IJPAM: Volume 85, No. 3 (2013)

A COMPARISON OF PERFORMANCE OF RESIDUAL
CONTROL CHARTS FOR TREND STATIONARY
AR(p) PROCESSES

Yupaporn Areepong
Department of Applied Statistics
Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Bangkok, 10800, THAILAND


Abstract. The main goal of this paper is to implement Statistical Process Control (SPC) with Residual Control Charts. In real life applications, such as in industries or manufacturing, many processes are described by autocorrelated observations. In addition to autocorrelation, some types of industrial processes also exhibit a particular kind of trend behavior. A typical example of process with autocorrelations arises in chemical processes. One of the main characteristics of a control chart are the Average Run Length (ARL0) (mean of false alarm times) and the Average Delay time ( ARL1) (mean delay of true alarm times). The main parameter observed for a given process is the mean shift. If a process has no mean shift, then the ARL0 should be sufficiently large. On the opposite side, when a mean shift occurs the ARL1 should be small in order to indicate the mean shift quickly. We compared the performance of the Shewhart - x, EWMA, and GMA residual control charts for autocorrelation observations with upward/downward linear trend. These comparisons are made for different magnitudes of the mean shift and various levels of autocorrelation.

Received: February 27, 2013

AMS Subject Classification: 60A05

Key Words and Phrases: Shewhart - x chart, exponentially weighted moving average control chart (EWMA), geometric moving average control chart (GMA), average run length (ARL)

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DOI: 10.12732/ijpam.v85i3.13 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 3