MGT 3114
Principles of Management and Production
Chapter 10, Quality Control
Production Operations Management, Stevenson
Quality Control : to assure that processes are performing in an acceptable manner. We
often make these assurances based on statistical data.
Remember Systems Theory?
Inputs

Inspection of raw materials
Acceptance Sampling
Transformation
SPC

Ouputs
Finished Goods Inspection
Acceptance Sampling
The purpose of inspection is to provide information on the degree to which items
conform to a standard.
Inspection Issues:
1. How much to inspect and how often? The amount of inspection needed is
governed by the costs of inspection and the expected costs of passing defective
items. Example: APIX film. Current thinking is every reduction in defective
output reduces costs.
a. Low- cost, high volume production: little inspection. Why?
b. High-cost, low volume production: more intensive inspection. Why?
c. Operations with a high proportion of human involvement necessitate more
inspection than mechanical operations. Why?
d. A primary goal of quality control is to reduce variation. In what? Why?
How does inspection help us reduce variation?
2. Where in the process should inspection occur?
a. raw materials/ purchased parts
b. finished goods (FG)
c. before a costly operation
d. before an irreversible process
e. before a covering process
f. In auto manufacturing, name an irreversible process, or a covering
process, or a costly operations and explain why you should inspect
BEFORE these operations.
3. Inspect at centralized location or on site? Do we inspect the product on the
production line or in a specialized facility like a lab? Are the advantages of
specialized lab tests worth the time and interruption needed to obtain results?
4. Inspect attributes or variables? Attributes are counted, such as number of defects
in the sample and variables are measured, usually on a continuous scale (in our
example, we will be using variables: the amount of fluid in a Coke bottle)
a. we use Statistical Process Control (SPC) to determine if the output of a
process conforms to the intent of the design. We take periodic samples
from the process and compare the results with a predetermined standard.
If the sample results are not acceptable, we stop the production process
and take corrective action. If the sample results are acceptable, the
process continues.
The Control Process
1. Define what is to be controlled. Identify the attribute or variable that you want to
control. How do you select? In our sweatshirt example, list things we should
control for, i.e., things that if they are not done correctly could result in a low
quality product: _______________, ______________, ________________,
_______________, ___________________.
2. Measure it!
3. Compare to a standard. Standards are our criteria for quality. For example, in our
sweatshirts, we may have standard for determining size. A size large, must be at
least 21 inches wide at center of front. Another standard may be that we require
10 stitches per inch.
4. Evaluate it! Even a process that is functioning as it should, will not yield output
that conforms exactly to a standard. A certain amount of random variation is
inevitable. For example, if there are 9 stitches per inch in one seam, should I
reject that sweatshirt as poor quality? If the measurement at the center is 21.25
inches, should I conclude that product is of poor quality? Slight variations from
the standard represent only random variation rather than more drastic changes in
the production process, known as non-random events. Non-random events or
non-random variability represent serious deviations from standards, and in turn
mean that our production process is out of control and quality is deteriorating.
5. If the process is out of control, take corrective action. Uncover the causes of nonrandom variation and make corrections to the process.
6. Evaluate corrective action by monitoring, then measuring and comparing to the
standard.
Understanding Variation
Our Coke bottles should have 64 ounces of fluid in each. We sampled 100 bottles and
found the following:
# of bottles
# of ounces in each
5
62.0
10
62.5
10
63.0
15
63.5
20
64.0
15
64.5
10
65.0
10
65.5
5
66.0
Graph the distribution of variation of the process
25
20
15
10
5
0
62 62.5 63 63.5 64 64.5 65 65.5 66
Distribution of the Cokei fill process
100 bottles
x-axis: ounces
y-axis: number of bottles
What are the parameters of the normal distribution? What is the mean? ______________
What is the standard deviation?______________________________
Sampling Distribution
We can’t measure the content of every single bottle. Instead we take samples of bottles
and measure the content of each bottle in the sample. For example, we might pull a
sample of 20 bottles every hour and measure the content of each of the 20 bottles, then
calculate the sample average (). At the end of the 24 hour period, we have 24 samples
and their means. If we graphed the distribution of the means of the 24 samples, this
would be the sampling distribution of the process, centered at (). So how do we know if
the process is in control?
Tschebysheff’s Theorem
 2 contains 95.% of the values in a normal distribution
 3 contains 99.7% of the values in a normal distribution
Where  is the standard deviation of the sampling distribution. Remember from
Statistics that the standard deviation is the standard measure of how far items are from
the mean.
Ounces
For the sampling distribution,
=
 = /square root of n
Control Charts
Control charts are time ordered plots of sample statistics, used to distinguish between
random and non-random variation. The basis for the control chart is the sampling
distribution (the mean of each of your samples). If we use  2 as our control limits,
95.5% of our sample averages should be in control. If we use  3 as our control limits,
99.7% of our sample averages should be in control. We are interested in finding
abnormalities or problems, non-random variation.....those averages outside of  3
because they tell you when the process is out of control. Each control chart will then
have an upper control limit (UCL) and a lower control limit (LCL) based on  3 or 
2. A sample average that falls between the two limits suggest that sample averages are
varying around the mean in a random and acceptable fashion. A sample average outside
the UCL or LCL suggests non-randomness - that the process is out of control.
Upper Control Limit (UCL) =
+z
Lower Control Limit (LCL) =
-z

 = process standard deviation
n = sample size
z = standard normal deviate
 = average of sample means
The quality inspector took 5 samples of our Coke fill process and found:
observation
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5
1
62.0
64.7
63.7
65.1
64.1
2
63.4
65.1
64.5
63.9
63.7
3
65.1
63.9
64.2
64.3
63.6
4
64.8
65.5
63.8
64.4
64.8
5
65.2
64.2
65.0
64.9
64.9
Sample total
=
=
=
=
=
Sample mean
=
=
=
=
=
(a) calculate the mean of each sample (  ).
(b) calculate the mean of the sample means ( )
(c) Based on previous experience the standard deviation of the process is .02 ounces.
Assuming we want to include 99.74 of our sample means as normal (  3), calculate
the upper and lower control limits, UCL and LCL.
(d) Plot the 5 sample averages on a control chart and decide if our process is in control or
not.
(e) After adjusting the machinery, our next 5 samples yielded sample means of 64.33,
64.37, 64.35, 64.36, and 64.32. Is out process now in control? Plot the sample figures on
the control chart.
Homework;
Page 297/455, Problem 1 & Problem 2 (make sure you draw you control chart in part b)