Distributions and Process Capability Control Charts for CPU and CPL Using Subgroup Information

Process capability analysis is a very well-known and widely accepted method of assessing the ability of a process to produce items within pre-assigned specification limits. Most of the process capability indices (PCI) available in literature are formulated in terms of the parameters of the concerned quality characteristics. However, since the actual values of these parameters are often unknown, their estimated values are used to evaluate the estimated capability of a process. One such estimation procedure may be to use the estimates of these parameters obtained from the corresponding control charts used to check the stability of the said process. In this article, we used this approach to redefine plug-in (natural) estimators of the two most famous PCI’s for unilateral specification limits viz., CPU and CPL. We formulated the corresponding unbiased estimators and uniformly minimum variance unbiased estimators (UMVUE), wherever possible, and their distributions as well. We also designed the process capability control charts of CPU and CPL based on these UMVUEs. For constructing these control charts, we used the estimators of the parameters of the quality characteristics as obtained from the corresponding X‾-S$\overline{X} - S$ and X‾-R$\overline{X} - R$ charts. These charts can be used to check the consistency of capability of a process and also to keep a constant vigil on the process. Two numerical examples have been discussed and it has been observed that our proposed process capability control charts are more efficient to detect changes in process capability than those already available in literature.