The grand mean and grand average range are computed first, and then the standard $A_2$/$D_4$/$D_3$ factors convert $\bar{R}$ into a control-limit spread around each chart's central line. …

Step 1 — Compute the grand mean $\bar{\bar{X}}$ (mean of the five sample means):

Step 2 — Compute the average range $\bar{R}$ (mean of the five sample ranges):

Step 3 — $\bar{X}$ chart control limits, using $A_2 = 0.577$ for $n=5$:

Step 4 — $R$ chart control limits, using $D_4=2.115$, $D_3=0$:

Step 5 — Check every sample point against both charts:

Using the wrong control-chart factor for the sample size (the $A_2$/$D_3$/$D_4$ values are specific to $n$, and must never be reused across a different sample size); adding $A_2\bar{R}$ to the average range instead of the grand mean when computing the $\bar{X}$ chart's limits; and forgetting that t …