Refer to given Exercise. Suppose the manufacturer has the ability to center the process such that the average thickness of the coating is at 0.005 mm, which is the target value. In doing so, the manufacturer estimates that the standard deviation of the process will be 0.018 mm. The cost of making this change in the process is estimated to be $1.50 per reel. Would it be cost-effective to make this change, compared to the original process? What would the annual savings or loss be if the annual production is 10,000 reels?
Exercise
A manufacturer of magnetic tapes is interested in reducing the variability of the thickness of the coating on the tape. It is estimated that the loss to the consumer is $10 per reel if the thickness exceeds 0.005 ±0.0004 mm. Each reel has 200 m of tape. A random sample of 10 yields the following thicknesses (in millimeters): 0.0048, 0.0053, 0.0051, 0.0051, 0.0052, 0.0049, 0.0051, 0.0047, 0.0054, 0.0052. Find the average loss per reel.