The questions are designed to help Susan Douglas understand the current capability of the extrusion process and quantify the benefit that may be achieved if the extruder could be transformed to a Six Sigma process.

1. If the extruder setting is accurate, what proportion of the rubber extruded will be within specifications?

2. Douglas has asked operators to take a sample of 10 sheets of rubber each hour from the extruder and measure the thickness of each sheet. Based on the average thickness of this sample, operators will decide whether the extrusion process is in control. Given that Douglas plans Three Sigma control limits; what upper and lower control limits should she specify to the operators?

3. If a bearing is worn out, the extruder produces a mean thickness of 403 thou when the setting is 400 thou. Under this condition, what proportion of defective sheets will the extruder produce? Assuming the control limits in question 2, what is the probability that a sample taken from the extruder with the worn bearings will be out of control? On average, how many hours are likely to go by before the worn path is detected?'

4. Now consider the case where extrusion is a Six Sigma process. In this case, the extruder output should have a standard deviation of 1.667 thou. What proportion of the rubber extruded will be within specifications in this case?

5. Assuming that operators will continue to take samples of 10 sheets each hour to check if the process is in control, what control limits should Douglas set for the case when extrusion is a Six Sigma process?

6. Return to the case of the worn bearing in question 3 where extrusion produces a mean thickness of 403 thou when the setting is 400 thou. Under this condition, what proportion of defective sheets will the extruder produce (for the Six Sigma process)? Assuming the control limits in question 5, what is the probability that a sample taken from the extruder with the worn bearings will be out of control? On average, how many hours are likely to go by before the worn bearing is detected?