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MGS 8020
Business Intelligence
Measure
Mar 26, 2015
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 1
Measure - SMART
“Voice of the Process”
(The “Voice of the Data”)
Based on natural (common
cause) variation
Tolerance limits
(The “Voice of the Customer”)
Customer requirements/Specs
Process Capability
A measure of how “capable” the
process is to meet customer
requirements
Compares process limits to
tolerance limits
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 2
Agenda
1.
Analysis Tools
2.
Control Charts
3.
Process Capability
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 3
Data Analysis Tools
Run Chart
0.58
12
10
8
6
4
2
0
Diameter
Defects
Scatter Diagram
0.54
0.5
0.46
0
10
20
Hours of Training
30
1
2
3
4
5
6
7
8
9
10
11 12
Time
Can be used to illustrate the relationships
between factors such us quality and training
Can be used to identify when equipment or
processes means are drifting away from specs
Histogram
Control Chart
Frequency
500
UCL
480
460
440
LCL
420
Data Ranges
Can be used to display the shape of variation
in a set of data
Georgia State University - Confidential
400
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Use to identify if the process is predictable (in
control)
MGS8020 Measure.ppt/Mar 26, 2015/Page 4
Cause and Effect Diagram
Machine
Man
Effect
Environmental
Method
Georgia State University - Confidential
Material
MGS8020 Measure.ppt/Mar 26, 2015/Page 5
Pareto Charts
Root Cause Analysis
80% of the
problems may be
attributed to 20%
of the causes
Design
Assy.
Instruct.
Georgia State University - Confidential
Purch.
Training
Other
MGS8020 Measure.ppt/Mar 26, 2015/Page 6
Agenda
1.
Analysis Tools
2.
Control Charts
3.
Process Capability
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 7
Statistical Process Control (SPC): Used to determine if process is within
process control limits during the process and to take corrective action
when out of control
Process in Statistical Control
Statistical process control is
the use of statistics to
measure the quality of an
ongoing process
UCL
LCL
A Process
is in control when all
points are inside the
control limits
Process not in Statistical Control
UCL
LCL
A Process
is not in control when one
or more points is/are
outside the control limits
Process not in Statistical Control
UCL
LCL
Georgia State University - Confidential
Special Causes
MGS8020 Measure.ppt/Mar 26, 2015/Page 8
When to Investigate
In Control
UCL
Even if in control the process should
be investigated if any non random
patterns are observed OVER TIME
LCL
1
Trend - Constant Increase/Decrease
2
3
4
5
6
UCL
Close to Control Limit
UCL
LCL
1
2
3
4
5
6
LCL
1
2
3
4
5
Cycles
UC
L
UCL
Consecutive Points Below/Above Mean
LCL
5
10
15
20
LCL
1
Georgia State University - Confidential
2
3
4
5
6
MGS8020 Measure.ppt/Mar 26, 2015/Page 9
Types of Variation
Special cause
(unexpected)
variation
Prediction
Common cause
(expected)
variation
Prediction
Georgia State University - Confidential
 Caused by factors that can be clearly
identified and possibly managed;
assignable causes evident, not in
statistical control
Short-term objective - to eliminate
unexpected variation Inherent in the
process
 Normal variation only, stable,
predictable, in statistical control
Long-term objective - to
reduce expected variation
MGS8020 Measure.ppt/Mar 26, 2015/Page 10
Control Chart Development Steps
1
2
Identify Measurement
INPUTS
OUTPUT
X’s
3
Y’s
Start
0.1
Sample
Sample
Size
Defective
p
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Total
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
1500
4
3
5
6
2
1
6
7
3
8
1
2
1
9
1
59
0.04
0.03
0.05
0.06
0.02
0.01
0.06
0.07
0.03
0.08
0.01
0.02
0.01
0.09
0.01
Improve Process
4
Determine Control Limits
Collect Data
Eliminate
Special
Causes
0.08
Reduce
Common
Cause
Variation
0.06
Improve
Average
0.04
0.02
Defects
0
0
2
4
6
8
10
12
14
16
18
A
Georgia State University - Confidential
B
C
D
MGS8020 Measure.ppt/Mar 26, 2015/Page 11
Quality Measures – Attributes & Variables
•
An attribute is a product characteristics such as color, surface texture,
cleanliness, or perhaps smell or taste. Attributes can be evaluated quickly
with a discrete response such as good or bad, acceptable or not, yes or no.
An attribute measure evaluation is sometimes referred to as a qualitative
classification, since the response is not measured.
•
A variable measure is a product characteristics that is measured on a
continuous scale such as length, weight, temperature, or time. For
example, the amount of liquid detergent in a plastic container can be
measured to see if it conforms to the company’s product specifications.
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 12
Control Charts
•
Control Charts have historically been used to monitor the quality of
manufacturing process. SPC is just as useful for monitoring quality in
services. The difference is the nature of the “defect” being measured and
monitored. Using Motorola’s definition – a failure to meet customer
requirements in any product or service.
•
Control Charts are graphs that visually show if a sample is within statistical
control limits. The control limits are the upper and lower bands of a control
chart. They have two basic purposes, to establish the control limits for a
process and then to monitor the process to indicate when it is out of control.
All control charts look alike, with a line through the center of a graph that
indicates the process average and lines above and below the center line
that represent the upper and lower limits of the process.
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 13
Control Charts for Attributes
•
•
The quality measures used in attribute control charts are discrete values
reflecting a simple decision criterion such as good or bad. A p-chart uses
the proportion of defective (defectives) items in a sample as the sample
statistics; a c-chart uses the actual number of defects per item in a sample.
p-charts
Although a p-chart employs a discrete attribute measure (i.e. number of
defective items) and thus is not continuous, it is assumed that as the
sample size gets larger, the normal distribution can be used to approximate
the distribution of the proportion defective.
Z
Source: Selected Chapters on Business Analysis – Ch15 Statistical Process Control
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 14
Control Charts for Attributes
~ p-chart
•
The p-formula – the sample proportion defective; an estimate of the process
average
Total defectives
Total sample
observations
•
k = the number of samples
n = the sample size
The standard deviation of the sample proportion
Normal Distribution: Z-Value
δp =
n
•
To calculate control limits for the p-chart:
Z
n
•
m
-3
-2
-1
0
1
2
3
Z
Z- VALUE is the number of Standard
Deviations from the mean of the Normal Curve
z = the number of standard deviations fromZthe process average. In the control
limit formulas for p-charts (and other control charts), z is occasionally equal to
2.00 but most frequently is 3.00. A z value of 2.00 corresponds to an overall
normal probability of 95 percent and z = 3.00 corresponds to a normal
probability of 99.74 percent.
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 15
Control Charts for Attributes
~ p-chart (Example)
•
The Western Jeans company produces denim jeans. The company wants
to establishes p-chart to monitor the production process and maintain high
quality. Western believes that approx. 99.74 percent of the variability in the
production process (z = 3.00) is random and thus should be within control
limits, whereas 0.26 percent of the process variability is not random and
suggests that the process is out of control.
•
The company has taken 20 samples (one per day for 20-days), each
containing 100 pairs of jeans (n=100), and inspected them for defects. The
total number of defectives are 200.
•
Find the control limits.
Z
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 16
Control Charts for Attributes
~ c-chart
•
f•
•
A c-chart is used when it is not possible to compute a production defective and
the actual number of defects must be used. For example, when automobiles are
inspected, the number of blemishes (i.e. defects) in the paint job can be counted
for each car, but a proportion cannot be computed, since the total number of
possible blemishes is not known.
= the total number of defects / total number of samples
The standard deviation
δc =
•
To calculate control limits for the p-chart:
Z
Z
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 17
Control Charts for Attributes
~ c-chart (Example)
•
The Ritz Hotel believes that approximately 99% of the defects (corresponding to
3-sigma limits) are caused by natural, random variations in the housekeeping
and room maintenance service, with 1% caused by nonrandom variability. They
want to construct a c-chart to monitor the housekeeping service.
•
15 inspections samples are selected by the hotel. An inspection sample
includes 12 rooms and the total number of defects is 190.
•
Find the control limits.
Z
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 18
Control Charts for Variables
~ R-chart
•
•
•
Variable control charts are for continuous variables that can be measured, such
as weight or volume. Two commonly used variable control charts are the range
chart (R-chart) and the mean chart (x-bar chart).
R-chart
In an R-chart, the range is the difference between the smallest and largest
values in a sample. This range reflects the process variability instead of the
tendency toward a mean value.
R is the range of each sample
k is the number of samples.
Z
Upper control limit
Lower control limit
Source: Selected Chapters on Business Analysis – Ch15 Statistical Process Control
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 19
Control Charts for Variables
~ R-chart (Example)
•
In the production process for a particular slip-ring bearing the employees have
taken 10 samples (during 10-day period) of 5 slip-ring bearings (n=5). Please
define the control limits for R-chart. The individual observations from each
sample are shown as follows:
Sample k
RR
1
2
3
4
5
1
5.02
5.01
4.94
4.99
4.96
4.98
0.08
2
5.01
5.03
5.07
4.95
4.96
5.00
0.12
3
4.99
5.00
4.93
4.92
4.99
4.97
0.08
4
5.03
4.91
5.01
4.98
4.89
4.96
0.14
5
4.95
4.92
5.03
5.05
5.01
4.99
0.13
6
4.97
5.06
5.06
4.96
5.03
5.02
0.10
7
5.05
5.01
5.10
4.96
4.99
5.02
0.14
8
5.09
5.10
5.00
5.08
5.05
0.11
9
5.14
5.10
4.99
4.99
Z
5.08
5.09
5.08
0.15
10
5.01
4.98
5.08
5.07
4.99
5.03
0.10
50.11
1.15
sum
average
Georgia State University - Confidential
0.115
MGS8020 Measure.ppt/Mar 26, 2015/Page 20
Control Charts for Variables
~ x-bar chart
•
For an x-bar chart, the mean of each sample is computed and plotted on the
chart; the points are sample means. The samples tend to be small, usually
around 4 or 5.
n is the sample size (or number of observations)
k is the number of samples
Upper control limit
Lower control limit
Georgia State University - Confidential
Z
MGS8020 Measure.ppt/Mar 26, 2015/Page 21
Control Charts for Variables
~ x-bar chart (Example)
•
Use the data from R-Chart and define the control limits for x-bar chart.
Z
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 22
Control Charts for Variables
~ Tabular values for X-bar and R charts (Given)
Sample Size n
A2
D3
D4
2
1.880
0
3.268
3
1.023
0
2.574
4
0.729
0
2.282
5
0.577
0
2.114
6
0.483
0
2.004
7
0.419
0.076
1.924
8
0.373
0.136
1.864
9
0.337
0.184
1.816
10
0.308
0.223
1.777
11
0.285
0.256
1.744
12
0.266
0.283
1.717
13
0.249
0.307
1.693
14
0.235
0.328
1.672
15
0.223
0.347
1.653
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 23
Control Charts for Variables
~ Tabular values for X-bar and R charts (Given)
Sample Size n
A2
D3
D4
16
0.212
0.363
1.637
17
0.203
0.378
1.622
18
0.194
0.391
1.608
19
0.187
0.403
1.597
20
0.180
0.415
1.585
21
0.173
0.425
1.575
22
0.167
0.434
1.566
23
0.162
0.443
1.557
24
0.157
0.451
1.548
25
0.153
0.459
1.541
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 24
Process Capability



Process Capability – A measure of how “capable” the process is to meet
customer requirements; compares process limits to tolerance limits. There
are three main elements associated with process capability – process
variability (the natural range of variation of the process), the process center
(mean), and the design specifications.
Process limits (The “Voice of the Process” or The “Voice of the Data”) based on natural (common cause) variation
Tolerance limits (The “Voice of the Customer”) – customer requirements
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 25
Agenda
1.
Analysis Tools
2.
Control Charts
3.
Process Capability
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 26
Process Capability
•
Variation that is inherent in a production process itself is called common
variation.
(1)
(3)
specification
specification
common variation
common variation
(2)
(4)
specification
specification
common variation
Georgia State University - Confidential
common variation
MGS8020 Measure.ppt/Mar 26, 2015/Page 27
Process Capability Ratio
•
One measure of the capability of a process to meet design specifications is the
process capability ratio (Cp). It is defined as the ratio of the range of the design
specifications (the tolerance range) to the range of process variation, which for
most firms is typically ±3δ or 6δ
•
If Cp is less than 1.0, the process range is greater than the tolerance range, and
the process is not capable of producing within the design specifications all the
time. If Cp equals 1.0, the tolerance range and the process range are virtually
the same. If Cp is greater than 1.0, the tolerance range is greater than the
process range.
•
Companies would logically desire a Cp equal to 1.0 or greater, since this would
indicate that the process is capable of meeting specifications.
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 28
Process Capability Ratio (Example)
•
The XYZ Snack Food Company packages potato chips in bags. The net weight
of the chips in each bag is designed to be 9.0 oz, with a tolerance of +/- 0.5
oz. The packaging process results in bags with an average net weight of 8.80 oz
and a standard deviation of 0.12 oz. The company wants to determine if the
process is capable of meeting design specifications.
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 29
Process Capability Index
•
•
•
The Process Capability Index (Cpk) differs from the Cp in that it indicates if the
process mean has shifted away from the design target, and in which direction it
has shifted – that is, if it is off center.
If the Cpk index is greater than 1.00 then the process is capable of meeting
design specifications. If Cpk is less than 1.00 then the process mean has moved
closer to one of the upper or lower design specifications, and it will generate
defects. When Cpk equals Cp, this indicates that the process mean is centered
on the design (nominal) target.
Please read Example 7 on page 354.
 X  LTL
UTL - X 

Cpk = min 
or

3
 3

where
•
x-bar is the mean of the process
•
sigma is the standard deviation of the process
•
UTL is the customer’s upper tolerance limit (specification)
•
and LTL is the customer’s lower tolerance limit
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 30
Interpreting the Process Capability Index

Cpk < 1
Not Capable

Cpk > 1
Capable at 3

Cpk > 1.33
Capable at 4

Cpk > 1.67
Capable at 5

Cpk > 2
Capable at 6
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 31
Process Capability Index (Example)
•
A process has a mean of 45.5 and a standard deviation of 0.9. The product
has a specification of 45.0 ± 3.0. Find the Cpk .
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 32
Process Capability Index (Example)
Cpk
 X  LTL
UTL - X 

= min 
or

3

3




= min { (45.5 – 42.0)/3(0.9) or (48.0-45.5)/3(0.9) }

= min { (3.5/2.7) or (2.5/2.7) }

= min { 1.30 or 0.93 } = 0.93 (Not capable!)

However, by adjusting the mean, the process can become capable.
Georgia State University - Confidential
MGS8020 Measure.ppt/Mar 26, 2015/Page 33