Some specialized containers are produced by a process that runs 8 hours per day. Nine containers are sampled hourly, each day for five days. The distance from the bottom of the container to the container's handle is of interest. The target value for this dimension is 4 cm, and the process standard deviation for this quality dimension is .1 cm . (This is known from extensive experience with the process.)
(a) What is a subgroup in this context? What is the subgroup size? How many subgroups make up the entire study?
(b) Give control limits for process monitoring when subgroup averages are plotted versus time.
(c) In addition to the chart in (b), a control chart for short-term process variation is to be made. Suppose that only subgroup averages and the smallest and largest values in a subgroup are available for analysis. What subgroup statistic can be used to do the charting? Give appropriate control limits and center line for the chart.
(d) Are the limits in (b) and (c) standards given or retrospective limits? Why?
(e) Suppose both the charts in (b) and (c) indicate that the process is stable. Is it then possible that any plotted subgroup mean is outside the limits from (b)? Is it possible that there are plotted values on the second chart outside control limits from (c)? Explain.