Data should usually be normally distributed revolving around a mean (average). In the example below, a bottle company fills their bottles to 16 oz. (mean); they are evaluating if their process is “in-control”. The amount in ounces over 16 oz. is normally distributed around the mean. Measurements need to be independent of one another. In the example, the measurements are in subgroups. The data in the subgroups should be independent of the measurement number; each data point will have a subgroup and a measurement number.
To find the mean, add all measurements in the subgroup and divide by the number of measurements in the subgroup. In the example, there are 20 subgroups and in each subgroup there are 4 measurements.
This will give you the overall mean of all the data points. The overall mean will be the centerline in the graph (CL), which is 13. 75 for our example.
UCL = CL + 3S LCL = CL – 3S The formula represents 3 standard deviations above and 3 standard deviations below the mean respectively.
In the above example, there is a line drawn at one, two, and three standard deviations (sigma’s) away from the mean. Zone C is 1 sigma away from the mean (green). Zone B is 2 sigma away from the mean (yellow). Zone A is 3 sigma away from the mean (red).
Any point falls beyond the red zone (above or below the 3-sigma line). 8 consecutive points fall on one side of the centerline. 2 of 3 consecutive points fall within zone A. 4 of 5 consecutive points fall within zone A and/or zone B. 15 consecutive points are within Zone C. 8 consecutive points not in zone C.
