Some process capability indices for unilateral specification limits—Their properties and the process capability control charts

Processes with smaller the better and larger the better types of quality characteristics and consequently the unilateral specification limits are very common in manufacturing industries. However, very little theoretical resources are available in literature, compared to the bilateral specification limits, for assessing the capability of such processes. In the present article, we have studied the expressions for the threshold value and relationship with proportion of non conformance for some of the process capability indices (PCIs) for unilateral specification limits. We have also explored the distributional aspects along with the uniformly minimum variance unbiased estimators of those PCIs based on both single-sample information as well as the information obtained from the corresponding X‾-R$\overline{X} - R$ and X‾-S$\overline{X} - S$ control charts. The process capability control charts for these PCIs have been designed as well for the purpose of the continuous assessment of the capability of a process over the entire production cycle. Finally, a numerical example has been discussed in the context of the theory developed in this article.