708 CHAPTER 14 Statistical Process Control Control Chart for Monitoring Means: The x Chart R Chart INTERPRETATION Examination of the R chart shows that there is a point that lies beyond the upper control limit, so we conclude that the variation of the process is out of statistical control. YOUR TURN. Do Exercise 7 “Pepsi Cans: R Chart.” DEFINITION An x chart is a plot of sample means. It includes a centerline located at x, which denotes the mean of all sample means (equal to the mean of all sample values combined), as well as another line for the lower control limit and a third line for the upper control limit. It is used to monitor the center in a process. Using the approach common in business and industry, the control limits are based on ranges instead of standard deviations. (See Exercise 14 for an x chart based on standard deviations.) Monitoring Process Mean: Control Chart for x Objective Construct a control chart for x (or an x chart) that can be used to determine whether the center of process data is within statistical control. Requirements 1. The data are process data consisting of a sequence of samples all of the same size n. 2. The distribution of the process data is essentially normal. 3. The individual sample data values are independent. Notation n = size of each sample, or subgroup x = mean of all sample means (equal to the mean of all sample values combined) KEY ELEMENTS Bribery Detected with Control Charts Control charts were used to help convict a person who bribed Florida jai alai players to lose. (See “Using Control Charts to Corroborate Bribery in Jai Alai,” by Charnes and Gitlow, The American Statistician, Vol. 49, No. 4.) An auditor for one jai alai facility noticed that abnormally large sums of money were wagered for certain types of bets, and some contestants didn’t win as much as expected when those bets were made. R charts and x charts were used in court as evidence of highly unusual patterns of betting. Examination of the control charts clearly shows points well beyond the upper control limit, indicating that the process of betting was out of statistical control. The statistician was able to identify a date at which assignable variation appeared to stop, and prosecutors knew that it was the date of the suspect’s arrest. C w h a b ja t
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