You are working for the ABC Operations System as a quality manager. Your team is currently examining a new product, ABC Perfect filter, which can perfectly prevent any virus, such as COVID-19 virus, to figure out the productâ€™s conformance quality. The most challenging part for the product is the filterâ€™s length of a special fiber.

â€¢ If the specification is such that no filter should be greater than 2.4 millimeters, assuming that the lengths of fiber are distributed normally, what fraction of the output is expected to be greater than this length? What if there is an upper and lower specification, where the upper length limit is 2.4 and the lower length limit 1.4, what fraction of the output is expected to be out of tolerance?

â€¢ What is the Cpk for the process? And what would be the Cpk for the process if it were centered (assume the process standard deviation is the same)? How can you interpret that? What percentage of output would be expected to be out of tolerance if the process were centered?

â€¢ Setup X-bar and Range control charts for the current process. Assume the operators will take samples of 10 filters at a time. Plot the data on your control charts. Does the current process appear to be in control? Regarding the control chart, please refer the 99.7% (provided by the lecture note) control chart parameter.

â€¢ If the process could be improved so that the standard deviation was only about .10 millimeters, what would be the best that could be expected with the processes relative to fraction defective?