ng bb 27 process capability
DESCRIPTION
TRANSCRIPT
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National GuardBlack Belt Training
Module 27
Process Capability
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CPI Roadmap – Measure
Note: Activities and tools vary by project. Lists provided here are not necessarily all-inclusive.
TOOLS
•Process Mapping
•Process Cycle Efficiency/TOC
•Little’s Law
•Operational Definitions
•Data Collection Plan
•Statistical Sampling
•Measurement System Analysis
•TPM
•Generic Pull
•Setup Reduction
•Control Charts
•Histograms
•Constraint Identification
•Process Capability
ACTIVITIES• Map Current Process / Go & See
• Identify Key Input, Process, Output Metrics
• Develop Operational Definitions
• Develop Data Collection Plan
• Validate Measurement System
• Collect Baseline Data
• Identify Performance Gaps
• Estimate Financial/Operational Benefits
• Determine Process Stability/Capability
• Complete Measure Tollgate
1.Validate the
Problem
4. Determine Root
Cause
3. Set Improvement
Targets
5. Develop Counter-
Measures
6. See Counter-MeasuresThrough
2. IdentifyPerformance
Gaps
7. Confirm Results
& Process
8. StandardizeSuccessfulProcesses
Define Measure Analyze ControlImprove
8-STEP PROCESS
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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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44Process Capability
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
Customer Queue Time
Service Cost / Order
Job Acceptance Rate
Service Treatment (complaints)
On-Time Delivery
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55Process Capability
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 processis greater than the specification limits
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66Process Capability
Process Capability – Cp
+3-3
Process Width
TLSL USL
99.7% of values
or6
LSL) - (USLCp
process the of variation Normal
(spec.) variation AllowedpC
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77Process Capability
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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88Process Capability
Process Capability – Cpk
This index accounts for the dynamic mean shift in the process – the amount that the process is off target
Calculate both values and report the smaller number
σ
LSLxor
σ
xUSLMinC pk
33
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99Process Capability
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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1010Process Capability
A Metaphor for Cp – Parking Vehicles 1
Cp ≈ 1.3
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.
+/- 3 σ(Voice of Process)
+/- 3 σ(Voice of Process)
+/- 3 σ(Voice of Process)
Voice of Customer
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1111Process Capability
A Metaphor for Cpk – Parking Vehicles 2
Cpk ≈ 1.3
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 .
+/- 3 σ(Voice of Process)
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1212Process Capability
A Metaphor for Cpk – Parking Vehicles 2
Cpk ≈ 0
Specifications(Voice of Customer)
Cpk ≈ 0: The center of the process is on (or equal to) a customer specification (either side)!
+/- 3 σ(Voice of Process)
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1313Process Capability
A Metaphor for Cpk – Parking Vehicles 2
Cpk ≈ -1
Cpk ≈ -1: The center of the process is outside the customer specifications (either side)!
Specifications(Voice of Customer)
+/- 3 σ(Voice of Process)
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1414Process Capability
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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1515Process Capability
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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1616Process Capability
Process Capability – CPU
USL- XCpu=
3s
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1717Process Capability
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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1818Process Capability
Minitab Exercise (Cont.)
1. Double click on C-5 Delivery Time to Place it in the box forSingle column
2. In the Subgroup sizeBox, type a 1 since ourSample size is one
4. Click on OK
3. For Upper Spec type in 30 minutes (given)
Note: For Process Capability you must have at least 1 Spec Limit
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1919Process Capability
Minitab Exercise (Cont.)
2442171901631361098255281
40
30
20
In
div
idu
al V
alu
e
_X=29.12
UCL=37.71
LCL=20.53
2442171901631361098255281
10
5
0
Mo
vin
g R
an
ge
__MR=3.23
UCL=10.55
LCL=0
265260255250245
35
30
25
Observation
Va
lue
s
36343230282624
USL
USL 30
Specifications
35302520
Within
O v erall
Specs
StDev 2.86364
C p *
C pk 0.1
Within
StDev 2.68251
Pp *
Ppk 0.11
C pm *
O v erall
Process Capability Sixpack of Delivery Time
I Chart
Moving Range Chart
Last 25 Observations
Capability Histogram
Normal Prob PlotA D: 1.947, P: < 0.005
Capability Plot
On both the I Chart and the Moving Range Chart, the points are randomly distributed between the control limits, implying a stable process .
The points on the Last 25 Observations chart make a random scatter, with no trends or shifts, which also indicates process stability.
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2020Process Capability
Minitab Exercise (Cont.)
2442171901631361098255281
40
30
20
In
div
idu
al V
alu
e
_X=29.12
UCL=37.71
LCL=20.53
2442171901631361098255281
10
5
0
Mo
vin
g R
an
ge
__MR=3.23
UCL=10.55
LCL=0
265260255250245
35
30
25
Observation
Va
lue
s
36343230282624
USL
USL 30
Specifications
35302520
Within
O v erall
Specs
StDev 2.86364
C p *
C pk 0.1
Within
StDev 2.68251
Pp *
Ppk 0.11
C pm *
O v erall
Process Capability Sixpack of Delivery Time
I Chart
Moving Range Chart
Last 25 Observations
Capability Histogram
Normal Prob PlotA D: 1.947, P: < 0.005
Capability Plot
The data in the Capability Histogram approximately follow the normal curve. On the normal probability plot, the points extend outside the 95% confidence interval and have a p-value < 0.05, which indicates that our data is non-normal .
Since the data is non-normal, we have consulted our MBB who conducted a more thorough analysis that indicated we are still OK using a normal probability analysis.
Cpk is 0.1Is our process capable?
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2121Process Capability
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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2222Process Capability
Process Capability – CPL (Cont.)
X - LSL Cpl= 3s
_
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2323Process Capability
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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2424Process Capability
Process Capability – Cpk (Cont.)
_
_
Cpk = Cpl or Cpu
(whichever is smaller)
,
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2525Process Capability
Calculate both values and report the smaller number.
Process Capability – Cpk
Cpk MinUSL x
orx LSL
3 3s s
_ _
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2626Process Capability
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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2727Process Capability
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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2828Process Capability
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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2929Process Capability
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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3030Process Capability
Streamlining the RC ARFORGEN Progression
Dataset
VARIABLEDEFINITION
(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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3131Process Capability
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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3232Process Capability
Streamlining the RC ARFORGEN Progression
Stat>Quality Tools>Capability Analysis>Binomial
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3333Process Capability
The defectives are “C-RAT” and the sample size is in “Control”
1. Double click on C-3 C-RAT toput it in the Defectives box
2. Double click onC-2 CONTROL to place it in theUse sizes in: box
3. Click on OK
Streamlining the RC ARFORGEN Progression
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3434Process Capability
Streamlining the RC ARFORGEN Progression
Sample
Pro
po
rti
on
28252219161310741
0.4
0.3
0.2
0.1
_
P=0.2738
UC L=0.3713
LC L=0.1762
Sample
%D
efe
cti
ve
252015105
32
30
28
26
24
Upper C I: 0.6543
%Defectiv e: 27.38
Lower C I: 25.64
Upper C I: 29.16
Target: 0.00
PPM Def: 273772
Lower C I: 256449
Upper C I: 291621
Process Z: 0.6014
Lower C I: 0.5487
(using 95.0% confidence)
Summary Stats
Sample Size
%D
efe
cti
ve
200150100
40
30
20
363024181260
6.0
4.5
3.0
1.5
0.0
Tar
Binomial Process Capability Analysis of C-RAT
P Chart
Cumulative %Defective
Rate of Defectives
Dist of %Defective
The „P-chart‟ details that the process is in control, with an average proportion of defectiveness at 27.38%. This means that the ARFORGEN process is being affected by variation within the variables that make up the C-RAT (equipment, personnel, and training).
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3535Process Capability
Sample
Pro
po
rti
on
28252219161310741
0.4
0.3
0.2
0.1
_
P=0.2738
UC L=0.3713
LC L=0.1762
Sample
%D
efe
cti
ve
252015105
32
30
28
26
24
Upper C I: 0.6543
%Defectiv e: 27.38
Lower C I: 25.64
Upper C I: 29.16
Target: 0.00
PPM Def: 273772
Lower C I: 256449
Upper C I: 291621
Process Z: 0.6014
Lower C I: 0.5487
(using 95.0% confidence)
Summary Stats
Sample Size
%D
efe
cti
ve
200150100
40
30
20
363024181260
6.0
4.5
3.0
1.5
0.0
Tar
Binomial Process Capability Analysis of C-RAT
P Chart
Cumulative %Defective
Rate of Defectives
Dist of %Defective
The „Cumulative % Defective‟ chart verifies that enough data was collected to represent the process.
Streamlining the RC ARFORGEN Progression
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3636Process Capability
Sample
Pro
po
rti
on
28252219161310741
0.4
0.3
0.2
0.1
_
P=0.2738
UC L=0.3713
LC L=0.1762
Sample
%D
efe
cti
ve
252015105
32
30
28
26
24
Upper C I: 0.6543
%Defectiv e: 27.38
Lower C I: 25.64
Upper C I: 29.16
Target: 0.00
PPM Def: 273772
Lower C I: 256449
Upper C I: 291621
Process Z: 0.6014
Lower C I: 0.5487
(using 95.0% confidence)
Summary Stats
Sample Size
%D
efe
cti
ve
200150100
40
30
20
363024181260
6.0
4.5
3.0
1.5
0.0
Tar
Binomial Process Capability Analysis of C-RAT
P Chart
Cumulative %Defective
Rate of Defectives
Dist of %Defective
The „Rate of Defectives‟ plot details a random distribution of data points, which means that the % defective is not influenced by the number of items sampled.
Finally, the „Dist of %Defective‟ chart details the overall distribution of the % defective from the sample.
See Appendix for analysis of other variables.
Streamlining the RC ARFORGEN Progression
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3737Process Capability
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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28252219161310741
0.4
0.3
0.2
0.1
Sample
Pro
po
rti
on
_P=0.2738
UC L=0.3713
LC L=0.1762
252015105
32
30
28
26
24
Sample
%D
efe
cti
ve
Upper C I: 0.6543
%Defectiv e: 27.38
Lower C I: 25.64
Upper C I: 29.16
Target: 0.00
PPM Def: 273772
Lower C I: 256449
Upper C I: 291621
Process Z: 0.6014
Lower C I: 0.5487
(95.0% confidence)
Summary Stats
200150100
40
30
20
Sample Size
%D
efe
cti
ve
363024181260
6.0
4.5
3.0
1.5
0.0
%Defective
Fre
qu
en
cy
Tar
Binomial Process Capability Analysis of C-RAT
P Chart
Tests performed w ith unequal sample sizes
Cumulative %Defective
Rate of Defectives
Histogram
Binomial Capability Analysis – Data Display
Shows Percent Defective and Process Z (Sigma Level)
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Normal Capability Analysis – Display Options
Normal Data
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36343230282624
USL
LSL *
Target *
USL 30
Sample Mean 29.1203
Sample N 266
StDev (Within) 2.87033
StDev (O v erall) 2.68901
Process Data
C p *
C PL *
C PU 0.10
C pk 0.10
Pp *
PPL *
PPU 0.11
Ppk 0.11
C pm *
O v erall C apability
Potential (Within) C apability
PPM < LSL *
PPM > USL 281954.89
PPM Total 281954.89
O bserv ed Performance
PPM < LSL *
PPM > USL 379619.67
PPM Total 379619.67
Exp. Within Performance
PPM < LSL *
PPM > USL 371778.52
PPM Total 371778.52
Exp. O v erall Performance
Within
Overall
Process Capability of Delivery Time
36343230282624
USL
LSL *
Target *
USL 30
Sample Mean 29.1203
Sample N 266
StDev (Within) 2.87033
StDev (O v erall) 2.68901
Process Data
Z.Bench 0.31
Z.LSL *
Z.USL 0.31
C pk 0.10
Z.Bench 0.33
Z.LSL *
Z.USL 0.33
Ppk 0.11
C pm *
O v erall C apability
Potential (Within) C apability
% < LSL *
% > USL 28.20
% Total 28.20
O bserv ed Performance
% < LSL *
% > USL 37.96
% Total 37.96
Exp. Within Performance
% < LSL *
% > USL 37.18
% Total 37.18
Exp. O v erall Performance
Within
Overall
Process Capability of Delivery Time
Capability Analysis – Cpk or Z Bench?
Displays Benchmark Z (Sigma Level)
and Percent above USL
Displays Cpk and PPM (Parts Per Million)
Enables comparison of process capability (SQL) between all processes no matter what kind of data
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118 data points collected
Non-normal distribution
Mean = 44 days
Lower Cust Spec = 0 days
Upper Cust Spec = 15 days
65% of observations outside customer spec
Z Bench = -.31
Required Deliverable
- Example -
Process Capability Template
420360300240180120600
LSLUSL
LSL 0
Target *
USL 15
Sample Mean 44.8136
Sample N 118
Location 3.09501
Scale 1.26378
Process Data
Z.Bench -0.31
Z.LSL 3.07
Z.USL -0.02
Ppk -0.01
O v erall C apability
% < LSL 0.00
% > USL 65.25
% Total 65.25
O bserv ed Performance
% < LSL 0.00
% > USL 62.03
% Total 62.03
Exp. O v erall Performance
Process Capability of WorkdaysCalculations Based on Lognormal Distribution Model
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4242
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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4343Process Capability
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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44
What other comments or questions
do you have?