Refer to given Exercise. Find the process capability index Cpk and comment on process performance. If the target value is 47.5 ppm, find the Cpm and Cpmk indices and comment on their values. If the process center is shifted to the midpoint between the specification limits, what proportion of the product will be nonconforming? Has it improved relative to the present setting of the process mean?
Exercise
A pharmaceutical company producing vitamin capsules desires a proportion of calcium content between 40 and 55 ppm. A random sample of 20 capsules chosen from the output yields a sample mean calcium content of 44 ppm with a standard deviation of 3 ppm. Find the natural tolerance limits of the process. If the process is in control at the present values of its parameters, what proportion of the output will be nonconforming, assuming a normal distribution of the characteristic?