You have just installed a new system that uses an interferometer to measure the thickness of polystyrene film. To control the thickness, you plan to measure three film specimens every 10 minutes and keep and s charts. To establish control you measure 22 samples of three films each at 10-minute intervals. Table 12.11 gives and s for these samples. The units are millimeters . Exercises 12.55 through 12.57 are based on this process improvement setting.

Question 12.57

12.57 Categorizing the output.

Previously, control of the process was based on categorizing the thickness of each film inspected as satisfactory or not. Steady improvement in process quality has occurred, so that just 15 of the last 5000 films inspected were unsatisfactory.

  1. What type of control chart discussed in this chapter might be considered for this setting, and what would be the control limits for a sample of 100 films?
  2. Explain why the chart in part (a) would have limited practical value at current quality levels.

12.57

(a) A chart would be appropriate. , so use 0. (b) The chance of an unsatisfactory film is so small that we only expect 0.3 in each sample of 100. But if a sample has 2 defects, is already over than the UCL and would signal an out-of-control process, which isn’t true.