Question: The R data frame pistonrings,4 available in the R package qcc, consists of 40 samples, each of size 5, of the inside diameter of piston

The R data frame pistonrings,4 available in the R package qcc, consists of 40 samples, each of size 5, of the inside diameter of piston rings for an automotive engine. The first column of the data frame gives the diameter measurements, and the second column is a sample (rational subgroup) indicator. The first 25 samples were taken when the process was thought to be in control; this is indicated by “TRUE” on the third column of the data frame. Use the data to estimate the in-control diameter mean and standard deviation, construct a 3σ X chart, and check if any of the remaining subgroups indicate an out-of-control state.

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