Elliptical safety region plots for C_(pk)

摘要

Purpose: To develop safety region plots for assessing the process capability at a given significance level. Summary: It is discussed about the importance of process capability index (C_(pk)) that is widely used when measuring the capability of a manufacturing process. Instead of finding the actual process capability, of late process capability plot is used that represent the capability region for a given set of process mean and standard deviation. It is observed that since in most situations the process parameters - mean and standard deviation - are unknown and hence need to be estimated. This has prompted to focus on a graphical decision rule to be used when deeming a process capable at a given significance level. As a result an elliptical safety region is proposed which is centered at the process mean and standard deviation. Therefore, as long as the elliptical region is within the process capability plot, the process is deemed to be capable at the prefixed significance level and otherwise not. It is observed that under different conditions the elliptical region turns into other region such as circle and even straight line. (15 refs.)