Estimating non-conformance using the modified tolerance region method and the target distance method

Shirley J. Tanjong, Raafat N. Ibrahim, Mali Abdollahian, Magdalene Andrew-Munot

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In many cases, the quality of a manufactured product is determined by more than one characteristic and often, these quality characteristics are correlated. A number of methods for dealing with quality evaluation of multivariate processes have been proposed in the literature. However, some of these studies do not consider correlation among quality characteristics. In this paper, two new approaches for estimating the proportion of non-conformance for correlated multivariate quality characteristics with nominal specifications are proposed: (i) the modified tolerance region approach and (ii) the target distance approach. In the first approach, the p number of correlated variables are analysed based on the projected shadow of the p-dimensional hyper ellipsoid so that the ability to visualise the tolerance region and the process region for p > 2 is preserved. In the second approach, the correlated variables are combined and a new variable called the target distance is introduced. The proportion of non-conformance results estimated using both methods were used to compute the multi-variate capability index and the total expected quality cost. This study also suggest modification to the NMCp index as proposed in Pan and Lee (2010) such that the process capability for p > 2 can be measured correctly. The application of both approaches is demonstrated using two examples and it is shown that both methods i.e. the modified tolerance region and the target distance methods are capable of estimating the capability of multivariate processes.

Original languageEnglish
Number of pages14
JournalInternational Journal of Engineering & Technology
Issue number3.18
Publication statusPublished - 2018


  • Correlated characteristics
  • Mahalanobis distance
  • Multivariate quality control
  • Proportion of non-conformance
  • Tolerance region

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