This document provides an overview of process capability analysis. It defines key terms like Cp, Cpk, CPU and CPL. Cp measures the width of the process relative to specifications. Cpk accounts for dynamic shifts in the process mean. The document uses examples and metaphors to illustrate the concepts and provides guidance on interpreting process capability output. It also outlines how to conduct process capability studies in Minitab and how to develop an action plan to improve incapable processes.

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UNCLASSIFIED / FOUO
National Guard
Black Belt Training
Module 27
Process Capability
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CPI Roadmap – Measure
8-STEP PROCESS
6. See
1.Validate 2. Identify 3. Set 4. Determine 5. Develop 7. Confirm 8. Standardize
Counter-
the Performance Improvement Root Counter- Results Successful
Measures
Problem Gaps Targets Cause Measures & Process Processes
Through
Define Measure Analyze Improve Control
TOOLS
•Process Mapping
ACTIVITIES
• Map Current Process / Go & See •Process Cycle Efficiency/TOC
• Identify Key Input, Process, Output Metrics •Little’s Law
• Develop Operational Definitions •Operational Definitions
• Develop Data Collection Plan •Data Collection Plan
• Validate Measurement System •Statistical Sampling
• Collect Baseline Data •Measurement System Analysis
• Identify Performance Gaps •TPM
• Estimate Financial/Operational Benefits •Generic Pull
• Determine Process Stability/Capability •Setup Reduction
• Complete Measure Tollgate •Control Charts
•Histograms
•Constraint Identification
•Process Capability
Note: Activities and tools vary by project. Lists provided here are not necessarily all-inclusive. UNCLASSIFIED / FOUO 2

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Learning Objectives
 Learn prerequisites for conducting process capability
studies
 Learn how Cp and Cpk are calculated and how to
interpret the Minitab output
 Learn how to handle continuous and attribute data
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Process Capability – What Is It?
 Most measures have some target value and acceptable limits of
variation around the target – usually set by the customer
 The extent to which the “expected” values fall within these
customer specification limits determines how capable the
process is of meeting its requirements
 Consider key measures of process performance in:
 Help Desk Responsiveness  Job Acceptance Rate
 Customer Queue Time  Service Treatment (complaints)
 Service Cost / Order  On-Time Delivery
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Process Capability – Cp
 Ratio of total variation allowed by the specification to the
total variation actually measured from the process
 Use Cp when the mean can easily be adjusted (i.e.,
transactional processes where resources can easily be added
with no or minor impact on quality) AND the mean is
monitored (so process owner will know when adjustment is
necessary – doing control charting is one way of monitoring)
 Typical goals 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
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Process Capability – Cp
Allowed variation (spec.) (USL - LSL)
Cp  or Cp 
Normal variation of the process 6
99.7% of values
-3 +3
Process Width
LSL T USL
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A Metaphor for Cp – Parking Vehicles 1
Cp measures the width of the vehicle
in the street and compares it to the
width of the parking place without
parking the vehicle.
Cp < 1
Cp ≈ 1
Cp >> 1
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Process Capability – Cpk
 This index accounts for the dynamic mean shift in
the process – the amount that the process is off
target
USL  x x  LSL 
C pk  Min  or
 3σ 3σ  
 Calculate both values and report the smaller number
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Process Capability – Cpk, CPU, CPL
Most common calculation of Process Capability
Ratio of the range between the sample mean and the
nearest specification to 3 standard deviations.
Use when the mean cannot be easily adjusted (i.e., Cycle
times, customer satisfaction indices, etc.)
Typical goals for Cpk are greater than 1.33 (or 1.67 if
safety related)
For Cpk Std. Deviation estimates use:
 Rbar/d2 [short term] (calculated from Xbar-R chart)
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A Metaphor for Cp – Parking Vehicles 1
+/- 3 σ
(Voice of Process)
Cp ≈ 1.3
+/- 3 σ
(Voice of Process) Voice of Customer
+/- 3 σ
(Voice of Process)
For Cp, it doesn‟t matter where the process is relative to the specifications,
only the width of the process to the width of the specifications.
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A Metaphor for Cpk – Parking Vehicles 2
Cpk ≈ 1.3 +/- 3 σ
(Voice of Process)
Cpk ≈ 1.3 : the process has room to move before exceeding a
customer specification. In other words, at least the driver and/or
the passenger can get out of the HMMWV .
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A Metaphor for Cpk – Parking Vehicles 2
+/- 3 σ
(Voice of Process)
Cpk ≈ 0
Specifications
(Voice of Customer)
Cpk ≈ 0: The center of the process is on (or equal to) a customer
specification (either side)!
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A Metaphor for Cpk – Parking Vehicles 2
Specifications
(Voice of Customer)
Cpk ≈ -1
+/- 3 σ
(Voice of Process)
Cpk ≈ -1: The center of the process is outside the customer specifications
(either side)!
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Uses of Capability Analysis
 Performed on existing processes as a means of
establishing a baseline of current operations (so it‟s
possible to tell when improvement has occurred)
 When done periodically, is a means of monitoring
change (good or bad) of a process for whatever
reason (system, personnel, environment, etc.)
 Can be done on any process that has a target spec.
established (target spec. is needed for the values in
numerator), and has a capable measuring system
(needed for valid values in denominator)
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Process Capability – CPU
 CPU indicates capability against an Upper
Specification Limit. In the next example, the
average delivery time of a Pizza Company is within
the 30 minute requirement. However, the histogram
shows that quite a few deliveries are exceeding the
30 minute upper spec. limit
 The CPU figure of 0.139 confirms that the process is
incapable (<1)
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Process Capability – CPU
USL- X
Cpu=
3s
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Minitab Exercise
 Open Minitab file: Exercise 235.mtw
 Click Stat>Quality Tools>Capability Sixpack>Normal
Note: This exercise is based on
a different dataset than previous
slides so different, unrelated
results can be expected.
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Minitab Exercise (Cont.)
1. Double click on
C-5 Delivery Time to
Place it in the box for
Single column
2. In the Subgroup size
Box, type a 1 since our
Sample size is one
3. For Upper Spec type
in 30 minutes (given)
4. Click on OK
Note: For Process Capability you must have at least 1 Spec Limit
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Minitab Exercise (Cont.)
Process Capability Sixpack of Delivery Time
I Chart Capability Histogram
40 USL
UCL=37.71
On both the I ChartS L 30 S pecifications
Individual Value
U
30
_
X=29.12 and the Moving Range
Chart, the points are
20
1 28 55 82 109 136 163 190 217 244
LCL=20.53
randomly distributed
24 26 28 30 32 34 36
Moving Range Chart
between the control
Normal Prob Plot
10 UCL=10.55 limits, D: 1.947, P : < 0.005
Aimplying a
stable process .
Moving Range
5 __
MR=3.23
0 LCL=0
1 28 55 82 109 136 163 190 217 244 20 25 30 35
Last 25 Observations
35
The points Capability Plot O v erall
Within
on Within Last 25
the
Observations chart make a
S tDev 2.86364 S tDev 2.68251
Values
30
random scatter, with pno *
Cp
C pk
*
0.1
O v erall
P
P pk 0.11
25 trends or shifts, which also
S pecs
C pm *
245 250 255
Observation
260 265
indicates process stability.
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Minitab Exercise (Cont.)
Process Capability Sixpack of Delivery Time
I Chart Capability Histogram
The data in the Capability Histogram
40 USL
UCL=37.71
approximately follow the normal curve. On the S pecifications
Individual Value
U S L 30
normal 30probability plot, the points extend _X=29.12
outside the 95% confidence interval and have
a p-value < 0.05, which indicates that our LCL=20.53
20
data is non-normal82. 109 136 163 190 217 244
1 28 55 24 26 28 30 32 34 36
Moving Range Chart Normal Prob Plot
Since the data is non-normal, we have UCL=10.55 A D: 1.947, P : < 0.005
10
consulted our MBB who conducted a more
Moving Range
thorough analysis that indicated we are still
5 __
OK using a normal probability analysis. MR=3.23
0 LCL=0
1 28 55 82 109 136 163 190 217 244 20 25 30 35
Last 25 Observations Capability Plot
35 Within Within O v erall
S tDev 2.86364 S tDev 2.68251
Values
Cpk is 0.1
30 Cp * Pp *
O v erall
C pk 0.1 P pk 0.11
25 Is our process capable? S pecs
C pm *
245 250 255 260 265
Observation
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Process Capability – CPL
 CPL indicates capability against a Lower
Specification Limit
 Army Lodging has been getting complaints about its
slow elevators and decided to collect data to
investigate. In this example, the speed of an
elevator computer is unacceptable below 150
cm/sec. The CPL of 1.48 indicates the process is
“capable” of meeting the specifications if it continues
within the same range of variation
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Process Capability – CPL (Cont.)
Cpl= X - LSL
3s
_
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Process Capability – Cpk
 Cpk is the index used when a process has a “two-sided”
specification
 Army Lodging is concerned that the temperatures of its
guest rooms may vary too widely. In this example, the
temperature of a guest room needs to be between 62 and
70 degrees Fahrenheit for the guest to be comfortable.
We determine Cpk by calculating both CPU and CPL
 Cpk is the smaller of the two!
 You can see that while almost no rooms are too cold, some
rooms are too hot – which is reflected in the Cpk of 0.36
(which is much less than 1)
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Process Capability – Cpk (Cont.)
Cpk = Cpl or Cpu
(whichever is smaller)
_
_
,
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Process Capability – Cpk
_ _
USL x x  LSL
Cpk  Min or 
 3s 3s 
Calculate both values and report the smaller number.
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Capability Action Plan
 Give highest priority to parameters with Cpk‟s less than
1.0 (center the dimension, reduce the variation or both)
 If possible, get tolerance relief. (If product/process is
mature, and there have been no customer problems,
what is the need for this formal spec when another “de
facto” spec has been used historically?)
 100% inspect, measure and sort
 Chart using the data from the measurements
 Use SPC Charting on parameters with Cpk‟s between 1.0
and 1.33 (or 1.67 if safety related)
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What About Attribute Data?
 Use Capability Analysis (Binomial) to produce a process
capability report when your data are from a binomial
distribution
 Binomial distributions are usually associated with recording the
number of defective items out of the total number sampled
 Examples:
 You might have a pass/fail measurement that determines whether
a service met expectations or not (e.g., late vs. not late). You
could then record the total number of deliveries made and the
number recorded as late
 Or, you could record the number of people who call in sick on a
particular day and the number of people scheduled to work each
day
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Capability Analysis for Attribute Data
 Use Capability Analysis (Binomial) if your data meet
the following conditions:
 Each item is the result of identical conditions
 Each item can result in one of two possible outcomes
(success/failure, go/no-go)
 The probability of a success (or failure) is constant for
each item
 The outcomes of the items are independent of each
other
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Streamlining the RC ARFORGEN Progression
 Open the Minitab dataset BPCAPA1.MTW
 Background:
 You are a Brigade Operations Officer and you want to assess the
overall readiness of your Brigade based on annual data from the
Unit Status Report system.
 You focus in on the monthly reports from the past year and count
the proportion of (defectives) units that were not meeting the
required status for readiness.
 You want to assess “how capable and ready” your Brigade is for
it‟s wartime or primary mission.
 Objective: Baseline the capability of the process
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Streamlining the RC ARFORGEN Progression
Dataset DEFINITION
VARIABLE (reference: AR 220-1)
CONTROL The aggregate number of required personnel, equipment on-hand, and
the number of collective training events for that year, per unit.
C-RAT The degree to which a unit has achieved prescribed levels of fill for
personnel, equipment, the operational readiness status of available
equipment, and the training proficiency status of the unit.
S-RAT Equipment supply status of a unit – equipment on-hand is based on the
quantity and type of required equipment that is available to the unit .
P-RAT Personnel status of a unit – based on the number and type of required
personnel available to the unit for the execution of the wartime or
primary mission for which the unit is organized or designed.
T-RAT Unit training status is based upon the unit commander’s assessment of
the unit’s training proficiency on mission-essential tasks, the number of
days required to achieve or sustain full mission-essential task
proficiency.
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Streamlining the RC ARFORGEN Progression
Process Capability Analysis
 We will first determine the overall unit C-RAT
process capability.
 Defectives: C-RAT
 Use Sizes in: CONTROL
 We can then follow the same steps for S-RAT, P-
RAT, and T-RAT.
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Streamlining the RC ARFORGEN Progression
Stat>Quality Tools>Capability Analysis>Binomial
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Streamlining the RC ARFORGEN Progression
 The defectives are “C-RAT” and the sample size is in “Control”
1. Double click on
C-3 C-RAT to
put it in the
Defectives box
2. Double click on
C-2 CONTROL to place
it in the
Use sizes in: box
3. Click on OK
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Streamlining the RC ARFORGEN Progression
Binomial Process Capability Analysis of C-RAT
P C har t Rate of Defectives
40
0.4
U C L=0.3713
% Defective
P r opor tion
0.3 _ 30
P =0.2738
0.2
LC L=0.1762
20
0.1
1 4 7 10 13 16 19 22 25 28 100 150 200
Sample Sample Size
C umulative % Defective Dist of % Defective
The „P-chart‟ details that the processtats
S ummary S
is Tar
32
in control, with an average proportion
(using 95.0% confidence)
6.0
of 30
defectiveness at 27.38%. er C I: e: 27.38
Low This
% Defectiv
4.5
% Defective
25.64
means that the ARFORGEN process is 29.16
28
U pper C I:
Target: 0.00 3.0
being affected by variation withinCthe 256449
26
P P M Def:
Low er I:
273772
1.5
variables that make up the C-RATC I: 291621
U pper
24 P rocess Z: 0.6014
(equipment, personnel, 25 training). 0.5487
and Low er C I:
0.0
5 10 15 20 0 6 12 18 24 30 36
Sample U pper C I: 0.6543
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Streamlining the RC ARFORGEN Progression
Binomial Process Capability Analysis of C-RAT
P C har t Rate of Defectives
40
The „Cumulative %
0.4
U C L=0.3713
% Defective
P r opor tion
Defective‟ chart
0.3 _
P =0.2738
30
verifies that enough
0.2
data was collected to
LC L=0.1762
20
0.1
represent the16process.28
1 4 7 10 13 19 22 25 100 150 200
Sample Sample Size
C umulative % Defective Dist of % Defective
S ummary S tats Tar
32 6.0
(using 95.0% confidence)
30 % Defectiv e: 27.38
4.5
% Defective
Low er C I: 25.64
U pper C I: 29.16
28 3.0
Target: 0.00
P P M Def: 273772
26 Low er C I: 256449 1.5
U pper C I: 291621
24 P rocess Z: 0.6014 0.0
5 10 15 20 25 Low er C I: 0.5487 0 6 12 18 24 30 36
Sample U pper C I: 0.6543
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Streamlining the RC ARFORGEN Progression
Binomial Process Capability Analysis of C-RAT
P C har t Rate of Defectives
40
0.4
U C L=0.3713
% Defective
P r opor tion
0.3 _ 30
P =0.2738
0.2
LC L=0.1762
20
0.1
The1 „Rate 7of 10 Sample 19 22 25 details a random
4 Defectives‟ plot 28
13 16 100 150
Sample Size
200
distribution of data points, which means that the
% defective is not influenced by the number of
C umulative % Defective Dist of % Defective
Tar
items sampled.
32
S ummary S tats
6.0
(using 95.0% confidence)
Finally, the „Dist of %Defective‟ chart efectiv e: the
30 %D
details 27.38 4.5
% Defective
Low er C I: 25.64
overall distribution of the % defective from the
28
U pper C I: 29.16
Target: 0.00 3.0
sample. P P M D ef: 273772
26 Low er C I: 256449 1.5
See Appendix for analysis of other variables.
U pper C I: 291621
24 P rocess Z: 0.6014 0.0
5 10 15 20 25 Low er C I: 0.5487 0 6 12 18 24 30 36
Sample U pper C I: 0.6543
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Example Results
 The overall process is in control; hence, the data can be taken to the
next phase on analysis.
 The voice of the process is suggesting that possible variables that
require investigating are: equipment readiness and training readiness.
 Equipment readiness covers three sub-variables:
 Equipment that are mission capable (percentage)
 Pacing items that are mission capable (percentage)
 Overall equipment readiness rating
 Training readiness collectively looks at the overall training
accomplishments of the unit (as determined by the unit commander).
There are several factors bearing down on the process (possible
“noise” in the system):
 Non-ARFORGEN training requirements (state mission)
 Overseas deployment training requirements – tasked by the higher
HQ
 Theater Security Exercise requirements – tasked by the higher HQ
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Binomial Capability Analysis – Data Display
Binomial Process Capability Analysis of C-RAT
P C har t Rate of Defectives
40
0.4
U C L=0.3713
% Defective
P r opor tion
0.3 _ 30
P =0.2738
0.2
LC L=0.1762
20
0.1
1 4 7 10 13 16 19 22 25 28 100 150 200
Sample Sample Size
Tests performed w ith unequal sample sizes
C umulative % Defective H istogr am
S ummary S tats Tar
32 6.0
(95.0% confidence)
30 % Defectiv e: 27.38
4.5
% Defective
Fr equency
Low er C I: 25.64
U pper C I: 29.16
28 3.0
Target: 0.00
P P M Def: 273772
26 Low er C I: 256449 1.5
U pper C I: 291621
24 P rocess Z: 0.6014 0.0
5 10 15 20 25 Low er C I: 0.5487 0 6 12 18 24 30 36
Sample U pper C I: 0.6543 % Defective
Shows Percent Defective and Process Z (Sigma Level)
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Normal Capability Analysis – Display Options
Normal Data
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Capability Analysis – Cpk or Z Bench?
Process Capability of Delivery Time Process Capability of Delivery Time
USL USL
P rocess Data Within P rocess Data Within
LS L * Ov erall LS L * Ov erall
Target * Target *
USL 30 P otential (Within) C apability USL 30 P otential (Within) C apability
S ample M ean 29.1203 Cp * S ample M ean 29.1203 Z.Bench 0.31
S ample N 266 C PL * S ample N 266 Z.LS L *
S tDev (Within) 2.87033 C P U 0.10 S tDev (Within) 2.87033 Z.U S L 0.31
S tDev (O v erall) 2.68901 C pk 0.10 S tDev (O v erall) 2.68901 C pk 0.10
O v erall C apability O v erall C apability
Pp * Z.Bench 0.33
PPL * Z.LS L *
PPU 0.11 Z.U S L 0.33
P pk 0.11 P pk 0.11
C pm * C pm *
24 26 28 30 32 34 36 24 26 28 30 32 34 36
O bserv ed P erformance E xp. Within P erformance E xp. O v erall P erformance O bserv ed P erformance E xp. Within P erformance E xp. O v erall P erformance
P P M < LS L * PPM < LS L * P P M < LS L * % < LS L * % < LS L * % < LS L *
P P M > U S L 281954.89 PPM > U S L 379619.67 P P M > U S L 371778.52 % > U S L 28.20 % > U S L 37.96 % > U S L 37.18
P P M Total 281954.89 PPM Total 379619.67 P P M Total 371778.52 % Total 28.20 % Total 37.96 % Total 37.18
Displays Cpk and Displays Benchmark Z
PPM (Parts Per Million) (Sigma Level)
and Percent above USL
Enables comparison of process capability (SQL)
between all processes no matter what kind of data
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Process Capability Template
Process Capability of Workdays
 118 data points collected Calculations Based on Lognormal Distribution Model
 Non-normal distribution
LSL
USL
 Mean = 44 days LS L
P rocess Data
0
O v erall C apability
Z.Bench -0.31
Target * Z.LS L 3.07
 Lower Cust Spec = 0 days USL 15 Z.U S L -0.02
 Upper Cust Spec = 15 days
S ample M ean 44.8136
S ample N 118 - Example - P pk -0.01
E xp. O v erall P erformance
Location 3.09501
% < LS L 0.00
S cale 1.26378
 65% of observations % > U S L 62.03
O bserv ed P erformance % Total 62.03
outside customer spec % < LS L 0.00
% > U S L 65.25
 Z Bench = -.31 % Total 65.25
0 60 120 180 240 300 360 420
Required Deliverable
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Exercise: Analyze Process Capability
Objective
Perform a process capability study for the GGA's Budget Department
Instructions
 Identify Primary Y metric
 Determine customer specification limits
 Calculate Z Bench - Sigma Quality Level (SQL)
Time = 15 Minutes
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Takeaways
 Once a process is in statistical control, you want to
determine if it is capable; that it is meeting specification
limits and producing “good” or satisfactory services or
deliverables from the service process
 You determine capability by comparing the width of the
process variation with the width of the specification limits
 Capability indices, Cp and Cpk, are ratios of the specification
tolerance to the natural process variation, and are a
straightforward way to assess process capability
 Because these indices are unitless, you can use capability
statistics to compare the capability of one process to another
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What other comments or questions
do you have?
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