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CHAPTER 8
Measuring and Controlling Quality
Teaching Note
This chapter presents the basic concepts of statistical process control. These include purposes,
control charting techniques, design and analysis of charts, managerial requirements for
implementation of SPC, and SPC considerations within service organizations. Key objectives for
this chapter should include:
• To define Measurement as the act of collecting data to quantify the values of product,
service, process, and other business metrics. Measures and indicators refer to the
• To learn that a unit of work is the output of a process or an individual process step. A
nonconformance is any defect or error associated with a unit of work. In manufacturing the
• To establish that throughput yield (TY) is the number of units that have no
• To identify metrics used in SPC, which fall into the categories of attributes or variables.
Variable measurements are concerned with the degree of conformance to specifications,
Chapter 8 – Measuring and Controlling Quality 2
• To introduce the concept of Defects per million opportunities (dpmo) = (Number of
• To explore the concept of the cost of quality (COQ) as a way to translate quality problems
into the language of upper management—money. Through the use of quality cost information,
management identifies opportunities for quality improvement, is aided in budgeting and cost
• To appreciate that process capability is the range over which the natural variation of a
process occurs as determined by the system of common causes; that is, what the process can
• To learn that pre-control is a technique for monitoring process capability over time. It is
particularly suited to machining applications, but should only be used when process
capability is rather good.
• To establish the importance of statistical process control as a means to give workers the
information that they need about when a process should be adjusted and when it should not
• To learn that capability and control are independent concepts. Ideally, a process should have
both high capability and be in control. If a process is not in control, it should first be brought
into control before attempting to evaluate process capability.
Chapter 8 – Measuring and Controlling Quality 3
• To understand that a control chart is simply a run chart to which two horizontal lines, called
control limits are added: the upper control limit (UCL) and lower control limit (LCL).
• To identify control chart patterns, including: when a process is in control, no points are
outside of control limits; the number of points above and below the center line is about the
same; the points seem to fall randomly above and below the center line; and most points (but
• To introduce the common control charts for variables (x- and R-charts;x – and s-charts;
and individual and moving range charts). and attributes (p-, np–, c- and u-charts), show
how they can be constructed, and describe their use in organizations. Charts for attributes
• To become aware of factors that must be understood in designing control charts, and how
one must be concerned with how the sample data are taken, the sample size, the sampling
frequency, and the location of the control limits. The process for constructing and using a
• To understand how ISO 9000:2000 places increased emphasis on the use of statistical
methods and the fact that a new ISO standard, 11462-1, has been designed to provide
guidance for organizations wishing to use SPC to meet these requirements.
Chapter 8 – Measuring and Controlling Quality 4
ANSWERS TO QUALITY IN PRACTICE QUESTIONS
Using a u-chart in a Receiving Process
1. See Spreadsheet CBT-u&ParetoChart.xlsx in the Instructor Reserve materials for
verification of the chart and complete calculations. The average number of packing slip
errors can be obtained by taking the square root of the sum of the errors and dividing by
the total number of packing slips reviewed.
For the u-chart conditions: 62 samples; total n = 5129, number of defects = 479
The first five values give us:
Smpl. n c u = c/n 3 UCL LCL
1 87 15 0.1724 0.0983 0.1917 0
Chapter 8 – Measuring and Controlling Quality 5
2. The Pareto chart shows which cost categories are of greatest concern in terms of defects
(see below). A separate chart for each category would help to pinpoint the contributing
0.25
0.30
CBT Company Attribute (u) Chart
Defects per unit
Lower control limit
Upper control limit
Center line
Chapter 8 – Measuring and Controlling Quality 6
Applying SPC to Pharmaceutical Product Manufacturing
1. Initially, descriptive statistics were calculated.
Descriptive Stats –
Pharmaceutical Products
Mean
4.9544
Standard Error
0.0014
Median
4.9555
Mode
#N/A
Standard Deviation
0.0083
Sample Variance
0.0001
Kurtosis
Skewness
Range
0.0314
Minimum
4.9354
Maximum
4.9668
Sum
173.4035
Count
Largest(1)
4.9668
25
30
35
40
CBT Packing Slip Error Causes
Chapter 8 – Measuring and Controlling Quality 7
UTL = 4.98, LTL = 4.92
Cp = UTL – LTL = 4.98 – 4.92 = 1.205
Histogram
5
6
7
8
9
Bin
Frequency
2. If the operators had plotted the first few points, within 8 or 9 samples they would have
noticed the pattern of values “hugging” the center line. It is likely that they would have
Chapter 8 – Measuring and Controlling Quality 8
3. The major lesson to be learned from this case is that SPC can work to the advantage of an
ANSWERS TO REVIEW QUESTIONS
1. Measurement is the act of collecting data to quantify the values of product, service,
process, and other business metrics. Measures and indicators refer to the numerical
is the percentage of faucets that have cosmetic defects.
2. The acronym SMART is used to characterize the elements that constitute a good
3. Dashboards typically consist of a small set of measures (five or six) that provide a quick
summary of process performance. This term stems from the analogy to an automobile’s
4. A non-conformance (sometimes called a defect) is when an item does not conform to a
5. Variables data is data such as length, time, weight, etc. that is measured along a
continuous scale. Attributes data assumes only two values: good-bad, pass-fail, etc. and is
6. When nonconformances per unit are measured, an item is being checked or physically
measured to ensure that one or more specifications are within tolerance limits. In contrast
Chapter 8 – Measuring and Controlling Quality 9
7. Cost of quality programs are valuable to managers because they translate poor quality
and its results into the language that managers use and understand — money. They serve
8. The four categories of quality costs are: prevention costs, appraisal costs, internal failure
costs, and external failure costs. The first are costs incurred to prevent non-conformance,
the second are costs incurred in measurement and data analysis, the third are costs of
9. Common types of measuring instruments (see folder on the Student Companion Site)
used in manufacturing today fall into two categories: “low–technology” and “high–
10. Modern measurement systems often use a combination of human operators and
technological instruments. Observed variation in process output stems from the natural
variation that occurs in the output itself as well as from the measurement system. The
Chapter 8 – Measuring and Controlling Quality 10
11. Metrology is the science of measurement. It formerly included only the measurement
processes involved in gauging the physical attributes of objects. Today, metrology is
12. Accuracy is defined as the closeness of agreement between an observed value and an
accepted reference value or standard. Accuracy is measured as the amount of error in a
measurement in proportion to the total size of the measurement. One measurement is
13. Calibration is the comparison of a measurement device or system having a known
relationship to national standards to another device or system whose relationship to
14. Repeatability, or equipment variation (EV), is the variation in multiple measurements
of a quality characteristic by an individual using the same instrument. Repeatability
indicates how consistent a measuring instrument is. Repeatability is influenced by the
15. Repeatability and reproducibility (R&R) require a study of variation and can be
addressed through statistical analysis. R&R studies must be done systematically, and
require quite a number of steps. A repeatability and reproducibility study is conducted in
the following manner (Note: formulas are omitted for the sake of brevity).
Chapter 8 – Measuring and Controlling Quality 11
1. Select m operators and n parts. Typically at least 2 operators and 10 parts are
chosen. Number the parts so that the numbers are not visible to the operators.
Part variation (PV) measures the variation among different parts. Part variation is
determined by multiplying the range of part averages, Rp, by a constant K3. Then,
the total variation, TV, is calculated as:
Constants K1 and K2 are chosen and depend on the number of trials and number
of operators, respectively. These constants provide a 99 percent confidence
interval on these statistics. An overall measure of repeatability and reproducibility
(R&R) is given by:
Chapter 8 – Measuring and Controlling Quality 12
Repeatability and reproducibility are often expressed as a percentage of the
tolerance of the quality characteristic being measured. The American Society for
Quality suggests the following guidelines for evaluating these measures of
repeatability and reproducibility:
16. Process capability is the range over which the natural variation of a process occurs as
determined by the system of common causes. It is the ability of the combination of
17. A process capability study is a carefully planned study designed to yield specific
information about the performance of a process under specified operating conditions.
18. The following are brief definitions of the various process capability indexes:
Cp is the ratio of the specification width to the natural tolerance of the process
Chapter 8 – Measuring and Controlling Quality 13
19. A process is said to be in statistical control when variations in the process are due only to
common causes (no special causes are present). A process may be in statistical control
but not capable of meeting design specifications. Thus, design specifications are
20. If a process is thought to include special causes of variation, practitioners sometimes use
alternative capability indexes, called process performance indexes: Pp, Ppl, Ppu, and Ppk.
21. In many manufacturing operations such as machining, it is important to ensure that all
parts are produced within specifications. Pre-control is a simple technique for ensuring
that a process that has relatively good capability remains in control. The idea behind pre–
Chapter 8 – Measuring and Controlling Quality 14
22. To develop control charts for variables, such as
x
– R charts and
x
– s charts, an analyst
must take a number of samples (usually 25-30) of a certain size (usually 3-10 items per
sample) from a process that is thought to be in statistical control, and calculate the sample
means and ranges. Using standard statistical methods, the grand mean (mean of the
23. The characteristics that one looks for in interpreting control charts are those that indicate
whether or not the process is remaining in control, or whether assignable causes have
crept into throw the process out of control. These might be detected through using the
24. The s-chart is sometimes used in place of the R-chart because the sample standard
25. A chart for individual measures may be particularly useful in small batch production,
where only a few items are produced. It is also useful to measure individual items in
Chapter 8 – Measuring and Controlling Quality 15
26. An np-chart is a chart that shows the number of items from a sample that are non–
conforming. This is in contrast to the p-chart, which shows the fraction of a sample that is
27. C-charts are used to monitor and control the number of defects when the group size for
the sample remains constant. For example, if a 8 samples of 30 toy boats is taken from a
28. ISO 9000:2000 emphasizes the use of statistical methods. The standards require
“applicable methods, including statistical techniques” be identified and used for
29. Rational subgroups are samples that are chosen to be as homogenous as possible, so that
each sample reflects the system of common causes or assignable causes that may be
30. Choosing the proper sample size involves several trade-offs. A small sample size is
desirable because it minimizes the opportunity for within sample variation due to a
31. Sampling frequency considerations are closely related to those of sample size. From a
statistical standpoint, taking large samples frequently is desirable, but not economical.
Although no hard-and-fast rules exist, samples should be taken frequently enough to
provide an opportunity to detect changes in process characteristics as soon as possible,
Chapter 8 – Measuring and Controlling Quality 16
Chapter 8 – Measuring and Controlling Quality 17
NOTE: THERE IS AN ARTICLE IN QUALITY ENGINEERING THAT PROVIDES
EXAMPLES OF PROJECTS AN INSTRUCTOR CAN DO IN CLASS:
SOLUTIONS TO PROBLEMS
Author’s Note: In this chapter, charts, graphs, and summarized solutions are taken from Excel
spreadsheets. Note that the templates have been tailored for the problem size in each problem
solution, whereas the blank templates are designed as “one size fits all” versions. Typically,
those templates are designed for problems of 25 or 50 samples. They may be modified by using
the unlocked versions of the spreadsheet templates on the Instructor Materials website. It would
be a good idea to make a backup copy of the original template before attempting to modify it for
other uses.
Note: Data sets for many problems in this chapter are available in the Excel workbook
C08Data.xlsx in the folder for this chapter on the Student Companion Site, as well as in the
Instructors materials. Click on the appropriate worksheet tab as noted in the problem (e.g., Prob.
8-01) to access the data. The Excel templates for control charts used in this chapter are available
in the Excel Templates folder on the Student Companion Site, as well. These are locked and
cannot be modified by the students.
1. EL Specialty Manufacturing Company makes an artificial leather-like product for the
fashion accessory market. The material is made in sheets and has the appearance of a thin
rug. Each sheet is 36 inches wide and 100 feet long and is wound into a roll. The quality
manager has requested that 100 rolls be inspected. Thirty eight non-conformances were
found.
a. Calculate the nonconformances per unit (NPU) and the throughput yield (TY).
b. If the production process consists of three steps, with step 1 having a TY of 83 percent;
step 2; 90 percent, and step 3, 92 percent what is the rolled throughput yield (RTY), and
the proportion nonconforming?
Answer
1. a. To calculate the NPU, use:
NPU = Number of nonconformances found/number of units inspected = 38/100 = 0.38
Chapter 8 – Measuring and Controlling Quality 18
2. Wellplace Insurance Company processes insurance policy applications in batches of 100.
One day, they had 10 batches to process and, after inspection, it was found that four
batches had nonconforming policies. One batch had 3 nonconformances, another had 5,
another had 2, and another had 1 nonconformance. What were (a) the proportion
nonconforming for each batch, (b) the nonconformances per unit (NPU), in total for the
10 batches, and (c) the total throughput yield (TY) for the 10 batches?
Answer
2. 1) the proportion nonconforming for each batch, was 0.03, 0.05, 0.02, and 0.01
3. Flybynight Airlines measured their numbers of lost bags in one month and found that
they had lost 130 bags for 10,000 customers. If the average number of bags per customer
is 1.3, how many errors per million opportunities (epmo) does this represent? The
worldwide rate of baggage mishandling reported by SITA (Société Internationale de
Télécommunications Aéronautiques) in 2011 was 12.07 per 1,000 passengers. If the
average number of checked bags per passenger is assumed to be 1.3, how many errors per
million opportunities (epmo) does this represent? How does this compare with the rate
for Flybynight – better or worse?
Answer
3. epmo = (Number of defects discovered) /opportunities for error x 1,000,000
Thus, a defect rate of 130 bags for 10,000 customers, if the average number of bags per
customer is 1.3 is:
Chapter 8 – Measuring and Controlling Quality 19
4. Broadwork Electronics manufactures 500,000 circuit boards per month. A random
sample of 5,000 boards is inspected every week for five characteristics. During a recent
week, two defects were found for one characteristic, and one defect each was found for
the other four characteristics. If these inspections produced defect counts that were
representative of the population, what are the dpmo’s for the individual characteristics
and what is the overall dpmo for the boards?
Answer
4. But for the individual characteristics, we have:
5. Analyze the cost data in the Excel workbook C08Data.xlsx for the Costcutin Co. What
percent of sales are represented by each category of cost? What are the implications of
these data for management?
Answer
5. Original Data:
Product
A B C
External failure
30%
19%
10%
55%
31%
28%
11%
39%
36%
11%
26%
Chapter 8 – Measuring and Controlling Quality 20
time-phased data per product were provided, no trend can be established for various
product indexes.
Comparison of the data shows that both internal and external failure costs appear to be
very high for product A, internal failure cost and appraisal costs appear to be high for
Costcutin Company
$ 000’s
$Qual. Cost – A
$Qual. Cost – B
$Qual. Cost – C
External failure
$ 96.85
$ 31.93
$ 16.77
Internal failure
$ 177.56
$ 52.09
$ 46.94
Appraisal
$ 35.51
$ 65.54
$ 60.36
Prevention
$ 12.91
$ 18.49
$ 43.59
Prob08-05.xlsx
6. Prepare a pie chart showing the different quality cost categories and percentages for the
Great Press Printing Company. See the data in the Excel workbook C08Data.xlsx.
0
20
40
60
80
100
120
140
160
180
200
External
failure
Internal
failure
Appraisal Prevention
Cost – $Thousands
COQ Category
Costcutin’s Cost of Quality
$Qual. Cost – A
$Qual. Cost – B
$Qual. Cost – C
