Multi-variate-attribute quality control (MVAQC)

When the number of quality characteristics, in the form of variables or attributes, exceeds unity and there exists a non-zero correlation between them, then one is dealing with either a multivariate or multi-attribute quality control problem. Monitoring these quality characteristics independently can be very misleading. Control charts, as one of the statistical quality control tools, are generally applied for both variable and attribute quality characteristics. In the variable domain, a measurable characteristic of a product or process that affects the quality of the process output is measured and controlled by using variable control charts. In the attribute domain, the number of, or percentage of, defects in products or defective products is calculated and controlled. In multivariate quality control, several dependent variable characteristics are measured and monitored simultaneously. Similarly, in multi-attribute quality control, more than one dependent attribute characteristic is considered simultaneously. From the literature review, all previous works have focused on either multivariate or multi-attribute quality control individually due to differences between the nature of these two concepts. Naturally, variable characteristics follow variable distributions such as the normal distribution. The appearance of these types of distributions is that of a smooth curve. However, attribute characteristics follow discrete distributions like the Binomial and Poisson. The appearance of discrete distributions is that of a series of vertical “spikes” with the height of each spike proportional to the probability. The pattern of these kinds of distributions is discrete and usually with skewness. Nevertheless, it is common for engineers to appeal to the continuous symmetric normal distribution for designing any control charts. Developing a model which is applicable in the multivariate-attribute case as a combination of multivariate and multi-attribute may fill a gap in the tool box available to quality professionals. As an example of where both variable and attribute characteristics may jointly determine the quality of a process, consider a metal forming process with punching and bending operations. Here, the weight and thickness of metal sheet may be i variable characteristics and the shape of the bent sheet and crumpling of the punched hole may be attribute characteristics. The first of the attribute characteristics may be checked with a gauge and the latter checked visually. In this research a new model is developed for quality control in multi-variate-attribute situations. Through this model, the original correlated and skewed quality characteristics are transformed in two steps to a set of uncorrelated and non-skewed variables which can be monitored as individual variables and by using univariate control charts including Shewhart control charts, MCUSUM and EWMA. In the proposed model, the out-ofcontrol states for the transformed variables can be traced back to the original variables to find the responsible one, which is not the case with many of the existing multivariate and multi-attribute methods. Two simulation studies are carried out to analyse the performance of the proposed model and compare it with the leading alternative. These studies clearly show the advantages of this new method, such as being more predictable, more sensitive and easier to understand.