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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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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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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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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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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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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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- XCpu=

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 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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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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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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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.)

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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Calculate both values and report the smaller number.

Process Capability – Cpk

Cpk MinUSL x

orx LSL

3 3s s

_ _

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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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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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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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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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What other comments or questions

do you have?


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