Joint X-Bar and R Charts Under Shift in Mu or Sigma


St. John, Ralph C.; Bragg, Daniel J.   (1991, ASQC)   Bowling Green State University, Bowling Green, OH

Annual Quality Congress, Milwaukee WI    Vol. 45    No. 0
QICID: 9699    May 1991    pp. 547-550
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Article Abstract

This abstract is an edited version of the author's original.

Many authors have discussed the Average Run Length (ARL) of control charts which monitor the mean of a process, when there is a shift in the process mean mu. Recently Ng and Case (1989) have discussed the ARL of control charts to monitor the range of a process, when there is a shift in the process standard deviation sigma. These and other authors discuss the properties of individual X-bar and Range charts.

The authors of this paper believe that it is more appropriate to study the properties of joint X-bar and Range charts, since that is the way these charts are used in many applications. This approach has been used in the economic design of control charts (see, for example, Rahim (1989)). With the exception of Crowder (1987), who studied the properties of joint individuals and moving range charts, there is little in the literature on this subject.

The standard Shewhart charts are often supplemented by various rules. The authors have investigated the properties of various combinations of the four AT&T rules. The three properties of the joint X-bar and Range charts which the authors of this paper have studied are: (1) the ARL of the joint charts, (2) the frequency of "misleading" signals, and (3) the distribution of "hits" for the various AT&T rules used.


X-bar control charts,Average run length (ARL),Control charts,R (range) chart,Shewhart control chart,Software,Standard deviation

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