For an X-bar control chart the subgroup size is often between 1 and 10. However the desired subgroup size to detect significant changes depends on a number of factors:
Type I error probability (α) – A Type I error occurs when we conclude that a control chart is giving us an out-of-control signal but the process is actually stable. This may be considered as a “false alarm.” In control chart applications, α = 0.0027 is often used. This is done so that the control limits trap 99.73% of the statistic that is being plotted on the control chart.
Type II error probability (β) – A Type II error occurs when we fail to detect an out-of-control condition when the process is actually not stable. As the Type II error is decreased, the required sample size increases.
The process standard deviation (σ) – As standard deviation decreases, the required sample size decreases. As the standard deviation increases, a larger size is needed.
The desired chart sensitivity (D) – D is the difference between the current process average and a new average, which represents a significant change. In other words, D represents the change in the process average that we are seeking to detect. So as it decreases, the required sample size increases.