quality characteristic triggers the nonconforming shift. In contrast to most current studies that identify the contributors of shifts in multivariate normal processes, this study discusses the contributors of fraction nonconforming shifts in multivariate binomial processes. First, a test that can be applied to detect outliers in a multivariate binomial distribution is proposed. In addition, a stepwise test method that can be used to determine the contributors of fraction nonconforming shifts in a multivariate binomial process is then developed. Numerical results indicate that the method proposed is effective in determining the contributors of fraction nonconforming shifts for a multivariate binomial process.