Modified weighted standard deviation index for adequately interpreting a supplier’s lognormal process capability

The process capability index has become an efficient tool for measuring a supplier’s process performance. C_pk(WSD) is one popularly used index for assessing non-normal process capability when the process violates the normality assumption. Unfortunately, this index cannot accurately reflect the process yield, so it may produce a serious result if the practitioner compares the calculated C_pk(WSD) value with the capability requirement to determine whether the process meets that requirement. Hence, this study modifies C_pk(WSD) to provide an adequate measure of lognormal process capability. In addition, an estimator of this modified index is also provided. Simulations show that the bias of this estimator is slight, and the coverage probability of capability testing is close to the nominal confidence. This means that our proposed method is adaptable for use.