نمودار کنترل نوع میانگین متحرک
Abstract
1. Introduction
2. Adaptive EWMA chart
3. Proposed adaptive control chart
4. Performance of the proposed adaptive control chart
5. Conclusions
Acknowledgment
Declarations of interest
Reference
Abstract
Exponentially weighted moving average (EWMA) control charts are typically used for faster detection of shifts in the process mean, relative to a Shewhart control chart, when the degree of shift is small. Normal guidelines suggest using a small (large) value of the weighting constant, λ, for detecting smaller (larger) shifts in the process mean. Prior research has suggested that the choice of λ should depend on the observed data and have considered the use of a weighting constant, that varies and adapts as monitoring continues and new data are collected. One such adaptive control chart, called the AEWMA chart, utilizes a rather computationally complex scheme to determine the weighting constant λ and it requires knowledge of the size of the shift, to specify whether it is “small” or “large”. A complex twophase optimization scheme is then solved to yield “good solutions”. As an alternative, we propose an adaptive EWMA-type control chart that does not require knowledge of the degree of the shift. Further, the computational scheme is easier and completed in one stage. The performance of the proposed chart is studied using simulations, where the degree of the shift in the process mean is varied over a wide range of values. Based on the average run length (ARL), as a performance measure, the proposed chart is demonstrated to perform uniformly better than the traditional EWMA chart with a constant weight. The proposed chart also performs better than the AEWMA chart for moderate to large shifts.
Introduction
The traditional Shewhart control chart technique, introduced in 1924 by Walter Shewhart, has been used in a variety of manufacturing and service industries. The commonly used control charts are those based on the sample mean (X¯), the range (R), the standard deviation (s), individual data (X) and the moving range (MR). In the first two situations (X¯ and R, X¯ and s), it is assumed that independent and identically distributed observations (X) are selected from a process, in subgroups, where the subgroup size is denoted by n. In the third situation, the subgroup size is 1 and the process is monitored based on individual observations (Mitra, 2016). The popular Shewhart control charts, while easy to implement, have the disadvantage that for small shifts in the process parameters, for example, the mean, it takes a rather long time to detect the shift. Consequently, control charts have been developed with the purpose of faster detection of small changes in the process parameters. These include the cumulative sum (CUSUM) chart and the exponentially-weighted moving average (EWMA) control chart (Albin, Kang, & Shea, 1997; Chen & Elsayed, 2002; Domangue & Patch, 1991; Klein, 1996; Lucas & Saccucci, 1990; Roberts, 1959). The traditional EWMA control chart is based on the monitoring statistic.