Question

The upper and lower control limits on control charts are usually set at a distance of +/- three times the standard deviation from the center line of the control chart. Use independent research to find the reasons why. Make sure you use the concept of type I and type II error in your discussion. Under what circumstances might a manager consider the use of limits at two times the standard deviation. What should the manager keep in mind when setting the limits at two standard deviations? Make sure you appropriately cite the sources used.

Answer 1

If we assume that the quality of a production process is normally distributed then we say that the production process is under a state of quality control with 99.73% confidence level if the average quality of samples of units produced taken at regular intervals of time from the process would vary around the estimated or specified average quality of the process within the below stated +/- 3 times the standard deviation limits:

(estimated or specified average-3xstandard deviation of averages, estimated or specified average+3xstandard deviation of averages)

It is due to the above reason the upper and lower control limits on control charts are usually set at a distance of +/- three times the standard deviation from the center line of the control chart.

Here, type one error is rejecting the process by stating the process is out of control even though there is a substantial quality for the units produced from the process .The manager will have a very less chance of occurrence of this type one error if he sets the upper and lower control limits on control charts are usually set at a distance of +/- three times the standard deviation from the center line of the control chart. As here the confidence level for the above limits is 99.73%, then the chance of occurrence of type one error is 0.27% only.

Also, type two error is accepting the process by stating the process is under control even though there is a poor quality for the units produced from the process. Mostly the more chance of occurrence of type one error leads to more chance of occurrence of type two error also. Therefore, Type one error is treated as more critical and dangerous and significant error than type two error. Not allowing more chance to type one error is more important than that of type two error. As the type one error has very less chance of 0.27% in the +/- three times the standard deviation limits, that is why managers mostly prefer to set the upper and lower control limits on control charts are usually set at a distance of +/- three times the standard deviation from the center line of the control chart.

Three sigma control limits can effectively detect the medium to large shifts in the quality of the production process but insensitive to small shifts in the quality of production process.

Under certain circumstances, a small to medium shift in the quality of production process may become a serious concern. Then in such situations, the manager considers the use of limits at two times the standard deviation. Because these limits can effectively detect the small to medium shifts in the quality of the production process . But here, the manager should keep in mind that the quality of production process is checked with 95.45% confidence level only and the chance of occurrence of type one error increases up to 4.55% which may lead to increase the chance of occurrence of type two error also. Also, the two sigma limits are ineffective in detecting the process instability.

The sources used for the above discussion are mentioned below:

1. Engineering Statistics Handbook.

            Retrieved from https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc31.htm

2. What Are Control Charts?

            Retrieved from https://www.sqconline.com/six-sigma-control-charts.html