نمودارهاي كنترل GWMA و DGWMA براي مشخصهﻫﺎي كيفي وصفي

GWMA and DGWMA Control Charts for Attribute Quality Characteristics

در نمودارهاي كنترل با حافظه، سرعت كشف شيفتهاي كوچك فرايند بيشتر از نمودارهاي كنترل شوهارت است؛ به‌طوري كه در سالهاي اخير نمودارهاي كنترل ميانگين متحرك موزون عمومي (GWMA‌) و ميانگين متحرك موزون عمومي دوگانه (DGWMA)، كاراتر از نمودارهاي ميانگين متحرك موزون نمايي (EWMA‌) و نمودارهاي ميانگين متحرك موزون نمايي دوگانه (DEWMA‌) معرفي شدهاند. اين نمودارها غالباً براي پايش مشخصههاي كيفي متغير، تحت فرض توزيع پيوستهي نرمال‌اند. مشخصههاي كيفي وصفي، برمبناي شمارش تعداد اقلام نامنطبق (با توزيع دوجملهاي) يا شمارش تعداد نقصها در واحد بازرسي (با توزيع پواسون)، كاربرد زيادي در كنترل فرايند آماري دارند. در اين نوشتار نمودارهاي كنترل GWMA و DGWMA براي مشخصههاي كيفي وصفي طراحي شده، و اثر تغيير پارامترهاي نمودارها بر نرخ هشدار غلط آنها بررسي مي‌‌شود. همچنين كارايي اين نمودارها در پايش مشخصههاي كيفي وصفي، با استفاده از شبيهسازي مونتكارلو با يكديگر و با نمودارهاي كنترل EWMA و DEWMA مقايسه مي‌‌شود. نتايچ حاصله حاكي است كه وقتي مشخصههاي كيفي وصفي پايش مي‌‌‌شوند، همچنان اين نمودارها كارايي خوبي در كشف شيفتهاي كوچك دارند.

Nowadays, statistical methods play a significant role in reducing waste and improving product quality at various stages of the product life cycle. Statistical process control (SPC), as the application of statistical methods, has been applied most frequently to monitor and control a process to ensure that it operates at its full potential to produce the conforming product. Moreover, control charts, known as Shewhart charts, are considered the most important tool in SPC. However, it has been shown that memory control charts, such as the Exponentially Weighted Moving Average (EWMA) control chart, can detect small shifts in a process faster than the Shewhart control chart. In other words, due to the added adjustment parameter, the memory control chart performs much better than the Shewhart control chart in monitoring small shifts of the process mean. The weighted moving average (GWMA) control chart is a generalization of the EWMA control chart. In recent years, the GWMA and the Double Generally Weighted Moving Average (DGWMA) control charts have demonstrated their higher efficiency compared to the EWMA control chart and the Double Exponentially Weighted Moving Average (DEWMA) control chart. Moreover, these charts are often designed for monitoring variable quality characteristics under normal distribution assumption. Attribute quality characteristics, which are based on counting the numbers of nonconformity with binomial distribution, or the numbers of nonconformity with Poisson distribution, have many applications in statistical process control. In this paper, we design the GWMA control chart and the DGWMA control chart for attribute quality characteristics and consider the effect of changing the parameters of charts on their false alarm rates. In addition, the performances of these charts are compared to each other (the EWMA control chart and the DEWMA control chart) using Monte Carlo simulation. Based on the results, it is seen that these new control charts also perform well in detecting small shifts when the attribute quality characteristics are monitored.