Process CapabilityASQ Section 1404

Ken FredrykMarch 10, 2015

Process CapabilityWe 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

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

Quantifiable comparison of Voice of Customer (spec limits) to Voice of the Process (control limits)Quantifiable comparison of Voice of Customer (spec limits) to Voice of the Process (control limits)

Process CapabilityConsider 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 contractValidate 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

requirementsWhen 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

to this

Non-Capable Process

Process target

Capable Process

Process target

from this

m m

Not a silver bullet!!

Causes of Low Process CapabilityExcess 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. ViewWhat Type of Data

Do You Have?

Attribute Data Variables Data

Collect Dataon Process

Collect Dataon Process

Analyze Datain Excel

Analyze Datain Minitab/Excel

State CapabilityDPU, Sigma Quality

Level, PPM

State CapabilityDPU, 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 CapableThe process has too much variation

• Without decreasing process variation, some out of specification product is inevitable

The process is not centeredThe 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 DistributionThe 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

m

LSLLSL USLUSL

+3+3-3-3

99.73% of values99.73% of values

Natural Process Variation

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

Process is barely capable as long as it remains centered within the

specification limits

3 3 ss

LSL USL

Process is capable and will remain so, even if the process average is moved.

Often called process shift

3 3 ss

LSL USL

m m

Examples of Non-Capable Processes

Product produced below the

lower spec limit.

Product produced beyond both

upper and lower spec limits.

3s 3s

LSL USL

Product produced above the

upper spec limit.

3s 3s

LSL USL

3s 3s

LSL USL

mmm

Capability Study OptionsA 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: 100-200 data points.)

150100500

15

14

13

12

11

10

9

Observation Number

Indiv

idual

V alu e

Process Data for Co2

X=12.64

UCL=14.18

LCL=11.10

150100500

15

14

13

12

11

10

9

Observation Number

Indiv

idual

V alu e

Process Data for Co2

X=12.64

UCL=14.18

LCL=11.10

Steps of a Capability Study1. Set the process to run as it normally would

and record the values of the input variables2. Execute the process over a period of time suitable3. to the purpose of the study

• Have all sources of variation been accounted for?3. Take plenty of notes4. 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 - sDefinition:

The number of total standard deviations (+/–) that would fit within the spec limits

• For example, a 3 s level would mean 6 standard deviations can fit within the specification limits

Sigma Level is a measure of the process performance

Compare % DefectiveWith and Without Shift

Calculated as the area under the curveCalculated using a “shift” factor

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 DefectsWith and Without Shift

Graphical View of Sigma Levels

+1 s

+3 s

+2 s

LSL USL

+4 s

+6 s

+5 s

LSL USL

m m

Process Capability – CpRatio of total variation allowed by the specification to

the total variation actually measured from the processTypical 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 limitsCp takes into account only process spread and not

location

If Cp < 1, then the variability of the process is greater than the specification limitsCp takes into account only process spread and not

location

Process Capability – Cp

ORCp = Allowable variation (spec width)Process Variation

Cp = USL – LSL 6

• Typical values:– Marginal Cp = 1.00– Acceptable Cp=1.33– Good Cp = 1.67– Six Sigma level Cp = 2.00

One-Sided Capability Ratios

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

CPU = USL – Xbar

3

CPL = Xbar - LSL 3

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

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

• K ³ 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

CPK = CP (1-K)

m

Negative Cpk

• Negative Cpk occurs when the mean is outside the USL or LSLe.g. Cpk = -0.5

Process mean is outside the specification limit

3s 3s

LSL USL

Capability versus Performance• Capability Ratios (CP and CPK)

– use a short-term estimate of sigma (s) obtained from the within-subgroup 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 ProcessUSLLSL

Process Capability

Process Performance

Over time, a process tends to shift by approximately 1.5 Over time, a process tends to shift by approximately 1.5

Capability Example

Sample data of pin diameters

• Data collected over 27 days

• Sub-group size 5

• Tolerance is 0.1587 – 0.20885P G A Approach (aka KFred rule of thumb: Always do PGA)

Capability Example DataSample1 Sample2 Sample3 Sample4 Sample5 Subroup

0.184 0.189 0.179 0.174 0.175 10.18 0.189 0.189 0.192 0.194 2

0.182 0.172 0.195 0.197 0.199 30.189 0.185 0.179 0.18 0.184 40.187 0.187 0.192 0.175 0.177 50.177 0.19 0.189 0.177 0.179 60.187 0.195 0.179 0.187 0.18 70.189 0.179 0.192 0.179 0.18 80.185 0.187 0.195 0.184 0.184 90.187 0.179 0.174 0.184 0.17 10

Control Chart by Subgroup

Capability Analysis 1

Normality Test

Capability Analysis by Subgroup

Capability Analysis 1

Capability Analysis 1

Capability Analysis 2

Capability Analysis 2Excel Based

UCL X 0.189891 # of Samples 135 USL 0.20885 Cp 1.84LCL X 0.177709 # of Sub Groups 27 LSL 0.15875 CpU 1.67UCL R 0.022325 Sub Group Size (n) 5 UCL X 0.1921498 CpL 2.01

Max Value 0.197 LCL X 0.1799687 Cpk 1.67Min Value 0.175 UCL R 0.022325 Cr 0.54

UCL X 0.193343 Range 0.022 Z USL 4.7039663LCL X 0.178776 X Double Bar 0.186059 Z LSL -5.63658UCL R 0.022325 R Bar 0.01 % Above USL= 0.0% Pp 1.72

St. Dev. (Rbar/d2 ) 0.004538 % Below LSL= 0.0% PpU 1.57St. Dev. (Indiv.) 0.004845 % In Spec= 100.0% PpL 1.88

Upper PC line 0.196325 Normality Normal % Out of Spec= 0.0% Ppk 1.57Lower PC line 0.171275 Pr 0.58

X Median Chart Limits

Pre-Control Limits

Process Data Potential (Rbar/d2 ) Capability

Potential (Indiv.) Capability

X Bar R Chart Limits

Capability Study

Cap_Study_.xls.xlsx

Capability Analysis Comparison

Potential (Within) CapabilityCp 1.77CPL 1.48CPU 2.06Cpk 1.48Overall CapabilityPp 1.71PPL 1.43PPU 2.00Ppk 1.43

Potential (Within) CapabilityCp 1.77CPL 1.94CPU 1.61Cpk 1.61Overall CapabilityPp 1.72PPL 1.88PPU 1.56Ppk 1.56

Original Data (Non-Normal)Minitab

Transformed Data Minitab

Cp 1.84CpU 1.67CpL 2.01Cpk 1.67Cr 0.54

Pp 1.72PpU 1.57PpL 1.88Ppk 1.57

Potential (Rbar/d2 ) Capability

Potential (Indiv.) Capability

Original Data (Non-Normal)Excel

Capability Analysis Comparison

Potential (Within) CapabilityCp 1.77CPL 1.94CPU 1.61Cpk 1.61Overall CapabilityPp 1.72PPL 1.88PPU 1.56Ppk 1.56

Original Data Subgroup Size 5 Original Data Subgroup Size 1

Potential (Within) CapabilityCp 1.92CPL 2.09CPU 1.75Cpk 1.75Overall CapabilityPp 1.72PPL 1.88PPU 1.57Ppk 1.57

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

Results

But what if we haveonly 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 AnalysisDate No. Leaks No. Brakes

8/1/1998 28 7708/2/1998 7 8908/3/1998 11 9308/4/1998 27 9608/5/1998 11 8008/6/1998 5 11708/7/1998 8 10108/8/1998 21 9908/9/1998 16 9908/10/1998 21 10108/11/1998 7 6308/12/1998 23 10108/13/1998 1 6508/14/1998 5 10008/15/1998 11 10008/16/1998 15 9908/17/1998 10 10008/18/1998 4 1010

I and MR Chart for Rate

Is the process stable?

0Subgroup 10 20

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

Ind

ivid

ua

l V

alu

e

X=0.01382

3.0SL=0.03989

-3.0SL=-0.01224

0.00

0.01

0.02

0.03

Mo

vin

g R

an

ge

R=0.009801

3.0SL=0.03202

-3.0SL=0.00E+00

I and MR Chart for Rate

Avg.

Def

ect R

ate

What Are the Defects per Unit (DPU)?

Formula:

Example:

DPU = Total # Defects Total Units Produced

DPU = 231 = 0.0137418 16810

What Are the Defects per Million Opportunities (DPMO)?

Formula:

Example:DPMO = 231 (1M) = 13,741.8 16810

DPMO = DPU X 1,000,000 Total Opportunities for a Defect in One Unit

What Is the Process Sigma Level?Procedure:Use the Excel file sigmacalc.xls

ATTRIBUTE SIGMA CALCULATOR

Characteristic Under Study: Brakes

# of Units 16810Opportunity For Defects / Unit 1Defects 231

DPU 0.01374182DPMO 13741.82035SIGMA (With Shift) 3.71

Another Example Attribute Capability Study

Process: Bank Loan Application ReviewObjective: 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 Review500 random applications reviewed5 fields per form are required to be completed by

the applicantOperational definition of a defect

• Missing, illegible or wrong format fields260 defects identified

Sigma Calculator

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 centeringA 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

ReferencesDean Cristolear

• Cap_Study.xlsiSixSigma.org6Sigma.orgASQ.org

• Six Sigma Forum Magazine May 2005: –Capability Indexes: Mystery Solved

Questions?