Six Sigma
Green Belt
Process Capability Analysis

-6
-4
-2
0
2
4
6
Sigma Quality Management
1
Capability Defined:
Six Sigma
Green Belt
“How well does our process' output
(product or service) meet the valid
requirements of the customer?”
2
Six Sigma
Green Belt
Frequency Charts
Frequency
25
20
15
10
5
1
Average = 3.2 errors/day
Date: 1/2/96
Prep’d: NPO
2
3
4
5
6
7
8
9
Number of
Shipping Errors
(each Day)
3
Six Sigma
Green Belt
Histogram
Histogram– Refrigerant Fill Weights (lb.)
– Manual Process
30.0
Frequency
Average- 7.6 lbs
24.0
18.0
Date: 6/95
Prep’d: M. Lippen
12.0
6.0
0.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
Fill Weights (lbs)
4
Interpretation
Symmetrical
Six Sigma
Green Belt
Many processes’ outputs take this shape, especially those where an attempt is being made to
produce the product or service at some target or nominal value.
If a data sample is periodically obtained from a random process and the average of the
sample is calculated, the histogram of averages will always assume this shape.
Skewed
The time to complete a process will often appear skewed. Most of the events will fall in a
clump to the right or left, with only a few data in a “tail.”
Other data that often appear skewed are times or cycles to failure.
Extreme Skewness
Here the data appears to be pushed up against some boundary. This is often the case when
there is a lower or upper limit that the data can assume. For example, some time data can
appear extremely skewed when it is possible to complete the process in very short times
(close to zero).
If a product is inspected and rejected if it does not meet a specification, the “good” products
will take on this shape after inspection.
5
Interpretation (Continued)
Six Sigma
Green Belt
Exponential
This shape can appear if there is a “birth-to-death” process being measured and the failure
time is measured. This is also the shape that a radioactive decay process will produce and
either the quantity of material remaining or the disintegration rate is measured periodically.
Plateau
This is a shape where we suspect that two processes are being mixed together, whose mean
values are not very far apart.
Another time this shape can appear is when an automatic compensating control is fitted to a
machine or process. When the process output reaches a certain value, the control adjusts
the machine to a lower (or higher) value.
Twin-Peaked
This is an example of two processes, whose outputs are mixed together. For example, two
production lines’ outputs are mixed and the histogram data is collected at a final inspection
point.
This is an invitation to stratify the data. Usually, one of the processes will perform better than
the other. If you can understand why, then the other process can be changed to perform as
well.
Outliers
Sometimes, special circumstances will cause the production process to produce outliers. For
example, during a colonoscopy procedure, some patients become rather resistant. The time
required to “produce” these colonoscopies will show up as an outliers when combined with
data from normal procedures.
6
Six Sigma
Green Belt
Capability - Picture
One-Sided Specification
Pr ocess Out put does not
meet Cust omer
Req uir ement s
Specificat ion Limit
Qualit y
Char act er ist ic
7
Six Sigma
Green Belt
Capability - Picture
Two-Sided Specification
Lower Spec
Limit
Qualit y
Upper Spec Char act er ist ic
Limit
8
Six Sigma
Green Belt
Inherent Process Capability
Customer's Tolerance =
Upper Specification Limit Lower Specification Limit
Reasonable Width of
Process Variation – 6
Standard Deviations
Mean
Region A
Quality
Characteristic
Region B
Region C
9
Inherent Process Capability - Cp
Six Sigma
Green Belt
Inherent Process Capability = Upper Specification - Lower Specification
6 x Process Standard Deviation
Inherent Process Capability =
(One Spec Only)
|Specification - Process Mean|
3 x Process Standard Deviation
10
Six Sigma
Green Belt
Cp Values
C < 1
C = 1
p
Lower
Spec
p
Upper
Spec
Lower
Spec
Upper
Spec
C > 1
p
Lower
Spec
Upper
Spec
Lower
Spec
Upper
Spec
11
Six Sigma
Green Belt
Operational Process Capability - Cpk
Z min 
SL  X
s
where :
Z min - number of standard deviations the process
mean is from the specificat ion limit
SL - Upper or Lower Specificat ion Limit
X - Process Average
Z USL 
USL  X
s
(estimated from s / c4 or R / d 2 )
X  LSL
s
and
Z min  Minimum ( Z USL , Z LSL )
where :
Z min - minimum number of standard deviations the process
mean is from a specificat ion limit
USL - Upper Specificat ion Limit
LSL - Lower Specificat ion Limit
(an X - Bar chart is assumed to be available here)
s - Process Standard Deviation
Z LSL 
X - Process Average
(an X - Bar chart is assumed to be available here)
s - Process Standard Deviation
(estimated from s / c4 or R / d 2 )
C pk  Z min 3
where:
C pk - Operational Process Capability
12
Process Capability Studies





Six Sigma
Green Belt
Raw material sources,
Operators,
Gauge users,
Production rates, and
Environmental conditions.
USL  x 
 x  LSL 
 or 

Ppk  
3ˆ
3ˆ x
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Assessing Process Capability - Steps
Six Sigma
Green Belt
1. Accumulate data in subgroups of consecutive parts taken periodically from
production runs. If the same process produces a variety of part numbers with
different target dimensions, each different part should be treated as a
separate process unless we have evidence that the variation about the
targeted dimension is not affected by the normal value.
2. Data should be accumulated over a long enough period of time that all
sources of variation have an opportunity to be exhibited (25 subgroups of 4
taken over a “long” period of time is a guide). Check for process stability.
3. Test the data for shape of distribution.
4. If the distribution is normal, compute the standard deviation based on
individuals. If the data is not normal, either transform the data or perform a
capability analysis using the Weibull distribution (see Minitab, Help topics,
process capability: non-normal data for more information).
5. Calculate Pc based on six standard deviations divided into the available
tolerance.
6. Calculate Pc using standard deviation based on the average range. Compare
this with the value obtained in step 5 to see what the potential of the process
is given better controls or improved stability of mean performance.
14
Six Sigma
Green Belt
Capability and Six Sigma
Mean
Lower
Specification
Limit
-6
-5
-4
Upper
Specification
Limit
-3
-2
-1
0
1
2
3
4
5
6
Standard Deviations
15
Calculating Sigma – Measurement Data
Six Sigma
Green Belt
Mean
Lower
Specification
Limit
Upper
Specification
Limit
Area 2
Area 1
Measure
 USL  x 
Area  1  1  CumNorm

s


 LSL  x 
Area  2  CumNorm

s


where : CumNorm 
Cumulative Normal Distributi on
16
Calculating Sigma – Discrete Data
Six Sigma
Green Belt
d
6
DPMO 
 10
no
17
Six Sigma
Green Belt
First, Final, Normalized, Rolled-TP Yield
YFP
d
 1
no
d  d
YFINALPASS  1 
no
where : d  - number of defects detected and
eliminated prior to reaching the customer
d
 1
n o
i
YNORM
i
i
i
where : i - number of subprocess es
YRTP   YFPY i
i
18
Six Sigma
Green Belt
Sigma Assessment - Example
Market
Product
Process Step
Market Deal
Execute
Transaction
Execute
Transaction
Complete
Transaction
Defect Opportunities
 Misunderstand client
requirements
 Recording errors
 Error-caused amendments
 Recording Errors
 Order Errors
 Fulfillment Errors
Overall

Complete
Transaction





Inaccurate Price
Deal not compliant with
Regulations
Sales/Order Transaction
Mismatch
Confirmation Timeliness
Client/Company Confirmation
Mismatch
Lost Sale
19
Six Sigma
Green Belt
Sigma Scorecard
Calculated Using Basic Sigma
Method for Discrete Data
Process Step
Defect Opportunities
Market Product Misunderstand client
requirements
Execute
Transaction
Complete
Transaction
Overall
Data No. of No. of Defects Avg. Std. Upper DPMO Yield
Sigma Step
Step
Type Units Opp's.
Dev. Spec
(ST) Yield
Sigma
D
1000
1
120
120000 88.00%
2.67 93.83%
3.04
Recording errors
Inaccurate Price
Deal not compliant with
Regulations
D
D
D
1000
1000
1000
1
1
1
90
25
12
90000
25000
12000
91.00%
97.50%
98.80%
2.84
3.46
3.76
Error-caused
amendments
D
1000
1
100
100000
90.00%
2.78 93.23%
Recording Errors
Sales/Order Transaction
Mismatch
D
D
1000
1000
1
1
58
45
58000
45000
94.20%
95.50%
3.07
3.20
Order Errors
D
1000
1
8
8000
99.20%
3.91 97.58%
Fulfillment Errors
Confirmation Timeliness
D
C
1000
1000
1
1
22
22000
3 237525
97.80%
76.25%
3.51
2.21
Client/Company
Confirmation Mismatch
D
1000
1
67
67000
93.30%
3.00
Lost Sale
D
1000
1
89
89000 91.10%
2.85
Overall (Normalized) 95.55%
Process Yield:
Rolled Throughput Yield: 77.76%
2.5
0.7
Calculated Using Basic
Sigma Method for
Continuous Data
Overall Process Sigma:
The Product of SubProcess Yields (and
Failed Trade Yield)
2.99
3.47
Calculated Using First
Pass Yield Formula
and Short Term Sigma
3.20
Calculated Using Normalized Yield Formula
20
and Short Term Sigma