Case Problem $1$: Multex Digital

Liana Bonnet is a production quality control engineer for Multex Digital, a manufacturer of computer components. Part of Liana$$s job is to analyze batches of semiconductor wafers to ensure that the wafers are within design specifications. Wafers have to have a thickness of around $625$ microns but that thickness will vary due to the inherit inaccuracy of the machines creating the wafers. Liana needs to ensure that machines are operating correctly because a machine that is constantly creating wafers that are too thin or too thick will have to be removed from the assembly line and retuned

Liana has recorded data from $50$ machines batches with the sample size of each batch varying from $3$ to $10$ wafers. Liana wants you to report which of the $50$ machines are no longer operating within control limits$.$