9-13 A pharmaceutical company producing vitamin capsules desires a proportion of
ID: 3041647 • Letter: 9
Question
9-13
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 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?
I need the percentage of nonconforming product - what proportion of the output will be nonconforming a percentage: 11.18%, 9.18%, 7.18% or 5.18%?
9-16
Refer to Exercise 9-13. 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?
I need the value of Cpm that is asked for in sentence two, above. Cpm = .9420, .7420, .5420, or .3420 are my selections.
Explanation / Answer
9-13 Solution:
Given that, Proportion of calcium content desired by the pharmaceutical company lie between 40 and 55 ppm.
Sample size = 20
Sample mean, = 44 ppm
Standard deviation, = 3 ppm.
The process is in control at the present values of its parameters. Normal distribution of the characteristic is assumed.
The natural tolerance limits are given by,
(UNTL, LNTL) = (µ + 3, µ - 3)
= (44 + 3*3, 44 – 3*3)
= (53, 35)
The standard normal values at the upper and lower specification limits are:
Z1= (55 - 44)/3 = 3.67
Z2= (40-44)/3 = -1.33
Using standard normal tables, the proportion above the upper specification limit is 0.000, while the proportion below the lower specification limits is 0.0918.
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