A multi-stream process capability assessment using a nonconformity ratio based desirability function

Abstract

In this work a linear nonconformity ratio based desirability function (NCDU) is presented as a process capability index. NCDU avoids the use of two different indices for assessing the actual capability and the potential capability. Based on a real case study the performance of this index is compared to other indices in the literature. It was demonstrated that NCDU respects the ”higher the better” rule for any type of distribution and for any specification limits. Moreover, a boot- strap confidence interval is constructed for NCDU. The lower bootstrap confidence limit was used for capability judgment. The presented univariate index overcomes some shortcomings of the existing indices. However, in many cases the quality of a product is given through several quality characteristics. Hence an extension to the multivariate case of NCDU is given by the desirability index. Moreover, it was demonstrated that the geometric mean of the univariate indices is suitable for process capability assessment as it is proved that it could be written as a function of the joint nonconformity ratio for uncorrelated quality characteristics. A threshold for the capability judgment for the multivariate index (NCDM) and a condition under which the multivariate index respects the ”higher the better” rule were proposed. Furthermore, a condition under which the threshold for capability judgment could be used for correlated quality characteristics is presented. The performance of NCDM is compared to other multivariate indices from the literature through a simulated example. The implementation of NCDM revealed that it respects the ”higher the better rule” in the case study. Moreover, a bootstrap confidence interval was constructed for NCDM and the lower limit was used for capability judgment. ...