Question

1. 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.
   1. Find the natural tolerance limits of the process.
   2. 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?
   3. Calculate and interpret the process capability indices Cp for the process. Is the process capable?
   4. Find the process capability index Cpk, and comment on the process performance.
   5. 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?

Answer 1