IENG 486 - Lecture 21
Short Run SPC
4/9/2015
IENG 486 Statistical Quality & Process Control
1
Assignment
 Reading:

Chapter 6


Section 6.4: pp. 259 - 265
Chapter 9



Sections 9.1 – 9.1.5: pp. 399 - 410
Sections 9.2 – 9.2.4: pp. 419 - 425
Sections 9.3: pp. 428 - 430
 Homework:

CH 9 Textbook Problems:

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1a, 17, 26
Hint: Use Excel charts!
IENG 486 Statistical Quality & Process Control
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Review
 Shewhart Control charts

Are for sample data from an approximate Normal distribution

Three lines appear on all Shewhart Control Charts
 UCL, CL, LCL

Two charts are used:
 X-bar for testing for change in location
 R or s-chart for testing for change in spread

We check the charts using 4 Western Electric rules
 Attributes Control charts

Are for Discrete distribution data




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Use p- and np-charts for tracking defective units
Use c- and u-charts for tracking defects on units
Use p- and u-charts for variable sample sizes
Use np- and c-charts with constant sample sizes
TM 720: Statistical Process Control
3
Short Run SPC
 Many products are made in smaller quantities than
are practical to control with traditional SPC

In order to have enough observations for statistical control
to work, batches of parts may be grouped together onto a
control chart

This usually requires a transformation of the variable on
the control chart, and a logical grouping of the part
numbers (different parts) to be plotted.

A single chart or set of charts may cover several different
part types
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TM 720: Statistical Process Control
4
DNOM Charts
 Deviation from Nominal

Variable computed is the difference between the
measured part and the target dimension
xi  M i  Tp
where:
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Mi is the measured value of the ith part
Tp is the target dimension for all of part number p
TM 720: Statistical Process Control
5
DNOM Charts
 The computed variable (xi)
is part of a sub-sample of
size n


xi is normally distributed
n is held constant for all part
numbers in the chart group.
 Charted variables are x
and R, just as in a
traditional Shewhart
control chart, and control
limits are computed as
such, too:
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UCL  x  A2 R  A2 R
CL  x  0
LCL  x  A2 R   A2 R
UCL  D4 R
CL  R
LCL  D3 R
TM 720: Statistical Process Control
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DNOM Charts
 Usage:

A vertical dashed line is used to mark the charts at the point at
which the part numbers change from one part type to the next
in the group

The variation among each of the part types in the group
should be similar (hypothesis test!)

Often times, the Tp is the nominal target value for the process
for that part type


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Allows the use of the chart when only a single-sided
specification is given
If no target value is specified, the historical average (x) may
be used in its’ place
TM 720: Statistical Process Control
7
Standardized Control Charts
 If the variation among the part types within a
logical group are not similar, the variable may be
standardized

This is similar to the way that we converted from any normally
distributed variable to a standard normal distribution:

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Express the measured variable in terms of how many units of
spread it is away from the central location of the distribution
TM 720: Statistical Process Control
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Standardized Charts – x and R
 Standardized Range:

Plotted variable is
Ri
R 
Rj
s
i
where:
Ri is the range of measured values for the ith
sub-sample of this part type j
Rj is the average range for this jth part type
UCL  D4
CL  R j
LCL  D3
4/9/2015
TM 720: Statistical Process Control
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Standardized Charts – x and R
 Standardized x:

Plotted variable for the sample is
s
i
x 
where:
M i  Tj
Rj
Mi is the mean of the original measured values for
this sub-sample of the current part type (j)
Tj is the target or nominal value for this jth part type
UCL   A2
CL  0
LCL   A2
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TM 720: Statistical Process Control
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Standardized Charts – x and R
 Usage:

Two options for finding Rj:



Examples:


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Prior History
Estimate from target σ:
 d2 
R j  σ  
 c4 
Parts from same
machine with similar
dimensions
Part families – similar
part tolerances from
similar setups and
equipment
TM 720: Statistical Process Control
11
Standardized Charts – Attributes
 Standardized zi for Proportion Defective:

Plotted variable is
zi 

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Control Limits:
pi  p
p(1  p)
n
UCL  3
CL  0
LCL  3
TM 720: Statistical Process Control
12
Standardized Charts – Attributes
 Standardized zi for Number Defective:

Plotted variable is
zi 

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Control Limits:
npi  n p
n p(1  p)
UCL  3
CL  0
LCL  3
TM 720: Statistical Process Control
13
Standardized Charts – Attributes
 Standardized zi for Count of Defects:

Plotted variable is
zi 

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Control Limits:
ci  c
c
UCL  3
CL  0
LCL  3
TM 720: Statistical Process Control
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Standardized Charts – Attributes
 Standardized zi for Defects per Inspection
Unit:
ui  u
zi 
 Plotted variable is
u
n

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Control Limits:
UCL  3
CL  0
LCL  3
TM 720: Statistical Process Control
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Guidelines for Implementing
Control Charts
1.
Determine which process or product characteristic(s) to
control
2.
Determine where the charts should be implemented in
process
3.
Choose proper type of control charts
4.
Decide what actions should be taken to improve processes
5.
Select data-collection systems and computer software
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IENG 486 Statistical Quality & Process Control
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Determine Which Characteristic to
Control and Where to Put Charts
1.
2.
3.
4.
To start, apply charts to any process or product
characteristics believed important.
Charts found unnecessary are removed; others that may be
required are added.
(Usually more charts to start than after process has
stabilized)
Keep current records of all charts in use, i.e., types and
parameters of each.
If charts used effectively  number of charts for variables
increases and number of attributes charts decreases
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IENG 486 Statistical Quality & Process Control
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Determine Which Characteristic to
Control and Where to Put Charts
5.
6.
At beginning, use more attributes charts applied to finished
units, i.e., near end of process.
As more is learned about the process, these are replaced
with variables charts earlier in process on critical process
characteristics that affect nonconformities.
Rule of thumb: the earlier in the process that control can be
established, the better.
Control charts are an on-line process monitoring
procedure; Maintain charts as close to work center as
possible.
Operators and process engineers should be directly
responsible for using, maintaining and interpreting charts
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IENG 486 Statistical Quality & Process Control
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Choosing Proper Type of
Control Chart: Variables Charts

Use (x & R) or (x & S) charts when:
1.
2.
3.
4.
5.
6.
7.
8.
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New process or product coming online
Chronically troubled process
Wish to reduce downstream acceptance sampling
Using attributes charts but yield still unacceptable
Very tight specifications
Operator decides whether or not to adjust process
Change in product specs desired
Process capability (stability) must be continually
demonstrated
IENG 486 Statistical Quality & Process Control
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Choosing Proper Type of
Control Chart: Attributes Charts

Use p, np, c or u charts when:
1.
2.
3.
4.
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Operators control assignable causes and it is necessary to
reduce fallout
Process is complex assembly operation and product quality
measured in terms of occurrence of nonconformities: e.g.
computers, automobiles
Measurement data cannot be obtained
Historical summary of process performance is necessary.
Attributes charts are effective for summarizing a process for
management
IENG 486 Statistical Quality & Process Control
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Choosing Proper Type of
Control Chart: Individuals Charts

Use (x & MR), MA, EWMA, or CUSUM charts when:
1.
2.
3.
4.
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Repeated measures do not make sense
Inconvenient / impossible to obtain more than one
measurement per sample
Automated testing allows you to measure every unit
(EWMA chart may be best)
Data becomes available very slowly and waiting for a larger
sample is impractical.
IENG 486 Statistical Quality & Process Control
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