Operations
Management
Supplement 6 –
Statistical Process
Control
Operations Management, 9e
© 2006 Prentice Hall, Inc.
S6 – 1
Outline

Quality and Strategy

Defining Quality
 Different Views / Implications / Baldridge / Cost of Quality (COQ)

Ethics and Quality Management

International Quality Standards (ISO 9000 and 14000)

Total Quality Management (TQM)
 W. Edwards Deming
 Seven Concepts of TQM

The Role of Inspection
Continuous improvement
Six Sigma
Employee empowerment
Benchmarking
Just-in-time (JIT)
Taguchi concepts
Knowledge of 7 TQM tools
Will not cover or test Taguchi concepts (Quality Loss
Function) on pg 202
© 2006 Prentice Hall, Inc.
–
Check sheeets
–
Scatter Diagrams
–
Cause-and-Effect Diagrams
–
Pareto Charts
–
Flowcharts
–
Histograms
– SPC (Supplement 6)
S6 – 2
Control Charts
Constructed from historical data, the purpose of control charts is
to help distinguish between natural variations and variations due
to assignable causes
Walter Shewart of Bell Laboratories made the distinction
between the common and special causes of variation . . . He
developed a simple but powerful tool to separate the two –
the control chart.
- page 222
© 2006 Prentice Hall, Inc.
S6 – 3
Statistical Process Control (SPC)
A process used to monitor standards by taking
measurements and corrective action as a
product or service is being produced. (Pg.
222)
The application of statistical techniques to the
control of processes.
The application of statistical techniques to
monitor and adjust an operation. (APICS)
© 2006 Prentice Hall, Inc.
S6 – 4
Statistical Process Control (SPC)
Outline
1) Variation – Natural and Assignable
2) Control Charts for VARIABLES (eg, size and weight)
 Using x-Charts (Mean Charts)
 Using R-Charts (Range Charts)
3) Control Charts for ATTRIBUTES (eg, good/bad,
pass/fail)
 Using p-Charts
 Using c-Charts
© 2006 Prentice Hall, Inc.
S6 – 5
We Will Not Cover
•
•
•
•
•
•
•
Acceptance Sampling (pg )
OC Curves
Producer’s Risk / Consumer’s Risk
AQL
LTPD
Average Outgoing Quality (pg )
Cp and Cpk
© 2006 Prentice Hall, Inc.
S6 – 6
Statistical Process Control
(SPC)
 Variability is inherent in every process
 Natural or common causes
 Special or assignable causes
 SPC provides a statistical signal when
assignable causes are present
 The goal is to detect and eliminate
assignable causes of variation
© 2006 Prentice Hall, Inc.
S6 – 7
Variation and Process Control
When buying jeans- Do you know your size?
Then WHY do you try them on?
© 2006 Prentice Hall, Inc.
S6 – 8
What is Variation?
Nothing Ever Happens Exactly The
Same Way Twice
Variation is the Cause of This Phenomenon
Understanding Variation Is Critical To Effective
Management And Significant Business Results
© 2006 Prentice Hall, Inc.
S6 – 9
Common Cause Variation
or Natural Variations
(or Routine Variation)
 Affect virtually all production processes.
 Natural Variations are expected, and occur within
processes that are in statistical control.
 As a group, natural variations form a probability
distribution.
 For any distribution there is a measure of central
tendency (mean or the average value) and dispersion
(standard deviation, s)
 If the distribution falls within acceptable limits, the
process is said to be “in control” and natural variations
are tolerated.
© 2006 Prentice Hall, Inc.
S6 – 10
Special Cause Variation
or Assignable Variations
(or Exceptional Variation)
 Generally, special cause variations are due to a
change in the process.

-
Variations that can be traced to a specific reason.
Machine wear
Misadjusted equipment
Training
Bad materials
Identify and eliminate assignable variation.
© 2006 Prentice Hall, Inc.
S6 – 11
Types of Variation
Special Cause:
something different
happening at a
certain
time or place
Common Cause: always
present to some
degree in the process
It is critical to be able to distinguish between them.
© 2006 Prentice Hall, Inc.
S6 – 12
Why Does It Matter?
Because we want to avoid:
– Missing signals- Not taking action when
action is appropriate
– Misreading noise to be a signal of a
change
• Wasting time by taking action when
none is appropriate
• TAMPERING!!
© 2006 Prentice Hall, Inc.
S6 – 13
Tampering Drives the Search for Answers…
But there aren’t any!!
What
happened?
The Big Gear Turns
I’ll go
find out.
What’s
going on?
I’m looking!
I’m looking!
I’m looking
The Big Gear Turns A Notch And The Little Gears Whirl
In A Frenzy Trying To Keep Up
© 2006 Prentice Hall, Inc.
S6 – 14
SPC Uses Samples
To measure the process, we take samples and
analyze the sample statistics following these
steps
Frequency
(a) Samples of the
product, say five
boxes of cereal
taken off the filling
machine line, vary
from each other in
weight
Each of these
represents one
sample of five
boxes of cereal
# #
# # #
# # # #
# # # # # # #
#
# # # # # # # # #
Weight
or length, etc - continuous
Figure S6.1
© 2006 Prentice Hall, Inc.
S6 – 15
Frequency
(b) After enough
samples are
taken from a
stable process,
they form a
pattern called a
distribution
The solid line
represents the
distribution
Weight
© 2006 Prentice Hall, Inc.
S6 – 16
Frequency
(c) There are many types of distributions, including the
normal (bell-shaped) distribution, but distributions
do differ in terms of central tendency (mean),
standard deviation or variance, and shape
Central tendency
Weight
© 2006 Prentice Hall, Inc.
Variation
Weight
Shape
Weight
S6 – 17
© 2006 Prentice Hall, Inc.
Frequency
(d) If only natural
causes of
variation are
present, the
output of a
process forms a
distribution that is
stable over time
and is predictable
Prediction
Weight
S6 – 18
Frequency
(e) If assignable causes
are present, the
process output is
not stable over time
and is not
predictable
?
?? ??
?
?
?
?
?
?
?
?
?
??
?
?
?
Prediction
Weight
The manager’s first objective is to ensure that the
process is capable of operating under control, with only
natural variation.
The second objective is to identify and eliminate
assignable variations so that the process will remain
under control, and be predictable.
“Since prediction is the essence of management, the ability
to know what to expect when a process is behaving
predictably is invaluable.”
© 2006 Prentice Hall, Inc.
S6 – 19
Control Charts
Constructed from historical data, the
purpose of control charts is to help
distinguish between natural variations
and variations due to assignable causes
© 2006 Prentice Hall, Inc.
S6 – 20
Process Control
Frequency
Lower control limit
(a) In statistical
control and capable
of producing within
control limits
Upper control limit
(b) In statistical control
but not capable of
producing within
control limits
(c) Out of control
Size
(weight, length, speed, etc.)
© 2006 Prentice Hall, Inc.
Figure S6.2
S6 – 21
Types of Data
Variables
 Characteristics that
can take any real
value
 May be in whole or
in fractional
numbers
 Continuous random
variables
Attributes
 Defect-related
characteristics
 Classify products
as either good or
bad or count
defects
 Categorical or
discrete random
variables
Matters in terms of which Control Chart to use.
© 2006 Prentice Hall, Inc.
S6 – 22
Attribute Data vs. Continuous Data
Let's say you are measuring the size of a marble. To be
within specification, the marble must be at least 25mm
but no bigger than 27mm.
If you measure and simply count the number of marbles
that are out of spec (good vs bad) you are collecting
attribute data.
However, if you are actually measuring each marble and
recording the size (i.e 25.2mm, 26.1mm, 27.5mm, etc)
that's continuous data, and you actually get more
information about what you're measuring from continuous
data than from attribute data.
© 2006 Prentice Hall, Inc.
S6 – 23
CONTROL CHARTS FOR
VARIABLES (Continuous Data)
• X-bar chart (x): tells us whether
changes have occurred in the mean or
in the central tendency of a process.
• R chart: indicates whether or not a gain
or loss in dispersion has occurred. R
charts track the range within a sample.
© 2006 Prentice Hall, Inc.
S6 – 24
Central Limit Theorem
Regardless of the distribution of the population,
the distribution of sample means drawn from the
population will tend to follow a normal curve
1. The mean of the sampling
distribution (x) will be the same
as the population mean m
2. The standard deviation of the
sampling distribution (sx) will
equal the population standard
deviation (s) divided by the
square root of the sample size, n
© 2006 Prentice Hall, Inc.
x=m
sx =
s
n
S6 – 25
Population and Sampling
Distributions
Three population
distributions
Distribution of
sample means
Mean of sample means = x
Beta
Standard
deviation of
s
the sample = sx = n
means
Normal
Uniform
|
|
|
|
-3sx
-2sx
-1sx
x
|
|
+1sx +2sx +3sx
95.45% fall within ± 2sx
99.73% of all x
fall within ± 3sx
© 2006 Prentice Hall, Inc.
|
Figure S6.3
S6 – 26
Control Charts for Variables
 For variables that have continuous
dimensions
 Weight, speed, length, strength, etc.
 x-charts are to control the central tendency
of the process
 R-charts are to control the dispersion of the
process
 These two charts must be used together
© 2006 Prentice Hall, Inc.
S6 – 27
Setting Control Chart Limits – Continuous
(Variables) Data
To calculate UCL and LCL for
x-Charts when we know s
POM:
Module = Quality Control
File-New-x bar charts
Select mean, standard deviation (since that’s what we know)
Enter the # of sigma depending on what we want the Control
Limits to include (for example, 3s = 99.73%)
Enter sample size, mean and standard deviation
Solve, and POM will return the UCL and LCL.
© 2006 Prentice Hall, Inc.
S6 – 28
Example S1 Pg. 226-227
Hour 1
Sample
Weight of
Number
Oat Flakes
1
17
2
13
3
16
4
18
n=9
5
17
6
16
7
15
8
17
9
16
Mean 16.1
s=
1
© 2006 Prentice Hall, Inc.
Hour
1
2
3
4
5
6
Mean
16.1
16.8
15.5
16.5
16.5
16.4
Hour
7
8
9
10
11
12
Mean
15.2
16.4
16.3
14.8
14.2
17.3
Control limits to include 99.73%
Avg Mean of the 12 samples = 16
Std Dev = 1
Sample Size = 9
LCL = 15 oz
UCL = 17 oz
S6 – 29
Example S1 Pg. 226-227
Calculating Control Limits in POM
© 2006 Prentice Hall, Inc.
S6 – 30
Setting Control Chart Limits
Control Chart
for sample of
9 boxes
Variation due
to assignable
causes
Out of
control
17 = UCL
Variation due to
natural causes
16 = Mean
15 = LCL
| | | | | | | | | | | |
1 2 3 4 5 6 7 8 9 10 11 12
Sample number
© 2006 Prentice Hall, Inc.
Out of
control
Variation due
to assignable
causes
S6 – 31
Setting Control Chart Limits – Continuous
(Variables) Data
To calculate UCL and LCL for
x-Charts when we DO NOT know s
POM:
Module = Quality Control
File-New-x bar charts
Select mean, range
Enter the # of sigma depending on what we want the Control
Limits to include (for example, 3s = 99.73%)
Enter sample size, mean and range
Solve, and POM will return the UCL and LCL.
© 2006 Prentice Hall, Inc.
S6 – 32
Example S2 Pg. 228
Process average x = 16.01 ounces
Average range R = .25
Sample size n = 5
In POM, File New, X-Bar, Data Form: Mean, Range
UCL = 16.154
LCL = 15.866
© 2006 Prentice Hall, Inc.
S6 – 33
So that is how we calculate UCL and LCL
for X-bar charts, (when we know std dev. and when we do
not know it) which is appropriate for continuous data.
X-bar charts are for the process AVERAGE.
© 2006 Prentice Hall, Inc.
S6 – 34
R – Chart
 Type of variables control chart
 Shows sample ranges over time
 Difference between smallest and
largest values in sample
 Monitors process variability
 Independent from process mean
We need R-Charts because in addition to being interested in
the process average, we need to know the process dispersion
or Range.
© 2006 Prentice Hall, Inc.
S6 – 35
Setting Control Chart Limits – Continuous
(Variables) Data
To calculate UCL and LCL for
Range Charts
POM:
Module = Quality Control
File-New-x bar charts
Select mean, range
Enter the # of sigma depending on what we want the Control
Limits to include (for example, 3s = 99.73%)
Enter sample size and range (leave the mean blank)
Solve, and POM will return the UCL and LCL.
© 2006 Prentice Hall, Inc.
S6 – 36
Setting Control Limits For R-Chart
Example S3 Pg. 228
Average range R = 5.3 pounds
Sample size n = 5
POM: x-bar, data form = mean,range
SS = 5, Avg Range = 5.3
3 sigma
UCL = 11.2 pounds
LCL = 0 pounds
© 2006 Prentice Hall, Inc.
S6 – 37
So now we know how to calculate UCL and LCL for both
the process average and the process range or dispersion.
So far we are only talking about control charts for
VARIABLES (continuous dimensions).
© 2006 Prentice Hall, Inc.
S6 – 38
Mean and Range Charts
(a)
(Sampling mean is
shifting upward but
range is consistent)
These
sampling
distributions
result in the
charts below
UCL
(x-chart detects
shift in central
tendency)
x-chart
LCL
UCL
(R-chart does not
detect change in
mean)
R-chart
LCL
Figure S6.5
© 2006 Prentice Hall, Inc.
S6 – 39
Mean and Range Charts
(b)
These
sampling
distributions
result in the
charts below
(Sampling mean
is constant but
dispersion is
increasing)
UCL
(x-chart does not
detect the increase
in dispersion)
x-chart
LCL
UCL
(R-chart detects
increase in
dispersion)
R-chart
LCL
Figure S6.5
© 2006 Prentice Hall, Inc.
S6 – 40
Key point: both x-bar and R charts are required to
accurately track a process.
© 2006 Prentice Hall, Inc.
S6 – 41
Limitations of Mean-Based Metrics
•
Any comparisons are LIMITED
– Can’t identify patterns or trends
•
Actions based on averaged data may be FLAWED
•
Single points give no indications of the SHAPE, CENTER or SPREAD
•
Our customers feel and remember VARIATION, not AVERAGES
On AVERAGE He’s
Comfortable!!
© 2006 Prentice Hall, Inc.
S6 – 42
Control Charts for Attributes
(Rather than Continuous)
 For variables that are categorical
 Good/bad, yes/no,
acceptable/unacceptable
 Measurement is typically counting
defectives
 Two types of attribute control
charts:
 Percent defective (p-chart)
 Number of defects (c-chart)
© 2006 Prentice Hall, Inc.
S6 – 43
Example S4 (Pg 231)p-Chart for Data Entry
Sample
Number
1
2
3
4
5
6
7
8
9
10
Number
of Errors
Fraction
Defective
6
5
0
1
4
2
5
3
3
2
.06
.05
.00
.01
.04
.02
.05
.03
.03
.02
Sample
Number
Number
of Errors
11
6
12
1
13
8
14
7
15
5
16
4
17
11
18
3
19
0
20
4
Total = 80
Fraction
Defective
.06
.01
.08
.07
.05
.04
.11
.03
.00
.04
In POM, File-New, P Charts, # of Samples = 20
Enter sample size = 100 and the defects for each.
© 2006 Prentice Hall, Inc.
S6 – 44
S4 P-chart POM Example
One data entry clerk
is out of control.
© 2006 Prentice Hall, Inc.
S6 – 45
p-Chart for Data Entry
UCLp = p + zsp^ = .04 + 3(.02) = .10
Fraction defective
LCLp = p - zsp^ = .04 - 3(.02) = 0
.11
.10
.09
.08
.07
.06
.05
.04
.03
.02
.01
.00
–
–
–
–
–
–
–
–
–
–
–
–
UCLp = 0.10
p = 0.04
|
|
|
|
|
|
|
|
|
|
2
4
6
8
10
12
14
16
18
20
LCLp = 0.00
Sample number
© 2006 Prentice Hall, Inc.
S6 – 46
p-Chart for Data Entry
UCLp = p + zsp^ = .04 + 3(.02) = .10
Fraction defective
Possible
LCLp = p - zsp^ = .04 - 3(.02) =
0
assignable
causes present
.11
.10
.09
.08
.07
.06
.05
.04
.03
.02
.01
.00
–
–
–
–
–
–
–
–
–
–
–
–
UCLp = 0.10
p = 0.04
|
|
|
|
|
|
|
|
|
|
2
4
6
8
10
12
14
16
18
20
LCLp = 0.00
Sample number
© 2006 Prentice Hall, Inc.
S6 – 47
Example S5 (Pg. 233) c-Chart for Cab Company
Over a 9-day period,
received the following
number of from irate
passengers: 3, 0, 8, 9, 6, 7,
4, 9, 8 total = 54.
File-New, c-Chart,
enter # of samples = 9
© 2006 Prentice Hall, Inc.
S6 – 48
Patterns in Control Charts
Upper control limit
Target
Lower control limit
Figure S6.7
© 2006 Prentice Hall, Inc.
Normal behavior.
Process is “in control.”
S6 – 49
Patterns in Control Charts
Upper control limit
Target
Lower control limit
Figure S6.7
© 2006 Prentice Hall, Inc.
One plot out above (or
below). Investigate for
cause. Process is “out
of control.”
S6 – 50
Patterns in Control Charts
Upper control limit
Target
Lower control limit
Figure S6.7
© 2006 Prentice Hall, Inc.
Trends in either
direction, 5 plots.
Investigate for cause of
progressive change.
S6 – 51
Patterns in Control Charts
Upper control limit
Target
Lower control limit
Figure S6.7
© 2006 Prentice Hall, Inc.
Two plots very near
lower (or upper)
control. Investigate for
cause.
S6 – 52
Patterns in Control Charts
Upper control limit
Target
Lower control limit
Figure S6.7
© 2006 Prentice Hall, Inc.
Run of 5 above (or
below) central line.
Investigate for cause.
S6 – 53
Patterns in Control Charts
Upper control limit
Target
Lower control limit
Erratic behavior.
Investigate.
Figure S6.7
© 2006 Prentice Hall, Inc.
S6 – 54
Which Control Chart to Use
Variables Data
 Using an x-chart and R-chart:
 Observations are variables
 Collect 20 - 25 samples of n = 4, or n =
5, or more, each from a stable process
and compute the mean for the x-chart
and range for the R-chart
 Track samples of n observations each
© 2006 Prentice Hall, Inc.
S6 – 55
Which Control Chart to Use
Attribute Data
 Using the p-chart:
 Observations are attributes that can
be categorized in two states
 We deal with fraction, proportion, or
percent defectives
 Have several samples, each with
many observations
© 2006 Prentice Hall, Inc.
S6 – 56
Which Control Chart to Use
Attribute Data
 Using a c-Chart:
 Observations are attributes whose
defects per unit of output can be
counted
 The number counted is often a small
part of the possible occurrences
 Defects such as number of blemishes
on a desk, number of typos in a page
of text, flaws in a bolt of cloth
© 2006 Prentice Hall, Inc.
S6 – 57
Backup
© 2006 Prentice Hall, Inc.
S6 – 58
Sampling Distribution
Sampling
distribution
of means
Process
distribution
of means
x=m
(mean)
© 2006 Prentice Hall, Inc.
Figure S6.4
S6 – 59
Steps In Creating Control
Charts
1. Take samples from the population and compute
the appropriate sample statistic
2. Use the sample statistic to calculate control limits
and draw the control chart
3. Plot sample results on the control chart and
determine the state of the process (in or out of
control)
4. Investigate possible assignable causes and take
any indicated actions
5. Continue sampling from the process and reset the
control limits when necessary
© 2006 Prentice Hall, Inc.
S6 – 60
Automated Control Charts
© 2006 Prentice Hall, Inc.
S6 – 61
Limitations of Mean-Based
Metrics
Be careful of mean-based metrics
Month
January
February
Average
Department A
99
1
50
Department B
49
51
50
– Seen in typical monthly reports
– Example:
• 2 departments delivering product to customers
• On the monthly report, they
both appear the same (avg = 50)
• If you were the customer, would you view them both as the
same??!
– Comparisons to beware of:
• Monthly averages
• Variance from target
• YTD values
• YTD variance
• Variance from same month last year
© 2006 Prentice Hall, Inc.
S6 – 62
Variance Based Metric Example:
Executable Orders
QUESTION: What Action Should You Take???
– NCR MRO Report
CURRENT MONTH
LAST MONTH
95.0%
63.9%
100.0%
83.3%
72.8%
–
PLAN
% Var
May-00
YTD
Solution Sales Process
ACTUAL
ACTUAL
% Var
95.0%
-0.8%
94.2%
Executable Orders
94.3%
-0.8%
25.0%
-154.0%
63.5%
Order Changes
95.2%
-280.7%
GCP
Order
Metrics
Report
95.0%
5.3%
100.0%
Bid Review Compliance
98.8%
3.9%
Executable 77.8%
Order rate increased 0.6
points
from 94.4%
in Review
March to 95.0% in April.84.2%
This compares
favorably
95.0%The NCR
-18.1%
SOWs
Available
at Bid
-11.4%
to the April 1999 result of 92.9%. The Americas region decreased 0.5 points to 97.8% this month, the Asia/Pacific
66.1%region increased
-1.1% 12.565.3%
Rate ofEMEA
Sales increased
Opportunities
($M) from 86.1%70.3%
points from 82.6%Win
to 95.1%,
2.3 points
to 88.4%, and6.4%
the Japan
PLAN
PRIOR YR
95.0%
25.0%
95.0%
95.0%
66.1%
92.8%
57.1%
N/A
N/A
64.0%
region increased 0.3 points to 91.8%. TSG gained 5.0 points to 94.0%, FSG decreased 0.5 points to 92.2%, and
RSG lost 0.2 points to 96.7%.
On a YTD basis, the improving April results drove the April 2000 YTD to 94.3% for NCR Total -- 1.0 points higher
than a year ago YTD. The Americas’ 97.5% is 1.6 points higher than the April 1999 YTD of 95.9%, Asia Pacific is 5.6
points higher at 87.5%, EMEA is 0.9 points higher at 88.4%, and the Japan Region is 2.8 points higher at 91.1%.
The April 2000 YTD result of 92.6% for TSG is 1.6 points higher than last year, FSG is 0.7 points higher at 92.5%,
and RSG is 0.7 points higher at 95.9%. Worldwide, ‘EO29-Plant reported configuration as invalid’ was the top cause
of rejected orders with 78 rejections, which was 27.5% of the 284 rejections.
© 2006 Prentice Hall, Inc.
2000 YTD
% Executable
Orders
# Executable
Orders
# Orders
% Executable
Orders
# Executable
Orders
# Orders
% Executable
Orders
# Orders
% Executable
Orders
# Executable
Orders
# Orders
% Executable
Orders
1,143
1,229
93.0% 1,339
1,492
89.7%
4,529
4,975
91.0%
1,235
1,387
89.0%
921
980
94.0%
4,149
4,481
92.6%
FSG
1,612
1,767
91.2% 2,314
2,526
91.6%
6,984
7,610
91.8%
2,004
2,162
92.7%
1,586
1,720
92.2%
6,111
6,610
92.5%
RSG
2,771
2,876
96.3% 3,149
3,334
94.5% 10,585
11,123
95.2%
3,903
4,028
96.9%
2,315
2,395
96.7%
9,434
9,839
95.9%
Other
215
219
99.0%
1,147
1,195
96.0%
380
389
97.7%
527
538
98.0%
1,353
1,393
97.1%
NCR
5,763
6,117
92.9% 23,322
24,997
93.3%
7,522
7,966
94.4%
5,349
5,633
95.0% 21,047
22,323
94.3%
98.2%
506
94.2% 7,332
511
7,892
# Executable
Orders
# Orders
Apr-00
TSG
# Executable
Orders
% Executable
Orders
Mar-00
1999 YTD
# Orders
Apr-99
# Executable
Orders
Mar-99
S6 – 63
Variance Based Metric Example
Executable Orders
•
Now what action should you take???
– Red/Yellow/Green color-coding based upon variance from target
– 1 problem… where does the 2% value come from???
• Is this level of variance an appropriate threshold for action???
% Executable Orders (1/99 - 5/00)
0.97
0.96
0.95
0.94
0.93
0.92
0.91
0.9
0.89
Ja
nF e 99
b9
M 9
ar
-9
Ap 9
rM 99
ay
-9
Ju 9
n9
Ju 9
l-9
Au 9
gS e 99
p9
O 9
ct
N 99
ov
D 99
ec
-9
Ja 9
nF e 00
b0
M 0
ar
-0
Ap 0
rM 00
ay
-0
0
0.88
© 2006 Prentice Hall, Inc.
• One would assume that
RED bars indicate a
SERIOUS PROBLEM
and YELLOW bars
indicate a POTENTIAL
PROBLEM
–Looks like you should
be acting almost
EVERY MONTH!
–Time to beat people
up for their lousy
performance, right?!!
S6 – 64
Control Chart (Process Behavior) Executable
Orders (1/99 - 5/00)
• Process is STABLE
• No trends or shifts
Green
96
UCL=96.7%
Target
94
Yellow
95
Avg=93.6%
93
92
Red
% Executable Orders
97
Blue
Control Chart for % Executable Orders
91
LCL=90.5%
90
Jan 99
May-99
Oct-99
Mar-00 May 00
Date
• EO Results between 90.5%
and 96.7% are EXPECTED!
• Current process only capable
of performing in this range
• EVEN THOUGH THIS
DOES NOT ACHIEVE THE
TARGET!!
• Reacting to values between
90.5% and 96.7% is a
COMPLETE WASTE OF
TIME!!
• Variation within these limits
is due solely to RANDOM
CHANCE!
• Process Improvement
required to more consistently
meet the target (Six Sigma
Project needed)
• Existing BSC color-coding is
misleading
• Has NOTHING to do with
actual capability of the
process!
Existing Balanced Scorecard color-coding for EO metric (+/-2% Variance from 95% target)
© 2006 Prentice Hall, Inc.
S6 – 65
Frequency Plot (Histogram)
Executable Orders (1/99 - 5/00)
QUESTION: Does knowing the average value (93.6%) provide a
complete picture for how this process is performing???
Process Capability Analysis for % Ex Orders
Avg=93.6%
• Frequency Plot shows # of
occurrences at specific
values over a period of time
(1/99 - 5/00)
• Knowing only the mean
(average) blinds you to
the actual range of values
(from 91% to 95.5%)
• Discover that data is
approx. normally
distributed
Target=95%
*
*
.0000
Count (# Values)
.5901
17
03702
17820
bility
*
*
-0.45
-0.45
*
bility
90
91
92
94
95
% Executable Orders (1/99 - 5/00)
Observed Performance
< LSL
PPM
* Prentice
© 2006
Hall,
Inc.
93
941176.47
Expected ST Performance
PPM < LSL
913014.09
96
97
Expected LT Performance
PPM < LSL
884277.92
S6 – 66
Another Variance Metric Example:
Selecting a Single Supplier
• You are part of a group whose task is to select a single
supplier for a given item. You have narrowed the search to
three companies whose products are about equal in all
respects and far superior to their competitors in product
quality. You are now going to look at delivery data gathered on
each supplier over the past 40 weeks. Each supplier has
delivered one shipment every week and you have the data on
how close to the promised date each shipment was delivered.
Supplier A: Average shipment is 1.5 days late
Supplier B: Average shipment is 3.0 days late
Supplier C: Averages shipment is 0.3 days late
– Discussion: What do these data tell you about the
three suppliers?
© 2006 Prentice Hall, Inc.
S6 – 67
Supplier A & B Delivery Data
• The delivery data for the suppliers shown with frequency plots.
• Minus means ahead of schedule.
• What circumstances might you choose one over the other?
Frequency Plots for Lateness
Suppliers A, B, and C
Plot of the Number of Days Late
Mean
Supplier A
Std.Dev.
1.5
1.3
Supplier B
3.0
0.5
Supplier C
0.3
2.6
-3
© 2006 Prentice Hall, Inc.
-2
-1
0
1
2
3
4
S6 – 68
Supplier A & B Delivery Data
• The same delivery data is displayed in time plots showing
the data in sequence from week 1 though week 40
consecutively. Discussion: What do these data tell you about
the three suppliers?
Late
5
Lateness in Days
= Supplier A
= Supplier B
= Supplier C
On Time
0
-5
Early
5
10
15
20
25
30
35
40
Week
© 2006 Prentice Hall, Inc.
S6 – 69
if a process is in statistical control it is predictable with
only common variation.
At that point, we can seek to improve the system.
An in-control process is not necessarily a process
capable of producing within specifications.
There are measures to get a handle on that...Cp and
Cpk.
But don't actually require the students to compute or
interpret Cpk results.
© 2006 Prentice Hall, Inc.
S6 – 70
Which Chart to Use
Variables Data
X-bar, R
Individuals chart
Attribute Data
p-chart
Count Data
c-chart
© 2006 Prentice Hall, Inc.
Variables are characteristics that have continuous dimensions, such as:
Weight, Speed, Length, Strength – infinite possible values
– each data point represents a single measurement.
For continuous dimensions, use control charts to monitor Central
Tendancy (mean) and Dispersion (range).
Xbar chart: tells us if there have been changes in the mean or C.T. of a
process.
The R-Chart indicates whether or not a gain or loss in dispersion has
occurred.
X-BAR AND R CHARTS GO HAND-IN-HAND WHEN MONITORING
VARIABLES – THEY MEASURE THE TWO CRITICAL PARAMETERS.
P-charts measure the % defective in a sample.
Use for % defective units.
Use when you can count the number of defective
units.
S6 – 71
Advanced Variation-based Metric Issue:
Continuous vs. Discrete
•
Continuous Variables are Preferable
– Whenever possible, or when given the choice… select/gather
continuous variables!
• Crucial to consider during data collection planning when
flexibility exists to identify and/or define various types of metrics
to track for a project
– Continuous variables are more “information rich”
• Discrete variables capture only yes/no, met/not met, etc.
• Continuous variables also capture “by how much”
• More flexibility in the use of analysis tools w/ continuous
variables
•
Unfortunately, the tendency is to utilize discrete variables
– Discrete are usually more easy to define and easier to measure
• Majority of Balanced Scorecard metrics in prior years have been
discrete
© 2006 Prentice Hall, Inc.
S6 – 72
Control Charts = Process Behavior Charts
An In-Control Process = A Predictable Process
An Out–of-Control Process = An Unpredictable Process
Variation is either routine or exceptional.
© 2006 Prentice Hall, Inc.
S6 – 73