عنوان مقاله [English]
The Taguchi method is an effective method for improving the quality of processes or products. This method tries to decrease the effects of noise factors on a response variable, so that a response variable would be robust towards variations in noise factors. Hence, changes in external circumstances will have a minimum effect on the response variable, and the product or the process can be used with little change in response variables under any situation. Taguchi introduced the signal to noise ratio (SNR) for considering and analyzing response variables. This method considers the distance of the process mean from the target, as well as the variation between observations, and tries to decrease variations and bring the response mean to the target. Although this index has some advantages, it is inefficient for considering a multivariate problem, because the correlation between responses is neglected
using this index. Hence, another method should be applied to introduce single measurement or multi objective techniques which need weight vector for responses. In this paper, a new method is developed as an alternative for SNR according to the Euclidean distance and process region. It is based on correlations between variables, by which different patterns can be identified and analyzed. It is also a useful way of determining the similarity of an
unknown sample set to a known one. It differs from Euclidean distance and takes into account the correlations of the data set. In addition, it is scale-invariant, i.e. not dependent on the scale of measurements.
The process region represents observations, according to their variance and correlation. Hence, as the variation of observations increases, the volume of the process region increases. This concept is used in many methods, such as
process capability indices, as a measurement of variation between observations.The proposed index accounts for the distance of the process mean from the target (using Euclidean distance) and variations of observations (using process
region). This method is capable for application to multivariate normal cases and presents a single index to consider those problems. An important advantage of the proposed index (called MSN) is that the correlation between responses is considered. So, there is no need to apply any other techniques, such as principal component analysis or other multi criteria decision techniques to the problem.