Q.A machine drills hole in a pipe with a mean diameter of $0.532$ cm and a standard deviation of $0.002$ cm. Calculate the control limits for mean of 5 samples .

A control chart plots a sample statistic against a Central Line and Upper/Lower Control Limits computed from the process's own past data. For a measured (variable) characteristic, the $\bar{X}$ chart tracks the process average using $UCL/LCL = \bar{\bar{X}} \pm A_2\bar{R}$, while the $R$ chart tracks the process spread using $UCL = D_4\bar{R}$, $LCL = D_3\bar{R}$, where $A_2$, $D_3$, $D_4$ are standard factors looked up for the sample size used (for $n=5$: $A_2=0.577$, $D_3=0$, $D_4=2.115$). A point falling outside either chart's control limits signals an assignable cause needing investigation. Control limits must never be confused with tolerance limits: control limits describe …