# Sample Size, Control Distance, and Type I and Type II Errors in Control Charts

Type I and Type II errors in control charts (or in statistics) are difficult to explain concepts. When trying to explain the impact of the sample size and the control distances in the magnitude of Type I and Type II errors, it becomes exponentially more difficult to explain.

The embedded visualization shows three distributions:

• A population distribution (PDF: g(x)) with the average m = 12 and the s.d. S = 0.5. The process target is t = 12.
• A sampling distribution (PDF: f(x)) with the sample size n = 4 and the standard error = S/sqrt(n)
• A sampling distribution (PDF: h(x)) with a “derailed mean” c = 12.32

It uses the following control charts specifications.

• A control chart with the control distance of k = 1.96, ucl = t + k*s, and lcl = t – k*s

If you are familiar with the sampling distribution, the size of k will determine the size of both the Type I error and Type II error, and the size of n will determine the size of Type II error.

You can refer to the attached in-class exercise note to adapt it to your teaching/learning needs. This visualization to helps you to see how Type I error and Type II error changes as you:

• Change the sample size n
• Change the control distance k
• Change the mean of the process m

Go to the visualization: https://www.desmos.com/calculator/hccg2zkpon