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Textile Process Control Problem Based on customer requirements, engineers at International Textile have developed the following specifications for a key fabric cutting process (in terms of the acceptable size/dimension of the fabrics): USL=15.20 inches, and LSL=14.80 inches The product quality remains acceptable as long as the fabric size remains between 14.80 and 15.20 inches. Currently the process uses a brand new cutting machine and the process output has a mean size of 15.00 inches, with a standard deviation of 0.08 inches. We assume the actual data conforms to a Normal distribution.
1. What is the product defective rate?
2. The customers require 3 sigma quality. Do you think the company can deliver that?
3. Based on the given information, the process is assumed to have an overall process average of 15.00 inches, and a process standard deviation of 0.08 inches. Now the company decides to take samples of 16 units periodically to collect data so they can judge if the process is in control. Calculate the process control limits (UCL and LCL).
4. Now the process average is assumed to be 15.20 inches and the process average is 0.10 inches. If we take a sample of 16 units and calculate the average size, what is the chance that this sample is an outlier (indicating the process is out of control)?
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