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IENG 486 - Lecture 12
Basic Control Charts
5/24/2017
IENG 486: Statistical Quality &
Process Control
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Assignment:
 Reading:


CH5: 5.3 (already read 5.1-5.2 & 5.4)
Start on CH6: all except 6.3.2 & 6.4
 Homework 4:
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Textbook Problems CH5: 9, 11, 13, 23, & 24
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General Model:
Shewhart Control Chart
 Suppose x is some quality characteristic,
and w is a sample statistic of x.
 Suppose mean of w is μw and std dev of w is σw, then:
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UCL = μw + Lσw
CL = μw
UCL = μw – Lσw
where L is the “distance” of the control limits from the center
line, and expressed in multiples (units) of the standard
deviation of the statistic, i.e. sw.
 This type of chart is called a Shewhart Control Chart
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IENG 486: Statistical Quality & Process Control
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Rational Subgroups
 Subgroups/Samples should be selected so that if
assignable causes are present:
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Chance for differences between samples is maximized
Chance for differences within a sample is minimized
 Use consecutive units of production
 Keep sample size small so that:
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New events won’t occur during sampling
Inspection is not too expensive
But size is large enough that x is normally distributed
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IENG 486: Statistical Quality & Process Control
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Symptoms of Two Common Sampling
Mistakes
 Data points hug centerline – Stratification
indicating sample averages are not normally distributed
x Chart
UCL
CL
LCL
 Data points hug control limits – Mixing
indicating sample averages are not normally distributed
x Chart
UCL
CL
LCL
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Stratification –
Sample Averages Hug Centerline
 Quality Characteristic:
 Amount of liquid filled into a container.
 Machine:
 4 heads fill 4 containers simultaneously.
 Each head has a slightly different mean
 Sample: select 4 bottles, 1 bottle ea. from heads 1, 2, 3, and 4
 Symptom: data points hug centerline indicating sample
averages are not normally distributed
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IENG 486: Statistical Quality & Process Control
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Stratification –
Why Does It Happen?
 Each head has a different mean.
 Why do points hug centerline?
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Ans: Estimate of s is wrong
So … the Control Charts limits are too wide
And … the data points hug centerline because the scaling to
detect a shift in process mean is off
sample 1
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sample 2
sample 3
IENG 486: Statistical Quality & Process Control
sample 4
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Mixing – Sample Averages
Hug Control Limits
 Quality Characteristic:
 Dimension of a part
 2 Similar Machines:
 Old one: produces 40% of parts
New one: produces 60% of parts
Old and new machines have different means
 Sample size = 4:
 All parts are mixed together
 Symptom: Data points hug control limits
samples 1 & 2
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samples 3 & 4
IENG 486: Statistical Quality & Process Control
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What to do if there is evidence of stratification or
mixing
 Examine your sampling procedure
 Make separate control charts for each
filling head (or machine)
 Problem: It may not be obvious that
samples are stratified or mixed
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Why Monitor Both Process Mean and Process
Variability?
Process Over Time
Process Doing OK
Lower
Specification
Limit
Control Charts
Upper
Specification
Limit
X-bar
R
X-bar
R
X-bar
R
Mean shift in process
Increase in process variance
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Teminology
 Causes of Variation:
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Assignable Causes
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 Meaning of Control:
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Keep the process from
operating predictably
Things that we can do
something about
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Common Causes

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Random, inherent
variation in the process
In Specification
Meets customer
constraints on product
In Statistical Control

No Assignable Causes
of variation present in
the process
IENG 486: Statistical Quality & Process Control
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