Example showing procedure for making c Control Charts

The data for the example is taken from an Exercise problem in Introduction to Statistical Quality Control by Douglas C. Montgomery.

Construction of c Control charts

Surface defects have been counted on 25 rectangular steel plates, and the data are shown below. The control chart for nonconformities is set up using this data. Save the raw data and draw the control chart. Compare the results with those given here


		------------------------------
		Plate           No. of
		No.         Nonconformities        
		------------------------------
		 1		   1
		 2		   0
		 3		   4
		 4		   3
		 5		   1
		 6		   2
		 7		   5
		 8		   0
		 9		   2
		 10		   1
		 11		   1
		 12		   0
		 13		   8
		 14		   0
		 15		   2
		 16		   1
		 17		   3
		 18		   5
		 19		   4
		 20		   6
		 21		   3
		 22		   1
		 23		   0
		 24		   2
		 25		   4
		------------------------------
		Mean        	  2.36
		------------------------------

The Upper Control Limit(UCL) and the Lower Control Limit(LCL) are calculated as follows:

LCL = mean -3 * sqrt(mean) = 0 (because less than 0)
UCL = mean +3 * sqrt(mean) = 6.968

The c chart is drawn with the Plate number on the x axis and the number of conformities on the y axis. The lines showing the Upper Control Limit, the Lower Control Limit and the mean are also drawn. The figure below shows the control chart.

[Download the image cchart.gif for
looking at the image]

It can be seen from the figure that the process is out of control as one of the points is out of the control limits. The possible reasons for the out of control behavior can be understood by looking at the Analysis of patterns on control charts.

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