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QUALITY CONTROL
Chapter 10
MIS 373: Basic Operations Management
Additional content from Jeff Heyl
LEARNING OBJECTIVES
• After this lecture, students will be able to
1.
2.
3.
4.
Explain the need for quality control.
List and briefly explain the elements of the control process.
Explain Type I and Type II errors
Explain how control charts are used to monitor a process and the
concepts that underlie their use.
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BACKGROUND KNOWLEDGE
• How many of you have had at least one statistics course?
• Normal distribution?
• Standard deviation?
• Z score?
MOTIVATIONS
• Making Beer Better With Quality and Statistics
• http://videos.asq.org/making-beer-better-with-quality-and-statistics
• Quality for Life: Psychic Pizza
• http://videos.asq.org/quality-for-life-psychic-pizza
WHAT IS QUALITY CONTROL?
• Quality Control
• A process that evaluates output relative to a standard and takes
corrective action when output doesn’t meet standards
• If results are acceptable no further action is required
• Unacceptable results call for correction action
• Phases of Quality Assurance
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INSPECTION
• Inspection
• An appraisal activity that compares goods or services to a standard
• Inspection issues:
1. What to inspect
• Count number of times defect occurs
• Measure the value of a characteristic
2. How much to inspect and how often
3. At what points in the process to inspect
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•
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Raw materials and purchased parts
Finished products
Before a costly operation
Before an irreversible process
• Costly, possibly destructive, and disruptive – non value-adding
• Full inspection vs. Sampling
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HOW MUCH TO INSPECT
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HOW MUCH TO INSPECT
1 defect in
Trying to catch: 1 thousand
unites
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1 defect in
1 million
unites
1 defect in
1 billion
unites
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CENTRALIZED VS. ON-SITE
INSPECTION
• Effects on cost and level of disruption are a major issue in
selecting centralized vs. on-site inspection
• Centralized
• Specialized tests that may best be completed in a lab
• More specialized testing equipment
• More favorable testing environment
• On-Site
• Quicker decisions are rendered
• Avoid introduction of extraneous factors
• Quality at the source
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STATISTICAL PROCESS
CONTROL (SPC)
• Quality control seeks
• Quality of Conformance
• A product or service conforms to specifications
• A tool used to help in this process:
• SPC
• Statistical evaluation of the output of a process
• Helps us to decide if a process is “in control” or if corrective action
is needed
• “In control” means that the variation in the provided
products/services is tolerable
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PROCESS VARIABILITY
• Two basic questions: concerning variability:
1. Issue of Process Control
• Are the variations random? If nonrandom variation is present, the
process is said to be unstable.
 Variations randomly distributed within control limits
2. Issue of Process Capability
• Given a stable process, is the inherent variability of the process
within a range that conforms to performance criteria?
 The control limits satisfy the design specification
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VARIATION
• Variation
• Random (common cause) variation:
• Natural variation in the output of a process, created by countless
minor factors
• Assignable (special cause) variation:
• A variation whose cause can be identified.
• A nonrandom variation
• Illustration: M&M’s
• Size
• Color
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VARIATION
• Common cause
•
•
•
•
•
•
•
•
•
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•
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Inappropriate procedures
Poor design
Poor maintenance of machines
Lack of clearly defined
standard operating procedures
Poor working conditions, e.g.
lighting, noise, dirt,
temperature, ventilation
Substandard raw materials
Measurement error
Quality control error
Vibration in industrial
processes
Ambient temperature and
humidity
Normal wear and tear
Variability in settings
MIS 373: Basic Operations Management
• Special cause
•
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•
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•
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Poor adjustment of equipment
Operator falls asleep
Faulty controllers
Machine malfunction
Fall of ground
Computer crash
Poor batch of raw material
Power surges
High healthcare demand from
elderly people
Broken part
Abnormal traffic (click fraud) on
web ads
Extremely long lab testing
turnover time due to switching to
a new computer system
Operator absent
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SAMPLING AND SAMPLE
DISTRIBUTION
• SPC involves periodically taking samples of process
output and computing sample statistics:
• Sample means
• The number of occurrences of some outcome
• Sample statistics are used to judge the randomness
of process variation
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SAMPLING AND SAMPLE
DISTRIBUTION
• Sampling Distribution
• A theoretical distribution that describes the random
variability of sample statistics
• The normal distribution is commonly used for this purpose
• Central Limit Theorem
• The distribution of sample averages tends to be normal
regardless of the shape of the underlying process
distribution
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DEMO
• Use simulation to test the Central Limit Theorem
THE NORMAL DISTRIBUTION
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CONTROL PROCESS
• Sampling and corrective action are only a part of the control
process
• Steps required for effective control:
•
•
•
•
•
•
Define: What is to be controlled?
Measure: How will measurement be accomplished?
Compare: There must be a standard of comparison
Evaluate: Establish a definition of out of control
Correct: Uncover the cause of nonrandom variability and fix it
Monitor results: Verify that the problem has been eliminated
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CONTROL CHARTS:
THE VOICE OF THE PROCESS
• Control Chart
• A time ordered plot of representative sample statistics obtained from
an ongoing process (e.g. sample means), used to distinguish
between random and nonrandom variability
• Control limits
• The dividing lines between random and nonrandom deviations from the
mean of the distribution
• Upper and lower control limits define the range of acceptable variation
• Upper control limit = UCL = mean + zσ
• Lower control limit = LCL = mean + zσ
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CONTROL CHART EXAMPLE
Variation
due to
assignable
causes
Out of
control
UCL
Variation due to
natural causes
Mean
LCL
| | | | | | | | | | | |
1 2 3 4 5 6 7 8 9 10 11 12
Sample number
Out of
control
Variation
due to
assignable
causes
• Each point on the control chart represents a sample of n observations
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ERRORS
• Type I error
• Narrow control limits
• Concluding a process is not in
control when it actually is.
• Manufacturer’s Risk
• Type II error
• Wide control limits
• Concluding a process is in
control when it is not.
Process
In-Control
Process
Out-of-Control
Alarm
No Alarm
Type I
no-error
no-error
Type II
• Consumer’s Risk
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ERRORS ILLUSTRATION
• Q: I always get confused about Type I and II errors. Can you
show me something to help me remember the difference?
Source: Effect Size FAQs by Paul Ellis
CONTROL CHARTS
Out of Control
In Control
Improved
UCL

LCL
• Every process displays variation in performance: normal or abnormal
• Control charts monitor process to identify abnormal variation
• Do not tamper with a process that is “in control” with normal variation
• Correct an “out of control” process with abnormal variation
• Control charts may cause false alarms – too narrow - (or missed signals –
too wide) by mistaking normal (abnormal) variation for abnormal (normal)
variation
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CONTROL CHARTS
• Data that are measured
• “x-bar” charts (Mean)
• Used to monitor the central tendency of a process.
• R charts (Range)
• Used to monitor the process dispersion
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X-BAR (SAMPLE AVERAGE) CHART
CONTROL LIMITS
𝑥
)
𝑘
𝑥 = 𝑥𝑥 = 𝜇𝑥 (=
k = number of samples
𝜎𝑥
𝜎𝑥 =
𝑛
n = sample size
𝑈𝐶𝐿𝑥 = 𝑥 + 𝑧𝜎𝑥 = 𝜇𝑥 + 𝑧 𝜎𝑛𝑥
𝐿𝐶𝐿𝑥 = 𝑥 − 𝑧𝜎𝑥 = 𝜇𝑥 + 𝑧 𝜎𝑛𝑥
commonly: z = 3
𝑈𝐶𝐿𝑥 = 𝑥 + 3𝜎𝑥 = 𝜇𝑥 + 3 𝜎𝑛𝑥
𝐿𝐶𝐿𝑥 = 𝑥 − 3𝜎𝑥 = 𝜇𝑥 + 3 𝜎𝑛𝑥
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X-BAR CHART
• Mean = 5.5.
• STD = 0.4 ft
6.5
• 99.74% within ± 3 STD
4.3
• 𝑥 ∓ 3𝜎 = 5.5 ∓ 3 ∗ 0.4 = [4.3,6.7]
5.1
5.5
5.9
6.7
5.5
•
(random) 9 students {6.5, 6.4, 6.6, 6.3, 6.7, 6.5, 6.6, 6.4, 6.5} each
within “normal”  average = 6.5 ft
•
Sample control limits  tighter than population
𝜎
=
𝑛
5.5 + 3
.4
=5.9
9
•
UCL= 𝑥 + 3
•
GROUP above “normal” (outside control limits)
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R-CHART: CONTROL LIMITS
• Range charts or R-charts are used to monitor process
dispersion
R Chart Control Limits
UCLR  D4 R
LCLR  D3 R
where
D3  a control chart factor based on sample size, n
D4  a control chart factor based on sample size, n
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MEAN AND RANGE CHARTS
(a)
These
sampling
distributions
result in the
charts
below
(Sampling mean is
shifting upward but
range is consistent)
UCL
x-chart
LCL
UCL
R-chart
LCL
MIS 373: Basic Operations Management
(x-chart
detects shift in
central
tendency)
(R-chart does not
detect change in
mean)
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MEAN AND RANGE CHARTS
(b)
These
sampling
distributions
result in the
charts
below
(Sampling
mean is
constant but
dispersion is
increasing)
UCL
x-chart
LCL
UCL
R-chart
LCL
MIS 373: Basic Operations Management
(x-chart does not
detect the
increase in
dispersion)
(R-chart detects
increase in
dispersion)
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RUN TESTS
• Even if a process appears to be in control, the data
may still not reflect a random process
• Analysts often supplement control charts with a run
test
• Run test
• A test for patterns in a sequence
• Run
• Sequence of observations with a certain characteristic
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RUN TESTS
A: Above
B: Below
U: Upward
D: Downward
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PATTERNS IN CONTROL CHARTS
UCL
UCL
Target
Target
LCL
LCL
Normal behavior. Process
is “in control.”
UCL
Target
LCL
Two plots very near
lower (or upper) control.
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One plot out above (or
below). Process is “out of
control.”
UCL
Target
LCL
Trends in either direction, 5
plots. Progressive change.
UCL
UCL
Target
Target
LCL
Run of 5 above (or below)
central line.
LCL
Erratic behavior.
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DEMO
• ASQ Control chart template
• http://asq.org/learn-about-quality/data-collection-analysistools/overview/asq-control-chart.xls
KEY POINTS
• All processes exhibit random variation. Quality control's
purpose is to identify a process that also exhibits nonrandom
(correctable) variation on the basis of sample statistics (e.g.,
sample means) obtained from the process.
• Control charts and run tests can be used to detect
nonrandom variation in sample statistics. It is also advisable
to plot the data to visually check for patterns.
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