Determining quality risk for correlated bivariate normal characteristics

Tanjong, Shirley Anak Johnathan; Ibrahim, Raafat N; Abdollahian, Mali

doi:10.1007/s00170-014-5623-z

Cited by 1 publication

(3 citation statements)

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“…In [9], the definition of modified tolerance volume based on [21] is adopted as it addresses the correlation within the multivariate normal data and it represents the original tolerances of each quality characteristic involved.…”

Section: The Mtr Methodsmentioning

confidence: 99%

“…In this study, similar technique to [9] was employed but with an improvement on the method of estimating the probability density by using multiple integrations on the joint probability density function ( ) bounded by the MTR. For example, Fig.…”

Section: The Mtr Methodsmentioning

confidence: 99%

“…For p-variate of quality characteristics y with lower specification limit (LSL) and upper specification limit (USL), estimated the total quality cost per unit for multivariate normal quality characteristics with nominal specifications by defining the rejection region as the region outside of the rectangular tolerance region. [9] showed that the multivariate LF based on rectangular region, as described in Fig. 1 underestimates the rejection cost for correlated quality characteristics, thus improved the model in [8] by assuming a modified tolerance region defined by the correlation structure between the bivariate normal quality characteristics.…”

Section: Multivariate Loss Functionsmentioning

confidence: 99%

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Estimating Non-Conformance Using the Modified Tolerance Region Method and the Target Distance Method

Tanjong

Ibrahim²,

Abdollahian

et al. 2018

IJET

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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 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 multivariate 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 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.

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Section: The Mtr Methodsmentioning

confidence: 99%

Section: The Mtr Methodsmentioning

confidence: 99%