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The capability analysis of production processes where there are more than one correlated quality variables is a complicated task. The problem becomes even more difficult when these variables exhibit nonnormal characteristics. In this paper, a new methodology is proposed to estimate process capability indices (PCIs) of multivariate nonnormal processes. In the proposed methodology, the skewness of the marginal probability distributions of the variables is first diminished by a root transformation technique. Then, a Monte Carlo simulation method is employed to estimate the process proportion of nonconformities (PNC). Next, the relationship between PNC and PCI is found, and finally, PCI is estimated using PNC. Several multivariate nonnormal distributions such as Beta, Weibull, and Gamma are taken into account in simulation experiments. A real-world problem is also given to demonstrate the application of the proposed procedure. The results obtained from both the simulation studies and the real-world problem show that the proposed method performs well and is able to estimate PCI properly. [ABSTRACT FROM AUTHOR]

The main usefulness of a capability index is to relate the actual variability of the process with the admissible one. This admissible variability is, in turn, related with the nonconforming proportion. Hence, the capability index should be closely related to the nonconforming proportion. In univariate and centered processes, the classical C p index explicitly admits this interpretation. For instance, if C p = 0.5, the standard deviation should be reduced to 50% to attain C p = 1. However, for noncentered processes and multivariate processes, there is a lack of capability indices that admit such an interpretation. This article fills this gap in the literature and proposes univariate and multivariate capability indices that have a direct interpretation of how much the variability of the process should increase or decrease to attain a unitary index. Some numerical examples are used to compare the proposed indices with the existing ones, showing the advantages of the proposals. [ABSTRACT FROM AUTHOR]

In this article, we propose a control chart for detecting shifts in the covariance matrix of a multivariate process. The monitoring statistic is based on the standardized sample variance of p quality characteristics we call the VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these p variances. The reasons to consider the VMAX statistic instead of the generalized variance | S| are faster detection of process changes and better diagnostic features, which mean that the VMAX statistic is better at identifying the out-of-control variable. User’s familiarity with sample variances is another point in favor of the VMAX statistic. An example is presented to illustrate the application of the proposed chart. [ABSTRACT FROM AUTHOR]