Process Capability
ASQ Section 1404
Ken Fredryk
March 10, 2015
Process Capability
We continually gather data on our process but can we
emphatically answer this question:
“How well can the process produce products to meet
costumer specifications?”
Gathering and analyzing data to answer that question
is called a Capability Study
Process Capability Definition
 The degree to which a process is able to meet
defined tolerance limits (aka specification limits)
 A measurable property of a process related to
customer specifications and process output
• Based on statistical evaluation of a process to
measure inherent variability compared to the
specification/tolerance limits
Process Capability Components
 Two factors of process capability
1. Measurement of inherent process characteristics
‒ Location of the mean
‒ Variation in terms of standard deviation
2. Specification Limits
 Expressed as a process capability performance index
• CP or CPK
• PP or PPK
Process Capability – Another View
Quantifiable comparison of Voice of Customer
(spec limits) to Voice of the Process (control limits)
Most process measures have some target value and
acceptable limits of variation around the target
The extent to which the “expected” values fall within
tolerance limits determines how capable the process is
of meeting its requirements
Process Capability
Consider key measures of process performance in:
• Help Desk Responsiveness
• Customer Queue Time
• Service Cost / Order
• Revenue / Employee
• Proposal Acceptance Rate
• Service Complaints
• On-Time Delivery
• Days On-Hand Inventory
Why Conduct a Capability Study?
 Process capability is a tool evaluate how well a
process can produce products or services that meet
customer specifications
 May be required to a secure a contract
 Validate new equipment
 Provides direction about how to improve process
performance
Uses of Capability Analysis
 Performed on existing processes as a means of
establishing a baseline of current operations
 Provide verification that processes meet contractual
requirements
 When done periodically is a means of monitoring
deterioration of a process (system, equipment,
environment, etc.)
Rationale of a Capability Study
Optimize process performance by minimizing
variation and centering around the target
Process target
from this
Process target
to this
m
m
Non-Capable Process
Capable Process
Not a silver bullet!!
Causes of Low Process Capability
Excess variation resulting from:
• Process design
‒ Poor design, lacking SOP, people, equipment,
training, measurement, material
‒ Remember the 6 M’s
• Unreasonably tight specifications
• Process not centered
Process Capability Requirements
Type of data determines how to conduct the study
• Attribute/discrete data
• Continuous/variable data
Process must be stable and in control
Need to identify distribution characteristics of data
• CP and CPK are sensitive to data normality
Reliable measurement system
• Measurement system must be verified prior to
conducting a Capability Study
‒ aka MSA
Process Capability – 30,000 ft. View
What Type of Data
Do You Have?
Attribute Data
Variables Data
Collect Data
on Process
Collect Data
on Process
Analyze Data
in Excel
Analyze Data
in Minitab/Excel
State Capability
DPU, Sigma Quality
Level, PPM
State Capability
DPU, Sigma, PPM,
Cp, Cpk, Pp, Ppk
Process Stability Is Crucial
 Stability is needed for process capability
• Process output will be predictable
• Nearly all outcomes (99.7%) will lie within ±3s
of the process mean for Normal Data
• Capability ratios will be meaningful
 When there is no stability, there is NO capability
• Process output will not be predictable
• The rule of ±3s does not apply
• Capability ratios will be meaningless
A Stable Process May Not Be Capable
The process has too much variation
• Without decreasing process variation, some out
of specification product is inevitable
The process is not centered
The specification limits are too close together
• The process does not have enough room to move.
Without a decrease in process variation or a
widening of the specifications, some out of
specification product is inevitable
Voice of the Process
Voice of the Customer
Process Capability Ratios
“Merge the Voices”
Normal Distribution
The area under sections of the curve can be used to
estimate the cumulative probability of a certain event
occurring
m
Process Capability: The Two Voices
99.73% of values
-3s
+3s
Natural Process Variation
m
LSL
USL
Process Capability
Voice of the Process
Always estimated by (±) 3 standard deviations
from the mean (the “Natural Process Limits”)
Therefore, six standard deviations in total
Visualizing Process Capability
Examples of Capable Processes
LSL
USL
LSL
USL
m
3s
m
3s
Process is barely capable as long as it
remains centered within the
specification limits
3s
3s
Process is capable and will remain so,
even if the process average is moved.
Often called process shift
Examples of Non-Capable Processes
LSL
USL
m
3s
3s
Product produced
beyond both
upper and lower
spec limits.
LSL
USL
3s
m
3s
Product produced
above the
upper spec limit.
LSL
3s
USL
m
3s
Product produced
below the
lower spec limit.
Capability Study Options
Process Data for Co2
15
UCL=14.18
IndividualValue
14
13
X=12.64
12
LCL=11.10
11
10
9
0
50
100
150
Observation Number
Process Data for Co2
15
UCL=14.18
IndividualValue
14
13
X=12.64
12
LCL=11.10
11
10
9
0
50
100
Observation Number
150
A short-term capability study
covers a relative short period of
time during which extraneous
sources of variation have been
excluded. (Guideline:
30-50 data points.)
A long-term capability study
covers a longer period of time in
which there is more chance for a
process shift. (Guideline: 100200 data points.)
Steps of a Capability Study
1. Set the process to run as it normally would
and record the values of the input variables
2. Execute the process over a period of time suitable
3. to the purpose of the study
• Have all sources of variation been accounted for?
3. Take plenty of notes
4. Measure and record values of the output
Steps of a Capability Study (continued)
5. Conduct Analysis (e.g. Minitab, Excel) to study:
• Stability
• Normal Plot
• Histogram
• Capability Ratios
6. Develop an action plan based on diagnostics.
Sigma Level - s
Definition:
 The number of total standard deviations (+/–) that
would fit within the spec limits
• For example, a 3s level would mean 6 standard
deviations can fit within the specification limits
 Sigma Level is a measure of the process performance
Compare % Defective
With and Without Shift
Calculated using a “shift” factor
Calculated as the area under the curve
Process Capability versus PPM Defects
 s level:
• A 6s level is  6
standard deviations or
sigmas from the mean
• This would be 12
standard deviations, or
12s!
• PPM: number of defects
per million opportunities
Compare PPM Defects
With and Without Shift
Graphical View of Sigma Levels
LSL
USL
LSL
USL
+1 s
+4 s
+2 s
+5 s
+3 s
m
+6 s
m
Process Capability – Cp
Ratio of total variation allowed by the specification to
the total variation actually measured from the process
Typical targets for Cp are greater than 1.33 (or 1.67 for
safety items)
If Cp < 1, then the variability of the process is greater
than the specification limits
Cp takes into account only process spread and not
location
Process Capability – Cp
Cp = Allowable variation (spec width) OR Cp = USL – LSL
6s
Process Variation
• Typical values:
– Marginal Cp = 1.00
– Acceptable Cp=1.33
– Good Cp = 1.67
– Six Sigma level Cp = 2.00
One-Sided Capability Ratios
 If a process has just one spec (either USL or LSL), a
one-sided capability ratio (CPU or CPL) is calculated
• It takes into account process spread and location
CPU = USL – Xbar
3s
CPL = Xbar - LSL
3s
 Typical Values (when the “shift” is taken into
consideration)
– Marginal CPU or CPL = 1
– Good CPU or CPL = 1.33
– Six Sigma CPU or CPL = 1.5
Centered Capability Ratio, CPK
 If the spec is two-sided, the centered capability
ratio can be calculated
• It is the smaller of CPU and CPL
CPK = Minimum (CPU or CPL)
Relationship Between CP and CPK
CPK = CP (1-K)
• K  0 is a “shift factor”
• CPK is always less than, or equal to CP
• Typical values (when the “shift” is
taken into consideration):
– Marginal CPK = 1
– Acceptable CPK = 1.33
– Six Sigma CPK = 1.5
m
Negative Cpk
LSL
USL
• Negative Cpk occurs
when the mean is
outside the USL or LSL
e.g. Cpk = -0.5
3s
3s
Process mean is outside the
specification limit
Capability versus Performance
• Capability Ratios (CP and CPK)
– use a short-term estimate of sigma (s) obtained from the withinsubgroup variation
– show what the process would be capable of if it did not have shifts and
drifts between subgroups
• Performance Ratios (PP and PPK)
– use a long-term estimate of sigma (s) obtained from within-subgroup
plus between-subgroup variation
– Show what the overall variation is
• Performance ratios will be worse (smaller) than the
corresponding capability ratios if the process has shifts and
drifts
The Dynamic Process
LSL
USL
Process Capability
Process Performance
Over time, a process tends to shift by approximately 1.5 s
Capability Example
Sample data of pin diameters
• Data collected over 27 days
• Sub-group size 5
• Tolerance is 0.1587 – 0.20885
P G A Approach
(aka KFred rule of thumb: Always do PGA)
Capability Example Data
Sample1 Sample2 Sample3 Sample4 Sample5 Subroup
1
0.175
0.174
0.179
0.189
0.184
2
0.194
0.192
0.189
0.189
0.18
3
0.199
0.197
0.195
0.172
0.182
4
0.184
0.18
0.179
0.185
0.189
5
0.177
0.175
0.192
0.187
0.187
6
0.179
0.177
0.189
0.19
0.177
7
0.18
0.187
0.179
0.195
0.187
8
0.18
0.179
0.192
0.179
0.189
9
0.184
0.184
0.195
0.187
0.185
10
0.17
0.184
0.174
0.179
0.187
Control Chart by Subgroup
Capability Analysis 1
Normality Test
Capability Analysis by Subgroup
Capability Analysis 1
Capability Analysis 1
Capability Analysis 2
Capability Analysis 2
Excel Based
X Bar R Chart Limits
UCL X
0.189891
LCL X
0.177709
UCL R
0.022325
X Median Chart Limits
UCL X
0.193343
LCL X
0.178776
UCL R
0.022325
Pre-Control Limits
Upper PC line
0.196325
Lower PC line
0.171275
# of Samples
# of Sub Groups
Sub Group Size (n)
Max Value
Min Value
Range
X Double Bar
R Bar
St. Dev. (Rbar/d2 )
St. Dev. (Indiv.)
Normality
Process Data
135
USL
27
LSL
5
UCL X
0.197
LCL X
0.175
UCL R
0.022
Z USL
0.186059
Z LSL
0.01
% Above USL=
0.004538
% Below LSL=
0.004845
% In Spec=
Normal
% Out of Spec=
Cap_Study_.xls.xlsx
0.20885
0.15875
0.1921498
0.1799687
0.022325
4.7039663
-5.63658
0.0%
0.0%
100.0%
0.0%
Potential (Rbar/d2 ) Capability
Cp
1.84
CpU
1.67
CpL
2.01
Cpk
1.67
Cr
0.54
Potential (Indiv.) Capability
Pp
1.72
PpU
1.57
PpL
1.88
Ppk
1.57
Pr
0.58
Capability Analysis Comparison
Original Data (Non-Normal)
Minitab
Potential (Within)
Capability
Cp
1.77
CPL
1.94
CPU
1.61
Cpk
1.61
Overall Capability
Pp
1.72
PPL
1.88
PPU
1.56
Ppk
1.56
Transformed Data
Minitab
Potential (Within)
Capability
Cp
1.77
CPL
1.48
CPU
2.06
Cpk
1.48
Overall Capability
Pp
1.71
PPL
1.43
PPU
2.00
Ppk
1.43
Original Data (Non-Normal)
Excel
Potential (Rbar/d2 ) Capability
Cp
1.84
CpU
1.67
CpL
2.01
Cpk
1.67
Cr
0.54
Potential (Indiv.) Capability
Pp
1.72
PpU
1.57
PpL
1.88
Ppk
1.57
Capability Analysis Comparison
Original Data Subgroup Size 5
Potential (Within)
Capability
Cp
1.77
CPL
1.94
CPU
1.61
Cpk
1.61
Overall Capability
Pp
1.72
PPL
1.88
PPU
1.56
Ppk
1.56
Original Data Subgroup Size 1
Potential (Within)
Capability
Cp
1.92
CPL
2.09
CPU
1.75
Cpk
1.75
Overall Capability
Pp
1.72
PPL
1.88
PPU
1.57
Ppk
1.57
Results
Is the process stable? YES
Are the data normally distributed? No
What is the standard deviation (within) of the
process?
Approximately 0.0047
What are CP and CPK? 1.77 and 1.61, respectively
What are the PPM (use the “within” performance)?
Approximately 1
But what if we have
only attribute data?
Attribute & Continuous Data Comparison
Attribute
Continuous
Process Capability from Count Data
 Process capability for count data is assessed
differently from continuous data
 Summary of process capability using count data
• Control Chart (I-MR)
• DPU, DPMO and Sigma Level metrics
• Ability to meet customer requirement
 Process must be stable; otherwise, there is no
capability
Attribute Capability Example
• Customer spec is sigma quality level > 3.5
• Last month 16,810 units were produced over 18 days
• 231 were defective
• Did we meet customer requirements?
Attribute Capability Analysis
• Does the control chart show a stable process?
• What are DPU?
• What are DPMO?
• What is the sigma level?
• Does the process meet customer requirements?
Attribute Capability Analysis
Date
8/1/1998
8/2/1998
8/3/1998
8/4/1998
8/5/1998
8/6/1998
8/7/1998
8/8/1998
8/9/1998
8/10/1998
8/11/1998
8/12/1998
8/13/1998
8/14/1998
8/15/1998
8/16/1998
8/17/1998
8/18/1998
No. Leaks
28
7
11
27
11
5
8
21
16
21
7
23
1
5
11
15
10
4
No. Brakes
770
890
930
960
800
1170
1010
990
990
1010
630
1010
650
1000
1000
990
1000
1010
Avg. Defect Rate
I and Chart
MR Chart for
RateRate
I and MR
for
0.04
3.0SL=0.03989
0.03
0.02
X=0.01382
0.01
0.00
-0.01
-3.0SL=-0.01224
-0.02
Subgroup
0
10
20
3.0SL=0.03202
0.03
0.02
0.01
R=0.009801
0.00
-3.0SL=0.00E+00
Is the process stable?
What Are the Defects per Unit (DPU)?
Formula:
DPU = Total # Defects
Total Units Produced
Example:
DPU = 231 = 0.0137418
16810
What Are the Defects per
Million Opportunities (DPMO)?
Formula:
DPMO =
DPU X 1,000,000
Total Opportunities for a Defect in One Unit
Example:
DPMO = 231 (1M) = 13,741.8
16810
What Is the Process Sigma Level?
Procedure:
Use the Excel file sigmacalc.xls
ATTRIBUTE SIGMA CALCULATOR
Characteristic Under Study:
# of Units
Opportunity For Defects / Unit
Defects
DPU
DPMO
SIGMA (With Shift)
Brakes
16810
1
231
0.01374182
13741.82035
3.71
Another Example Attribute
Capability Study
Process: Bank Loan Application Review
Objective: Determine the capability of completed
loan applications
 Inspect completed loan applications for defects
• What is a defect?
‒ Need operational definition of a defect
• Validate measurement system
– Conduct attribute MSA
• Tally defects
• Calculate sigma level
Another Example Attribute
Capability Study
Process: Bank Loan Application Review
500 random applications reviewed
5 fields per form are required to be completed by
the applicant
Operational definition of a defect
• Missing, illegible or wrong format fields
260 defects identified
Capability Summary
 Capability ratios are used to compare the VOC (specs)
to the VOP (natural process limits)
 For a capability ratio to be a good predictor of future
performance, the process must be stable
 The two key ways to improve process capability are to
reduce variation and to improve centering
 A capability ratio should never be interpreted without
a histogram of the process to ensure normality
 Because these indices are unit-less, you can use
capability statistics to compare the capability of one
process to another
References
Dean Cristolear
• Cap_Study.xls
iSixSigma.org
6Sigma.org
ASQ.org
• Six Sigma Forum Magazine May 2005:
–Capability Indexes: Mystery Solved