One stage in the manufacture of semiconductor chips applies an insulator on the chips. This process must coat the chip evenly to the desired thickness of 250 microns or the chip will not be able to run at the desired speed. If the coating is too thin, the chip will leak voltage and not function reliably; if the coating is too thick, the chip will overheat. The process has been designed so that 95% of the chips have a coating thickness between 247 and 253 microns. Twelve chips were measured daily for 40 days, a total of 480 chips.14
(a) Do the data meet the sample size condition if we look at samples taken each day?
(b) Group the data by days and generate X-bar and S-charts with control limits at ± 3 SE. Is the process under control?
(c) Describe the nature of the problem found in the control charts. Is the problem an isolated incident (which might be just a chance event), or does there appear to be a more systematic failure?