Section 3 Control Charts
Lesson S03-12
Text: Section 3 pages 73 – 75
Duration: 19 minutes
Sample Size Guidance
The sample size for an X̄ control chart is a function of:
- The process standard deviation
- The size of the shift we want to detect
- The allowable level of Type II Error (probability that the specified shift is not detected when the shift occurs)
We have already seen that the smaller the size of the shift that we want to detect, the larger the sample size we need. Also, reducing Type II error requires a larger sample size. Finally, the larger our standard deviation is, the larger the sample size that is needed to detect a specified process change.
The Sample Size Worksheet
An Excel file called “Control Chart Sample Size” (download with the link) and it allows sample sizes to be calculated for X̄ charts in order to detect a specified mean shift with a specified power. This worksheet allows the user to specify:
- Process Standard Deviation
- Amount of Shift to be Detected
- Power (Probability of Detection)
Download the Excel worksheet here: control-chart-sample-size.xls
Sample Size Calculations in Minitab
Sampling Frequency
For ongoing process monitoring, the sampling frequency is a function of the: – Risk of Undetected Process Changes
- Current Process Capability
- Type II Error Probability (probability that a process change is NOT detected on a given sample)
- Cost of Sampling
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