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Process Capability
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Process Capability Pg 1
The Breakthrough Strategy® And Process Capability
Calculate baseline
Process Capability
Assess Process
Capability after
improvements are made
1. Select Output Characteristic and identify
key process input and output variables
2. Define Performance Standards
3. Validate Measurement System
4. Establish Process Capability
5. Define Performance Objectives6. Identify Variation Sources
7. Screen Potential Causes
8. Discover Variable Relationships
9. Establish Operating Tolerances
10. Validate Measurement System
11. Determine Final Process Capability
12. Implement Process Controls
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Process Capability Pg 2
Module Objectives
By the end of this module the participants should be able to:
• Explain where capability analysis fit into the 12 Step
Breakthrough Strategy
• Compute capability statistics with Variable Data
• Compute capability statistics with Attribute Data
• Discuss the concepts of stability as a prerequisite for
Capability Analysis
• Utilize MINITAB® for capability studies
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Process Capability Pg 3
What Is Process Capability?
Process Capability is a measure of how well the process output
(Voice Of Process) meets the customer requirements(Voice Of Customer).
Process Capability is analogous to measuring how well
the car gets parked in the garage, time after time.
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Process Capability Pg 4
Why Use Process Capability?
Process Capability answers the following questions:
• How is the process performing?
• How well could the process perform?
• What can be expected tomorrow, next week?
• Are customer‟s expectations being met?
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Process Capability Pg 5
Data Types
Attribute Data System:
• Capability is defined in terms of PASS/FAIL or categories
Continuous Data System:
• Capability is defined in terms of
defects under the curve and
outside of the specification limits
% Good % Bad
S P E C
L S L
T A R G E T
U S L
DefectsDefects
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Process Capability Pg 6
Calculating Capability
All processes can be described by the Z
score, making process comparisons easy.
Attribute Data Variables Data
Six Sigma Product ReportCapability Analysis and Sixpack
and/or Six Sigma Process Report
Sigma (Z)
DPMO DPMO
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Process Capability Pg 7
Voice Of Process,Voice Of Customer
• Specification limits represent the Voice Of Customer, VOC
• The process output represents Voice Of Process, VOP
• Process Capability measures how well VOP “fits” within VOC
LSL(Lower
specification
limit)
USL(Upper
specification
limit)
Voice Of Customer, VOC
Voice Of Process, VOP
CTQ, CTD, CTC
Now let‟s review some basic capability metrics.
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Z score Transform
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Process Capability Pg 9
Z score Transformations
• If a data set is normally distributed, we use the mean and Standard Deviation to
determine the percentage (or probability) of observations within a selected range
• We can transform any normally distributed scale to its equivalent Z scale or score
using the formula below
• X will often represent a Lower or Upper Specification Limit (LSL and USL,
respectively) – It is the “Point of Interest”
• Z is the measure from the mean to the Point of Interest in Standard Deviations
X Z
Point of Interest
Mean
Z = 3
1
2
3
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Process Capability Pg 10
Z scale = units
are Standard
Deviations
10
86413
1412
-1-2-3 3210
USL
1610
Let's assume a process
µ = 10 and
σ = 2
Question 1: If my
Upper SpecificationLimit (USL) is 13,
how many mm
is the USL from
my mean?
Question 2: If theStdDev is 2,
how many StDevs
is my USL from
my mean?
X scale = units
are mm
Z = X - µσ
Z = 13 - 10
2
= 1.5
Z score Transformations
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Process Capability Pg 11
Z scale = units
are Standard
Deviations
864 1412
-1-2-3 3210
Z = X- µ
σ
1610
X scale = units
are Inches
X Z
? 1
10 ?
6 ?
? -3
? 1.5
? -2.25
13 ?15.5 ?
? 4
? -4
Z score Transformations – Exercise
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Process Capability Pg 12
Z scale = units
are Standard
Deviations
864 1412
-1-2-3 3210
1610
X scale = units
are mm
Given ±1σ = 68%, ±2σ = 95%, ±3σ = 99.73%: Answer the following:
X z % of
area
to
rightof X
% of
area
to left
of X
10
12
14
168
6
4
Z score Transformations – Probability Exercise
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Process Capability Pg 13
P(z > -1.5) =
1-.0668 = .9332 Yield 93.3%
Probabilities Using Z Table
Standard Normal Probabilities:
The table is based on the area P
under the Standard Normal
Probability curve to the left of the
“Point of Interest” (Z = -1.5)
z 0 0 .0 1 0 .0 2 0 .0 3 0 .0
-4 .0 0 .0 0 0 0 3 0 .0 0 0 0 3 0 .0 0 0 0 3 0 .0 0 0 0 3 0 .0 0 0 0
-3 .9 0 .0 0 0 0 5 0 .0 0 0 0 5 0 .0 0 0 0 4 0 .0 0 0 0 4 0 .0 0 0 0
-3 .8 0 .0 0 0 0 7 0 .0 0 0 0 7 0 .0 0 0 0 7 0 .0 0 0 0 6 0 .0 0 0 0
-3 .7 0 .0 0 0 1 1 0 .0 0 0 1 0 0 .0 0 0 1 0 0 .0 0 0 1 0 0 .0 0 0 0
-3 .6 0 .0 0 0 1 6 0 .0 0 0 1 5 0 .0 0 0 1 5 0 .0 0 0 1 4 0 .0 0 0 1
-3 .5 0 .0 0 0 2 3 0 .0 0 0 2 2 0 .0 0 0 2 2 0 .0 0 0 2 1 0 .0 0 0 2
-3 .4 0 .0 0 0 3 4 0 .0 0 0 3 2 0 .0 0 0 3 1 0 .0 0 0 3 0 0 .0 0 0 2
-3 .3 0 .0 0 0 4 8 0 .0 0 0 4 7 0 .0 0 0 4 5 0 .0 0 0 4 3 0 .0 0 0 4
-3 .2 0 .0 0 0 6 9 0 .0 0 0 6 6 0 .0 0 0 6 4 0 .0 0 0 6 2 0 .0 0 0 6
-3 .1 0 .0 0 0 9 7 0 .0 0 0 9 4 0 .0 0 0 9 0 0 .0 0 0 8 7 0 .0 0 0 8
-3 .0 0 .0 0 1 3 5 0 .0 0 1 3 1 0 .0 0 1 2 6 0 .0 0 1 2 2 0 .0 0 1 1
-2 .9 0 .0 0 1 8 7 0 .0 0 1 8 1 0 .0 0 1 7 5 0 .0 0 1 6 9 0 .0 0 1 6
-2 .8 0 .0 0 2 5 6 0 .0 0 2 4 8 0 .0 0 2 4 0 0 .0 0 2 3 3 0 .0 0 2 2
-2 .7 0 .0 0 3 4 7 0 .0 0 3 3 6 0 .0 0 3 2 6 0 .0 0 3 1 7 0 .0 0 3 0
-2 .6 0 .0 0 4 6 6 0 .0 0 4 5 3 0 .0 0 4 4 0 0 .0 0 4 2 7 0 .0 0 4 1
-2 .5 0 .0 0 6 2 1 0 .0 0 6 0 4 0 .0 0 5 8 7 0 .0 0 5 7 0 0 .0 0 5 5
-2 .4 0 .0 0 8 2 0 0 .0 0 7 9 8 0 .0 0 7 7 6 0 .0 0 7 5 5 0 .0 0 7 3
-2 .3 0 .0 1 0 7 2 0 .0 1 0 4 4 0 .0 1 0 1 7 0 .0 0 9 9 0 0 .0 0 9 6
-2 .2 0 .0 1 3 9 0 0 .0 1 3 5 5 0 .0 1 3 2 1 0 .0 1 2 8 7 0 .0 1 2 5
-2 .1 0 .0 1 7 8 6 0 .0 1 7 4 3 0 .0 1 7 0 0 0 .0 1 6 5 9 0 .0 1 6 1
-2 .0 0 .0 2 2 7 5 0 .0 2 2 2 2 0 .0 2 1 6 9 0 .0 2 1 1 8 0 .0 2 0 6
-1 .9 0 .0 2 8 7 2 0 .0 2 8 0 7 0 .0 2 7 4 3 0 .0 2 6 8 0 0 .0 2 6 1
-1 .8 0 .0 3 5 9 3 0 .0 3 5 1 5 0 .0 3 4 3 8 0 .0 3 3 6 2 0 .0 3 2 8
-1 .7 0 .0 4 4 5 6 0 .0 4 3 6 3 0 .0 4 2 7 2 0 .0 4 1 8 1 0 .0 4 0 9
-1 .6 0 .0 5 4 8 0 0 .0 5 3 7 0 0 .0 5 2 6 2 0 .0 5 1 5 5 0 .0 5 0 5
-1 .5 0 .0 6 6 8 1 0 .0 6 5 5 2 0 .0 6 4 2 5 0 .0 6 3 0 1 0 .0 6 1 7
-1 .4 0 .0 8 0 7 6 0 .0 7 9 2 7 0 .0 7 7 8 0 0 .0 7 6 3 6 0 .0 7 4 9
-1 .3 0 .0 9 6 8 0 0 .0 9 5 1 0 0 .0 9 3 4 2 0 .0 9 1 7 6 0 .0 9 0 1-1 .2 0 .1 1 5 0 7 0 .1 1 3 1 4 0 .1 1 1 2 3 0 .1 0 9 3 5 0 .1 0 7 4
-1 .1 0 .1 3 5 6 6 0 .1 3 3 5 0 0 .1 3 1 3 6 0 .1 2 9 2 4 0 .1 2 7 1
LSL
Z Tables may be found in the “Black
Belt Memory Jogger” and most stat
textbooks. We will use MINITAB to
calculate probabilities
- . .
-1 . 5 0 . 0 6 6 8 1
-1 . 4 0 . 0 8 0 7 6
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Process Capability Pg 14
Probabilities Using MINITAB
• Run: Calc Probability Distributions Normal
• Select Cumulative probability and enter –1.5 in the Input constant box
• Use MINITAB
‟s Cumulative
Probability Function to
convert the Z score to
determine the area under
the curve
Session Window Output:
Cumulative Distribution Function
Normal with mean = 0 andStandard Deviation = 1.00000
x P( X <= x )
-1.5000 0.0668How many “Zs” from the
mean and in what direction
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Process Capability Pg 15
Calculating The Area ToThe Right Of Any Point
• From the same distribution curve, the area to the right of the Z score
(point of interest or right tail) can be calculated by subtracting the areato the left of the Z score from 1.0 (the total area under a standard curve,
i.e., 100%)
• Given Z = 0.94:
MINITAB provides ananswer of .8264 or
82.64% is to the left of
the Point of Interest and
17.36% to the right
P(x > z) = 1-.8264 =
.1736 or 17.36%
.1736
Z=0.94
Normal
C C F
3210-1-2-3
0.4
0.3
0.2
0.1
0.0
.8264
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Process Capability Pg 16
Relating Z score From Area Under Curve
• Up till now, we knew the Z score (or value) and found the area
• We can also calculate the Z score if given an area
• The question is P(Z < ?) = 0.8264 (or how many Zs and in what
direction to cover 82.64% of the area under the curve)
• Determine the Z score or Point of Interest that is represented by the
total area of interest under the curve to the left of Z
Normal
C
C F
Z=?
3210-1-2-3
0.4
0.3
0.2
0.1
0.0
82.64%
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Process Capability Pg 17
Calculating Z score Or InverseCumulative Probability
• Use MINITAB‟s Inverse cumulative probability function to convert the
area of interest under the curve to the left of some Point of Interest tothe Z score value of that Point of Interest
• Calc Probability Distribution Normal
- Click “Inverse cumulative probability”
- Input constant = .8264
• Answer is in the
session window:
Inverse Cumulative Distribution Function
Normal with mean = 0 and
Standard Deviation = 1.00000
P (X < = x) x
0.8264 0.9400
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Process Capability Pg 18
Z Table Exercises
• Find the area under the curve to the right and to the left of each of the
following Z values:
1.1, 2.4, 3.2, 0.45, -2.2, -1.75
• Given a process with a mean of 20 and a Standard Deviation of 4, find
the area under the curve to the right and to the left of each of the
following X values:22, 26, 20, 18, 14
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Process Capability Pg 19
The Z score Transformation:
Z X
Z
Z
47.5 45
12 5.
Z X
DEFECTS
to the rightof the USL
USL=47.5
Suppose the diameters
of shafts are normally
distributed with a mean
of (45) and a Standard
Deviation of (1). Thecustomer derived Upper
Specification Limit is
(47.5). What is the
DPMO for this process?
From MINITAB, the probability that a shaft is
less than (47.5) is 99.38% and the probability
of a defect is (1 - .9938) or .0062%.
DPMO = .0062 x 1,000,000 = 6,200
Knowing the distribution and the Specification Limits allows the
prediction of capability!
Z score TransformationPractical Application – DPMO Calculation
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Process Capability Pg 20
Application Of Z score Transform
Assume that the average number of days an account receivable is on the
books until funds are received is 25 days, with a Standard Deviation of four days…
• What are the chances that an account receivable is not closed before 30
days? Give answer as both a % and, assuming that 30 days is our
Upper Specification Limit, a DPMO.
• How many days does it take until 20% of the accounts receivable have
been paid?
• How many days does it take until 99.99% of the accounts receivable
have been paid?
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Process Capability Pg 21
ZBench Calculation (1)
• One of the key metrics used in Six Sigma is the Z Benchmark or
simply ZBench
• It is a single metric that takes into account defects both beyond the
Upper Specification Limit and below the Lower Specification Limit
• For our example, let us establish a process
• µ = 10
• σ = 2
• USL = 13
• LSL = 8
• We will first look at the Upper and Lower cases separately
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Process Capability Pg 22
10
86413
1412
-1-2-3 3210
USL
Z = 13 - 10
2
= 1.5
1610
Let's assume a process
µ = 10 and σ = 2
Question: If myUpper Specification
Limit is 13,what
% of my production
is defective? (Brown
area under the curve) Answer: Use Z Table
or MINITAB for
Z =1.5
Probability
of a defect
is 6.68%
ZBench Calculation (2) P (Defects) Upper
USL = 13
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Process Capability Pg 23
10
864 1412
-1-2-3 3210
Z = 8 - 10
2= -1
1610
Same processµ = 10
and σ = 2
Question: If myLower Specification
Limit is 8, what % of
my production is
defective?
(Yellow area under the curve)
Answer: Use
MINITAB for Z = -1
Probabilityof a defect
is 15.87%
LSL = 8
ZBench Calculation (3) P (Defects) Lower
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Process Capability Pg 24
10
864
13
1412
-1-2-3 3210
USL
1610
Question: If myUSL is 13 and my LSL
is 8, what % of my
production
is defective?
(Brown and yellowareas under
the curve)
Answer: Use
MINITAB
for Z =1.5 and Z = -1
and then add the
probabilities of
defect from both sides
Probability
of a defect
past USL
is 6.68%
LSL
Probabilityof a defect
below LSL
is 15.87%
ZBench Calculation (4) P (Defects) Total
Probability
of a defecttotal
is 22.55%
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Process Capability Pg 25
Question:P(Z> USL) = 6.68 %
P(Z< LSL) = 15.87%
P(Total) = 22.55%
If I threw all my
defects on one side,
how many StDevs
would fit between the
mean and the line
where the defects
start? Answer: Use
MINITAB for p=.2255
ZBench Calculation (5) ZBench
If we know the area that is equal to the TOTAL defects, we can find
its associated Z score ZBench (One number that tells it all).
10
864 1412
-1-2-3 3210
1610
C ( )
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Process Capability Pg 26
10
864 1412
-1-2-3 3210
1610
Total
probabilityof a defect
is 22.55%.
From Z table
or MINITAB
find Z = .75
11.5
0.75
Total probability of a defect is
22.55% (area under curve to right)
ZBench is 0.75, you can fit
+0.75 Standard Deviations
between the mean and thePoint of Interest.
ZBench Calculation (6) ZBench
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Short Term vs. Long Term
P V i ti O Ti
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Process Capability Pg 28
Process Variation Over Time
Lot 1
Lot 2
C
T Q
Lot 3
Lot 4
Lot 5
Short Term Studies
Long Term Study
Sh t T L T
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Process Capability Pg 29
Short Term vs. Long TermSamples Of Data
Short Term Sample
• Free from assignable (special) causes
- Represents random (common) causes only
• Group of “like things”
• Collected across a narrow inference space- Frequently it is data from one lot of material, on one shift, on one
machine, with one operator
Long Term Sample
• Consists of random and assignable causes
• Collected across a broad inference space
- Data from several lots, many shifts, many machines and operators
Sh t T S l O S b
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Process Capability Pg 30
Short Term Samples Or Sub-groups
• Machine produces 60 jobs/minute
- Method 1: Collect sub-groups consisting of five consecutive pieces
taken on the hour
- Method 2: Collect sub-groups consisting of five pieces, each one
taken an hour apart
• Which method would you expect to have the least amount of variation?
• Which is a better estimate of short term variation?
Method 1 would provide a good estimate of short term variation.
Sh t T L T Z
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Process Capability Pg 31
• ZST (ZBench short term) is defined as the industry benchmark
• Represents 1.5 shift in process relative to specification target
- The rationale for a 1.5 sigma shift is based on a number of studies
conducted by Motorola. It is intended to be a rule of thumb or a best
estimate of the difference between short term and long term
capability.
Short Term vs. Long Term Z
Without a calculation, assume a 1.5 shift relative to target.
ShiftSTLT ZZZ
Sh t A d L T V i ti
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Process Capability Pg 32
Short And Long Term Variation
Long term variation is the combination of short term
variation, process shifts, and long term process drifts.
L S L
T A R G
E T
U S L
T i m e
Short Term
Variation
Long Term
Variation
Shift A d D ift Wh D It H ?
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Process Capability Pg 33
Shift And Drift, Why Does It Happen?
• Recall how our process output, Y, can be represented as follows:
• In other words, the process output (Y) is influenced by several input
variables (Xs)
• Some inputs may vary over long periods of time, others over short
periods of time
• Graphically, this might look like…
),...,,( 21 n x x x f Y
E f f e c t
Time
An X with “short
term” influence
An X with “long
term” influence
OK So Wh Worr Abo t Shift And Drift?
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Process Capability Pg 34
OK, So Why Worry About Shift And Drift?
• The long term capability represents actual performance of the process
over “long” periods of time • What time period is considered long?
- Long term in this case doesn‟t directly mean time
- It represents a time period where all the input variables have had a
chance to influence the process• For example…
- Multiple shifts, seasons, departments, lines, designers, etc.
• So thus, there isn‟t a specific number of data points that make data set
“long term”
What if we could take out the effects of long term shift and drift? The
variation remaining would only be short term, or what MINITAB refers to
as “within.” To do that, we need to understand Rational sub-grouping.
What Is A Rational Sub group?
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Process Capability Pg 35
Rational sub-grouping separates variation due to inputs that influence
the process in the short term from those that influence the process in thelong term.
In other words, a Rational sub-group is a group of data selected where you
have tested to determine the variability within the group is smaller than
the variability between groups. This allows estimation of pure short term
variability and the long term drift of the process.
2
Total =
2
Within +
2
Between
What Is A Rational Sub-group?
Variation due to Xs
changing in the
short term
Variation due to Xs
changing in the
long term
Let‟s see how this looks graphically.
How Sub grouping Works
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Process Capability Pg 36
How Sub-grouping Works
Sub-grouping allows for the mathematical separation of between
and within sub-group variation.
10
5
0
5040302010
• Long term
or Between
sub-group
Variation
• Short term
or Within
sub-groupVariation
Sub-group 1
Sub-group 2
Sub-group 3
Sub-group 4
Sub-group 5
How Do I Form Rational Sub groups?
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Process Capability Pg 37
How Do I Form Rational Sub-groups?
• As we collect our data, we should “data tag” it to facilitate grouping
• We can organize our data into groups where the variation is most likely
common cause, for example:
- Machines
- Plant
- Invoice types- Department
- Operator
- Shift
In summary, if we choose our sub-groups well and include only common
cause variation in them, we get an estimate of short term capability and
insight into what we could work on to minimize the long term shift and drift.
Now an example…
10
5
0
5040302010
Dept A
Dept B
Dept C
Dept D
Dept E
Definitions: Process Capability (C )
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Process Capability Pg 38
Definitions: Process Capability (Cp)In Real Life
Consider the task of parking a car in your garage. If the garage door
opening is larger than the width of the car, it is possible to park thecar inside.
Definitions: C
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Process Capability Pg 39
Definitions: Cp
• A capability index is a single value that expresses the ability of a
process to meet its requirements – There are several of these metrics;one of the most used is Cp
• Cp is the ratio of the tolerance width to the process width
• Bigger is better
VOP
VOC
6
LSLUSL
pC TOLERANCE
WIDTH OF DISTRIBUTION
Definitions: C In Real Life
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Process Capability Pg 40
Definitions: Cpk In Real Life
Sometimes, the car COULD make it, but alignment prevents it.
Definitions: C
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Process Capability Pg 41
• To assess the process relative to the USL, or drivers‟ side, use
this formula
• On the other side, compare the process to the LSL
3
USL
C pu
3 LSLC pl
Definitions: Cpk
Definitions: C
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Process Capability Pg 42
• To express the performance of the process as a whole, we consider
the limit closest to the process mean (the minimum of Cpu and Cpl )This is Cpk
• Cp can also be calculated from Cpu and Cpl – It is the average of these two values (recall that Cp does not take the process center
into account)
2),(avg
pl pu
pl pu p
C C
C C C
+
),min( pl pu pk C C C
Definitions: Cpk
Relationship Between C And C
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C
C
p
pk
1
1
C
C
p
pk
1
0
CC
p
pk
1
1
LSL USL Some details...
Relationship Between Cp And Cpk
• Cp is positive – It is the ratio of two
positive numbers
• Cpk can be positive, zero
or negative
• When Cpk is zero, yield is 50%
• When Cpk is negative, yield is less
than 50%
• If the process is centered,
Cpk = Cp
LSL USL
LSL USL
Short Term Capability Indices
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LSL
Short Term Process Width
Design Width – Voice Of Customer
USL
T
+ 3s- 3s
Short Term Capability Indices
Min{Cpu, Cpl}
Cp =
Cpk =
Cpu =
Cpl =
(USL – LSL)
6*σshort term
(USL – µ)
3*σshort term
(µ – LSL)
3*σshort term
Long Term Capability Indices For
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+ 3s
USLLSL
Process Width – Voice Of Process
Design Width – Voice Of Customer
T
- 3s
Long Term Capability Indices For Process Performance
Pp =
Ppk =
Ppu =
Ppl =
Min{Ppu, Ppl}
(USL – LSL)6*σlong term
(USL – µ)
3*σlong term
(µ – LSL)
3*σlong term
C k Relationship To Z
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Cpk Relationship To Z
Point of Interest =USL
Mean
ZUSL = ?
Z =
Point of
Interest
Process Standard
Deviation
– Process
Mean
1
Cpk = 1 corresponds to 3 Sigma performance.
13
3
3
Z
3σ
USLCpk
OK I‟m Ready
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OK, I m Ready Let‟s Calculate Capability
• Before collecting data from a process for capability calculations, there
are some things we need to consider
- What type of data is available? (Attribute or variable)
- Is the process stable and in control?
- Is the process output normally distributed?
Let‟s discuss each of the above questions.
Is The Process Stable And In Control?
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Is The Process Stable And In Control?
0
0.2
0.4
0.6
0.8
1
1.2
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43
?
?
?
?
?
?
?
? ?
3 . . .how it will vary in
the future.
1Based on past experience . . .
2 . . .we can
predict, within
limits . . .
If a process is in control, we can use the data to predict it‟s behavior in
the future, within limits. How do we assess it‟s state of control?
Variation And Control – Review
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Variation And Control Review
• All processes can exhibit two types of variation
- Common Cause
• Completely random, natural variation of a process. Common cause
variation arises out the process, or out of the way the process or
organized and updated.
- Special Cause
• Non-random process variation. It is the result of an event, an
action, or a series of events or actions. It is localized in nature.
A process that is in control is free of Special Cause Variation.
How do we separate Special Cause from Common Cause Variation?
Separating Common And Special Causes
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Process Capability Pg 50
Separating Common And Special CausesThe Control Chart
10
9
8
7
6
5
4
3
2
1
0
0 5 10 15 20
Upper Control
Limit
Lower Control
Limit
Mean
Observation number
O b s e r v
a t i o n v a l u e
Region of Common
Cause Variation
Region of Special Cause Variation
Region of Special Cause Variation
NOTE: The data within the
“Region of Common Cause
Variation” is also evaluated
for runs, trends or patterns
that are indicators of Special Cause Variation
(even though no points fall
outside the control limits).
The Control Chart provides a simple means of
identifying Special Cause Variation… We‟ll return to this
later to fully discuss Control Charts and their application
to both process monitoring and process improvement.
MINITAB Capability Example
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Process Capability Pg 51
MINITAB Capability ExampleStability Check
Open File: Process Capability.mpj data column, “Distance 25”
Stat Control Charts Variables Chart for Individuals I-MR
MINITAB Capability Example
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Process Capability Pg 52
MINITAB Capability ExampleStability Check
Observation
I n d i v i d u a l V a l u e
12110997857361493725131
11.0
10.5
10.0
9.5
9.0
_ X=9.769
UC L=10.542
LCL=8.997
Observation
M o v i n
g R a n g e
12110997857361493725131
1.00
0.75
0.50
0.25
0.00
__ MR=0.290
UC L=0.949
LCL=0
1
11
I-MR Chart of Distance 25
Is The Process
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Process Capability Pg 53
Is The ProcessOutput Normally Distributed?
• Capability Analyses should be done with a distribution type that best
fits the data
• Most Capability Analyses assumes that the data are from a
Normal Distribution
• If we incorrectly assume our data follows a Normal Distribution, our
performance metrics (DPMO, Z, Cp, Cpk, Pp and Ppk) will be incorrectand thus misleading
• Thus, we need to perform a check of normality – Non-normal
Capability Analysis is addressed in the next module
• Recall from the Basic Statistics Module, the Anderson-Darling test
for normality
MINITAB Capability Example
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Process Capability Pg 54
MINITAB Capability ExampleNormality Check
Distance 25
P e r c e n t
11.010.510.09.59.0
99.9
99
95
90
80
7060504030
20
10
5
1
0.1
Mean
0.421
9.769
StDev 0.3029
N 125
AD 0.370P-Value
Probability Plot of Distance 25Normal
Stat Basic Stats Normality Test
Normally distributed data will appear on the plot as a straight line
If the p-value from the Anderson-Darling test <
alpha of .05, the data is not normal
MINITAB Capability Example
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Process Capability Pg 55
MINITAB Capability Example
Stat Quality Tools Capability Analysis Normal
Enter
• Single column: „Distance 25‟.
• Sub-group size: „Sub-group 25‟ or 5
• LSL: 9
• USL: 11
Note that we‟re grouping
the five consecutive shots
taken by a given operator
MINITAB Capability Output
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Process Capability Pg 56
Capab y Ou pu
10.810.510.29.99.69.39.0
LSL Target USL
Process Data
S ampleN 125
StDev (Within) 0.243594
StDev (Ov erall) 0.303479
LSL 9
Target 10
USL 11
Sample Mean 9.76944
Potential (Within) Capability
CC pk 1.37O v erall C apability
Pp 1.10
P PL 0.85
P P U 1.35
Ppk
C p
0.85
C pm 0.87
1.37
C P L 1.05
C P U 1.68
C pk 1.05
O bserv ed Performance
PPM<LSL 0.00
PPM>USL 0.00
PPMTotal 0 .00
Exp. Within Performance
PP M<LSL 792.39
PPM > U S L 0.22
PPMTotal 792.61
Exp. O v erall Performance
PP M<LSL 5616.09
PPM>USL 25. 08
PPMTotal 5641.18
Within
Overall
Process Capability of Distance 25
0.00 ppm Observed…
Simply a count of the data points
outside the spec limits converted to
PPM
Using the within sub-group variation only
(red distribution),
792 ppm fall outside the spec limits
Using the overall
variation (black
dotted distribution,
5640 ppm fall outside
the spec limits
ProcessData
Capability
estimates with
the betweensub-group
variation
removed
Capability
estimates withno sub-grouping
Alternatively, We Can Display
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Process Capability Pg 57
y, p yThe Z Values Directly
In the Options menu of
Stat Quality Tools Capability Analysis Normal
10.810.510.29.99.69.39.0
LSL Target USL
Process Data
S ampleN 125
StDev (Within) 0.243594
StDev (Ov erall) 0.303479
LSL 9
Target 10
USL 11
Sample Mean 9.76944
Potential (Within) Capability
C C pk 1.37
O v erall C apability
Z.Bench 2.53
Z.LS L 2.54
Z.USL 4.05
Ppk
Z.Bench
0.85
C pm 0.87
3.16
Z.LS L 3.16
Z.USL 5.05
Cpk 1.05
O bserv ed Performance
PPM<LSL 0.00
PPM>USL 0.00
PPMTotal 0.00
Exp. Within Performance
PPM<LSL 792.39
PPM>USL 0.22
PPMTotal 792.61
Exp. O v erall Performance
PPM<LSL 5616.09
PPM>USL 25.08
PPMTotal 5641.18
Within
Overall
Process Capability of Distance 25
Process Capability Sixpack
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Process Capability Pg 58
p y p
What about checking for a stable, in-control process? We can check the
state of control, normality and get capability metrics all in one displayStat Quality Tools Capability Sixpack Normal
S a m
p l e M e a n
252321191715131197531
10.00
9.75
9.50
_ _ X=9.7694
UCL=10.0963
LCL=9.4426
S a m p l e R a n g e
252321191715131197531
1.0
0.5
0.0
_ R=0.567
UCL=1.198
LCL=0
Sample
V a l u e s
252015105
11
10
9
10.810.510.29.99.69.39.0
10.510.09.59.0
Within
Overall
Specs
Within
StDev 0.243594
C p 1.37
C pk 1.05
CC pk 1.37
Overall
StDev 0.303479
Pp 1.1
P pk 0.85
Cpm 0.87
1
Process Capability Sixpack of Distance 25
Xbar Char t
R Chart
Last 25 Subgroups
Capability Histogram
Normal Prob Plot AD: 0.370, P: 0 .421
Capability Plot
OK, All Set
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Process Capability Pg 59
,Still A Few Unanswered Questions
• What if I don‟t have long term data? What do I do?
• What will MINITAB do with short term data?
• Can I estimate long term capability from short term data?
• What if I don‟t have rational sub-groups?
All I Have Is Short Term Data And No
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Process Capability Pg 60
Rational Sub-groups… Now What?
• MINITAB wants long term data!
• If your data is short term and there are no obvious sub-groups, you canestimate short term capability by entering a 1 for sub-group size
• When doing this the overall capability, Pp, Ppk, is then considered to be
an estimate of the short term capability
• What is the within called?
- In this case, the within capability is based on the moving range and
thus is an estimate of the VERY short term capability
• Can I estimate the long term capability from my short term estimate?
- You can roughly estimate your long term capability from your short
term estimate, but be cautious – You don‟t know how much your process shifts and drifts
- This estimate is as follows:
Z shift = 1.5 is common industry benchmark
ZLT = ZST – Z shift
Summary For Variable Data
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Process Capability Pg 61
y
• Process Capability is assessed by comparing the process distribution to
the customer specifications (VOC vs. VOP)• For Continuous Data, we calculate Cp, Cpk, Pp, Ppk
• Rational sub-grouping can be used to identify improvement opportunities
• MINITAB “likes” long term data – If you have actual long term
performance and it will estimate your short term performance based onyour chosen sub-groups
• MINITAB will ALWAYS return short term and long term capabilities
regardless of the data you supply it – You must interpret results based on
your knowledge of the data
• If you have only short term data, you can roughly estimate
long term capability
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Attribute Capability Analysis:MINITAB Six SigmaProduct Report Module
Case Study 1
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Process Capability Pg 63
yStep 1: The Business Case (Identifying CTS‟s)
The Business Case
• The Duffers Golf Association (DGA) is interested in issuing a credit cardwith their logo on it – They have been soliciting various banks to
determine how well these banks can handle their account
• LDB has made claims that it can satisfy all of the DGA needs –
Based on this limited information the DGA has been evaluating
LDB‟s performance
• The DGA is evaluating several branches from the LDB‟s
many locations
We will evaluate the capability of the Left Dogleg Bank (LDB) to provide a
credit card service
Case Study 1
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Process Capability Pg 64
yBackground Information
Internal to LDB and for the purposes of this Case Study, issuing a credit
card is a four step process that entails:1. Data entry for credit card application
2. Background credit checks
3. Customer setup in the system
4. Issue the card
Case Study 1
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Process Capability Pg 65
Background Information
Within each step of the process, there are more detailed steps that allow
the applications to be converted into a credit card. Listed below are someof the detailed steps:
1.Data entry for credit card application
• Enter various customer demographic information
• Identify bank account numbers
2.Background credit checks• Verify savings
• Debt analysis
3.Customer setup in the system
• Demographic information
• Establish credit limits
4.Issue the card
• Create the card
Flow Chart Of Our Case Study
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Process Capability Pg 66
For Each Branch
Data Entry for
Credit
Application
• Demographics• Acct. #‟s
• Salary History
Credit Checks
• Verification of
Savings
• Ver. of Salary• Credit Report
• Debt analysis
Set person up
in system
• Demographics
• Credit Limits
Supplies
Issue Card
• Create Card
• Mate to mailer info
• Mail• Phone Verification
ClerkINSPECTOR
DGA Member
Received card
and activates
DGA Member
Customer AppliesLeft Dog-Leg Bank
DGA Corporate
evaluates satisfaction
of members
Detailed Flow Chart
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Process Capability Pg 67
(A Subset Of A Credit Card Process)
Start
Receive
Customer
Application
Selectappropriate
Credit
Bureau and
Request info
ReconcileCredit report
with
Applicant file
Does
the report
reconcile?
Was
Applicant
info entered
correctly?
End
Establish
person in
System
End
Reject Applicant
Walk to 3rd
floor and
check
against
Customer
application
Does
applicant meetrequirements?
Yes
No
Yes
No End
Call Credit
Bureau
Yes
Correct info
in Applicant
file
No
X's
- Applicant file
- List of Bureaus
- Computer System
Y's
- Selected
Bureau
- A Requested
Credit Report
X's
- Applicant file
- Requested
Credit Report
Y's
- Comparison of
Report and file
X's
- Comparison of
Report and file
Y's
- Reconciled
Report
Y's
- Identified
Gap
- Applicant
file
X's
- Identified Gap
- Applicant file
- Customer Application
Y's
- Checked Gap
against Application
X's- Reconciled
Report
- List of
Requirements
X's
- Identified Gap
- Applicant file
- Customer Application
Y's
- Corrected file
Step 2: Define Performance Standard
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Process Capability Pg 68
The Spec
• If you don‟t know what makes something good or bad, how can youmeasure the problem in terms of defects (DPMO)?
• If the definition of what makes a defect (the specification) is not in the
same units of measure as the selected CTS from Step 1, you have the
wrong spec
• The definition needs to be crystal clear and brief
• Does your customer agree with your spec?
• For our case a defect is any step (operation,) on any card, with anything
missing or incorrect – Each card has 16 Steps
What is a “good” Y? What is a “bad” Y?
Step 3: Validate Measurement System
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Process Capability Pg 69
Can I See?
• If you can‟t measure something, how do you know where you are,where you have been or where you are going?
• If your Measuring System is incapable, STOP and FIX IT
before proceeding
• Note: MSA must be done on any and all defects you wish to count(watch out if you have a visual inspection of six characteristics)
MUST be done before evaluating capability
Is it really Y?
Step 4: Establish Baseline Capability
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Process Capability Pg 70
Process Capability: A measurement of the capability of the process to
deliver product or services that meet the needs of the customer as definedby the product/service specifications – The most common
Six Sigma measurements of process capability are DPMO and ZBench
Baseline
• I know what needs to be fixed (Step1), what defines it as good or bad
(Step 2) and I can accurately measure it (Step 3) so:
- Now I can say how my process is performing in terms of long and
short term Z and DPMO
- I improve from here
• Common tools: Six Sigma “Product Report” for Attribute Data
What is your ability to make “good” Ys?
Product Capability Report Setup(A ib D )
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Process Capability Pg 71
(Attribute Data)
Total number of
Units (25 cards)
Number of
Opportunities for
defect in each unit
Number of
Defects at the
opportunitylevel
Descriptor:
In this case the
name of thebranch
Product Capability Report Dialog Box(Att ib t D t )
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Process Capability Pg 72
(Attribute Data)
MINITAB Command: Six Sigma Product Report
Product Capability Report Output(Att ib t D t )
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Process Capability Pg 73
Eagle 72500.0 1.500 2.957 0.29993229 25 16 * 29 25 400 1.16
Total 72500.0 1.500 2.95729 400
C omponent DPMO Z.Shift Z.ST YTPDefs
O bs
Units
O bs
Unit
perOpps
Cmplx Defs
A dj
Units
A dj
Opps
Total A dj
DPU
Report 7: Product Performance
(Attribute Data)
Data we entered
Total Opportunities
DPU = Defects Per Unit.
This is the average number
of Defects for every Credit
Card
Z score Short Term (calculated
from the DPMO Long Term andshifted 1.5)
DPMO = Defects Per Million Opportunities.
This is the average number of Defects for
each opportunity multiplied by a million.
Note as MINITAB assumes that Attribute
Data is collected “Long Term”, this is
assumed to be Long Term DPMO = “What
the Customer Feels”
Product Capability Report Additional Output(Att ib t D t )
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Process Capability Pg 74
(Attribute Data)
Z.Bench (Short-Term)
Z . S
h i f t
76543210
3
2
1
0
Technology
Zone of Average
Control
Typical
Zone of
Performance
Six Sigma
Report 8B: Product Benchmarks
Z.Bench (Short-Term)
D P M O
6543210
1000000
100000
10000
1000
100
10
1
Report 8A: Product Benchmarks
A Few Discussion Points
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Process Capability Pg 75
• Process should be stable – This implies that the process is not changing
over time creating significantly different defect rates- May be checked with daily Run Chart of defect rate or by use of an
Attribute Control Chart (more on this later)
- What should we do if our process is not stable?
• We must stabilize first otherwise we do not even know what our baseline is
• As was stated earlier, MINITAB assumes that due to the large amount of
data generally collected for Attribute Data Analysis, the collected data is
assumed to be long term – What the customer actually feels
Some Other Uses Of The ProductC bilit R t
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Process Capability Pg 76
Capability Report
• What if we wished to drill down further to see what department was
making the most errors so that we could target our fix?- See following slides to view a drill down of the Eagle Branch Data
by department
Drill Down
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Process Capability Pg 77
• CAUTION: The prior slides showed us getting the Process Capability at
the branch and company levels• In a real project, you will frequently have sufficient data to measure the
capability at a department level (four departments) or even the operation
level (all 16 sub operations in the total process)
• This “more targeted” evaluation may lead to strong hints as to where to
look for improvements
• As an example we will look at the same “Eagle Branch” data broken down
by the four departments – This time we will use credit cards
as units and each process step (operation) as an opportunity.
Capability Of Eagle By Department
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Process Capability Pg 78
Opps
Defs Units Unit Cmplx Defs Units Opps DPU DPMO Z.Shift
A dj
Z.ST YTP
Data Entry 8 25 4 * 8 25 100
O bs
0.32 80000.0 1.500 2.905 0.726149
C redit C heck 15 25 6 *
O bs
15 25 150 0.60 100000.0 1.500 2.782 0.548812
Set Up A ct 1
per
25 2 * 1 25 50 0.04 20000.0 1.500 3.554
A dj
0.960789
Issue C ard 5 25 4 * 5 25 100 0.20
A dj
50000.0 1.500 3.145 0.818731
Total 29 400 72500.0 1.500 2.957
Total
C omponent
Report 7: Product Performance
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Variable Capability Analysis:MINITAB Six SigmaProduct Report Module
Case StudyCatapult Distance
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Process Capability Pg 80
Catapult Distance
Let us revisit the Catapult File: 2270MB00a_Process Capability.mpj
As before we will evaluate capability of hitting a target of 10 inches with aLSL of 9 and a USL of 11
• Open MINITAB file
• Run Six Sigma Process Report
• Fill in as per next slide
Process Report Dialog Box
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Process Capability Pg 81
• For an initial look at the data we will
use the default which is the first tworeports. These will help us verify that
we have collected enough data and
assess the stability of
the process.
• Report two also contains information
to assess the capability of theprocess but we will check data
adequacy and stability first.
• Report 3 provides descriptive
statistics but we should check
stability first.
• Reports 4 – 6 are useful
diagnostic reports for
troubleshooting problems.
Report 1 – Summary
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Process Capability Pg 82
10.810.510.29.99.69.39.0
LSL USL
24222018161412108642
1.0000E+06
10000.000
100.000
1.000
0.000
Date:
Low er S pec: 9Nominal:
O pportunity :
Reported by :
Project:
Department:
Process:
C haracteristic:
Units:
U pper S pec: 11
A ctual (LT) Potential (ST)
Process Performance Process Demographics
A ctual (LT) Potential (ST)
Sigma
(Z.Bench)
DPMO
2.53
5641.2
3.94
40.4
Process Benchmarks
Report 1: Executive Summary
Actual process:
• Not perfectly centred• Long term variation
Process at entitlement:
• Perfectly centred
• Short term variation
Cumulative estimates of
DPMO:
• Short term
• Long term
Critical Metrics:
• ZST
• DPMOLT
Report 2
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Process Capability Pg 83
252321191715131197531
10.00
9.75
9.50
_ _ X=9.7694
UCL=10.0963
LCL=9.4426
Subgroup
252321191715131197531
0.4
0.2
0.0
_ S=0.2290
UCL=0.4783
LCL=0
ST
4.11 4.05
Z.LSL 4.11 2.54
Z.Bench 3.94 2.53
Z.Shift 1.41
LT
1.41P.USL 0.0000202 0.0000251
P.LSL 0.0000202 0.0056161
P.Total 0.0000404 0.0056412
Mean
Yield 100.00 99.44
DPMO 40.4 5641.2
Cp 1.37 *
Cpk
10
1.05 *
CC pk 1.37 *
Pp * 1.10
Ppk *
9.76944
0.85
StDev 0.244 0.303
Z.USL
119
10.73089.26922
119
10.67998.859
Xba r and S C har t
Process Tolerance
Specifications
Potential (ST) Capability
Process Tolerance
Specifications
A ctual (L T ) C apabilit y
Data Source:
Time Span:
Data Trace:
Capability Indices
Report 2: Process Capability for Distance 25
Process statistics and
capability metrics:
• Short term• Long term
X bar S Chart – Stability
Capability plots:
• Short term
• Long term
Interpretation Of Data
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Process Capability Pg 84
• Short term mean is the center
of the process specs• Short term Standard Deviation is
a measure of the Pooled or
“average” within
sub-group variation
• Short term ZBench is the “short
term” Sigma value of the process.
How many Standard Deviations
can fit between the short term
mean and the spec if all defects
are on one side?
• Long term mean is actual mean of
the collected data• Long term Standard Deviation is a
measure of the overall variation of
the process
– What the customer feels
• Long term ZBench is the “long term”
Sigma value of the process. How
many Standard Deviations can fit
between the long term mean and the
spec if all defects are on one side?
Z shift is the shift and drift difference between
Short Term ZBench and Long Term ZBench.
Interpretation(Cont‟d)
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Process Capability Pg 85
(Cont d)
• P. USL = Probability of a defect above the Upper Spec
• P. LSL = Probability of a defect below the Lower Spec
• P. Total = Total probability of a defect whether above the Upper Spec
or below the Lower Spec
• Yield = % good
• PPM = DPMO
• Cp and Cpk = short term indices
• Pp and Ppk = long term indices
Summary Takeaways
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Process Capability Pg 86
• Long term process is centered on mean of actual data and has a
variation associated with all the data – This is what the customer feels• Short term process is centered artificially at the center of the tolerance
and has a variation that is related to the Pooled (“average”) Standard
Deviation of a sub-group – This is the best we could do, if we centered
our process and held everything as constant as possible
• Six Sigma projects should always report, as a minimum, DPMO long
term (what customer feels) and ZBench short term (Entitlement – An
estimate of what we should be able to do with our present process)
Steps In Establishing Process Capability
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Process Capability Pg 87
• Pick out variable for study (Y)
• Set the process to run in “standard” mode
• Record values for key input variables
• ID potential variables for rational sub-grouping (variable data only)
• Run the process (no tweaking!)
• Take notes
• Record key output variable values
• Calculate Capability based on data type
- Variable – Review normality, stability, control then calculate capability using
Capability Analysis and Capability Sixpack- Attribute – Calculate capability using Six Sigma Product Report
• If sub-grouping was done successfully, review key input variables that changed
between groups and determine plan to control (variable data only)
Calculating Capability
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Process Capability Pg 88
All processes can be described by the Z
score, making process comparisons easy.
Attribute Data Variables Data
Six Sigma Product ReportCapability Analysis and Six-pack
and/or Six Sigma Process Report
Sigma (Z)
DPMO DPMO
Key Learning Points
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Process Capability Pg 89
•
•
•
•
•
Objectives Review
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Process Capability Pg 90
The participant should be able to:
• Explain where Capability Analyses fit into the12 Step Breakthrough Strategy
• Compute capability statistics with Variable Data
• Compute capability statistics with Attribute Data
• Discuss the concepts of stability as a prerequisite for Capability Analysis
• Utilize MINITAB for Capability Studies
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