ارايه‌ي شاخص نوين «نسبت سيگنال به اغتشاش» چند‌متغيره براي پاسخ‌هاي وابسته به هم

A New Multivariate Signal to Noise Ratio for Correlated Responses

روش تاگوچي، روشي موثر و كارا در افزايش كيفيت محصول يا فرايند است. هدف اين روش كاهش ميزان تاثير عوامل اغتشاش بر مقدار متغير پاسخ است به‌گونه‌يي كه متغير پاسخ نسبت به تغييرات عوامل اغتشاش مقاوم شود. تاگوچي به‌منظور بررسي و تجزيه و تحليل متغير پاسخ، نسبت سيگنال به اغتشاش را معرفي كرد. در اين مطالعه يك شاخص نوين سيگنال به اغتشاش، براساس فاصله‌ي اقليدسي و مساحت ناحيه‌ي فرايند براي متغيرهاي پاسخ وابسته به هم ارايه مي‌شود. معيار ارايه شده چنان است كه هم معياري است براي اندازه‌گيري فاصله تا هدف، و هم معياري است براي اندازه‌گيري ميزان تغييرات مشاهدات (مشتمل بر تغييرات ناشي از هر متغير و ناشي از كواريانس بين متغيرها). روش پيشنهادي در سه مثال مورد بررسي قرار گرفته، و كارايي روش پيشنهادي نشان داده شده است.

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.