CHAPTER 9: MANAGING FLOW VARIABILITY: PROCESS
CONTROL AND CAPABILITY
9.1 Objective
This chapter focuses primarily on product quality and process capability, although we try to position it
more generally as dealing with variability in any product measure such as cost, availability and response
time. We claim that they all vary from one flow unit to the next, and this variability leads to customer
9.2 Additional Suggested Readings
We have used in the past some HBR articles and HBS cases to discuss principles of TQM, when it was a
hot topic in 1980’s. For example, the following two go well together.
As TQM lost its appeal, most of us have moved away from teaching it, although some of us still include
at least part of it in our course. Given its qualitative and fuzzy nature, it has been received with mixed
success. More in line with this book, however, we have continued to teach the SPC tools. In the past we
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9.3 Solutions to the Problem Set
Problem 9.1
a. Given the symmetric shape of normal distribution around its mean, maximum conformance of the
output within the given specifications will be achieved by centering the process at the midpoint of
the specifications, i.e., at
= 32.5 gms. Now if we desire 98% of the output to conform to the
b. With n = 12, and
= 1.073 as above, we can now determine the ideal control limits on subgroup
Problem 9.2
a. In order to produce 98% of the boxes above 15.5 oz., the process mean must be z = 2.055 standard
b. With
= 16.53,
= 0.5, and n = 9, the control limits on the average weight in a sample of 9 boxes
are:
+ 3
/
9
= (16.03, 17.03). The observed average of 15.9 is below the lower control limit of
c. The FDA specifications require at least 15.5 ozs per box. To be a 6-sigma process, the filling
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Problem 9.3
From the 26 observations given, we can calculate the average number of errors per thousand transactions
m = 3.3077, which is much better than the industry average = 15. a. We can then determine the control
Problem 9.4
a. If the process mean
= 515, standard deviation
= 5 gms, and sample size n = 25, Control limits
are LCL =
−
25
= 512 gms and UCL =
+
25
= 518 gms
Problem 9.5
Given: process mean
= 6 cm, standard deviation
= 0.01 cm, and sample size n = 10,
Problem 9.6
If the specifications do not change, improvement in the sigma capability means the standard deviation
decreases. In that case, the control band should become narrower.
Problem 9.7
Currently, process mean
= 2.2 hours, and standard deviation
= 0.8 hours, so probability of processing
within 4 hours is
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Problem 9.8
If D is the diameter of basketballs produced, we need 95% of diameters to fall between 29.3 and 29.7.
Given a centered process and the symmetry of the normal distribution, this means only 2.5% below lower
Problem 9.9
a. False. Control limits only assure process stability. They have nothing to do with meeting
customer specifications.
b. True. As sample size increases, standard deviation of sample averages decreases, and the control
bands becomes narrower.
Problem 9.10
a. R chart and X-bar chart