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How to Calculate Control Charts

In quality improvement, a control chart is used to determine if a process is stable. In a control chart, data points are plotted on a graph and compared to upper and lower control-limits. The control limits are designed to contain 99 percent of all the data points of the process if the process is in control. If your data points routinely fall above or below these control limits, the process is deemed out of control. Causes for variation in process quality should be investigated and remediated before any systematic changes to the process as a whole can be made and evaluated.

Things You'll Need

Calculator
Graph paper

Instructions

- 1
  Arrange your data into columns. If you are studying the number of successful sales calls made per month by three sales centers over a three month period, the data would look like this:
  
  The first column would be month.
  
  Month
  
  January
  
  February
  
  March
  
  The second column would be Sales Center 1's data.
  
  Center 1
  
  4,888
  
  5,000
  
  5,245
  
  The third column would be Sales Center 2's data.
  
  Center 2
  
  4,456
  
  3,455
  
  3,344
  
  The fourth column would be Sales Center 3's data.
  
  Center 3
  
  4,567
  
  4,433
  
  3,344
- 2
  Compute the average number of sales over all the sales centers over each month period. The average is calculated by adding the sales together across all centers for each individual month and dividing by the total number of sales centers. The average are:
  
  January: (4,888+4,456+4,567)/3 = 4,637.0
  
  February: (5,000+3,455+4,433)/3 = 4,296.0
  
  March: (5,245+3,344+3,344)/3 = 3,978.7
- 3
  Compute the grand average which is the average of all sales across all sales centers. Add up all the sales and divide by the total number of observations.
  
  (4,888+4,456+4,567+5,000+3,455+4,433+5,245+3,344+3,344)/9 = 4,303.6
- 4
  Calculate the standard deviation of all the observations. This is known as the grand standard deviation. To calculate the standard deviation subtract each observation from the mean. Square each of these figures and take the sum of these squared deviations from the mean. In this example the sum of the squared deviations from the mean is 4,383,866. Divide this figure by the total number of observations minus 1. In this example 4,383,866/8 = 547983.3. The square root of this figure is the standard deviation. In this example, the grand standard deviation is 740.3.
- 5
  Calculate the estimated standard deviation by dividing the grand standard deviation by the square root of the number of observations in each time frame. The square root of 3 is 1.7 so 740.3/1.7 is 427.4.
- 6
  Calculate the upper control limits by taking the grand average and adding to it a constant of 1.96. Multiply this figure by the estimated standard deviation. In this example, the upper control limit is 4,303.6+1.96x427.4 = 5,141.3.
- 7
  Calculate the lower control limits by taking the grand average and subtracting a constant of 1.96. Multiply this figure by the estimated standard deviation. In this example, the upper control limit is 4,303.6-1.96x427.4 =3,465.9.
- 8
  Plot the average sales for each time period on a graph with a separate dot representing each data point. The horizontal or x-axis of the graph will be the months and the vertical axis will be the data values.
- 9
  Draw one horizontal line on the graph marking the upper control limit and one marking the lower control limit to complete the control chart.

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