A new process capability index under multiplicative adjustment of process mean and its demonstration procedures

In the process capability study, it has been undisputedly assumed that the standard deviation of a quality characteristic is unchanged even if its mean is adjusted for the purpose of process centering. However, this assumption is not valid for the case of the multiplicative adjustment of the mean, which appears more commonly in practice. In addition, little research has addressed the issue of "process capability demonstration". In this paper, a new process capability index is proposed for the nominal-the-best characteristic under the multiplicative adjustment of the mean, its lower confidence limit is derived, and a demonstration procedure is developed so that the required sample size can be determined to achieve a desired probability of successfully demonstrating that the process capability index meets the target with a specified level of confidence.