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Process Capability Index

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1.1. Why do we do Process Performance Calculation

• Document baseline performance

• Compare performance before and after

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1.2. Process Capability Study

• A process capability study is one of the major steps of the continuous improvement process. It is part of an overall strategy of Six Sigma and process improvement that has three objectives: – Obtain Stable processes – Reduce the Variability of key process outputs – Improve the Capability of key processes through the reduction of

variation and the centering of the process on its target value.

• The capability of a process is increased relative to required tolerances or process specifications by reducing the variation in the process and centering of process variables on their respective targets.

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2.0. Capability Indices for Continuous Data

• Capability is defined as the ability of a process to produce outputs that meet engineering and/or customer specifications.

• A capable process is one where the distributions of the process output measurements are centered on the target, and a very high percentage of the measurements fall within the specification limits.

• Process Capability Indices are “unitless” metrics used to measure and quantify the performance of a process – Cp and Cpk.

Process Capability is

Quantifiable comparison of Voice of Customer (Spec Limits)

to Voice of the Process (Process Spread).

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• A method of tracking the relative improvement of an individual process

over time.

• A method for estimating the percentage of defects or non-conforming

product.

• A means of comparing the capability of several processes, each with

different units of measurement and different specifications.

• A means for identifying the processes most in need of improvement.

• One set of acceptance criteria for transferring a process from a

development area to a manufacturing line.

• One set of qualification criteria for assessing suppliers.

2.2. Uses of Capability Indices

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• Process capability analysis generally consists of 4 steps:

– Step 1: Verify that the process is stable.

– Step 2: Determine if the data distribution is normal.

– Step 3: Calculate the Capability Indices Cp and Cpk

– Step 4: Make recommendations for process improvement.

2.3. Process Capability Study

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• Cp is a metric used to determine whether a new machine or process can

produce units that meet customer requirements or specifications provided that

the process is centered within that given specification.

• Cp index is defined as the Ratio of total variation allowed by the specification

(specification width) to the total variation actually measured from the process

(actual process spread).

6σ

LSLUSL

Spread)(ActualSpreadProcess

Spread)(AllowableWidthSpecCp

LSL USL

Allowable

Actual

2.4. Potential Process Capability Index (Cp)

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< 1.0 Poor Capability

1.0 - 1.5

Marginal Capability

> 1.5 Good Capability

> 2.0 6 s Capability

Cp Interpretation

LSL USL

2.5. Interpretation of Cp

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3 Processes with same Cp value but different capability (different ppm)

• Since Cp does not measure the location of the average of the actual spread

with respect to the center of the specification, a high Cp value does not

guarantee that the process is capable of producing products within spec.

• Cp, therefore, represents what the process could become when it is brought to

the design target (centered), hence the word “Potential”.

• Cp does not exist in processes with one-sided or unilateral specification limit.

T USL LSL

Cpk = 2.0 Cpk = 0.33 Cpk = 1.0

2.6. Limitation of Potential Process Capability Index (Cp)

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• Capability index - Cpk

• Cp does not take into account the closeness of the mean to the “target”.

• Cp by itself is insufficient to describe the capability of a process to conform to specifications.

• An index that does take into account where the mean of the sample is relative to the specification limits is Cpk.

• If the sample average is on the target

(i.e., xbar = target), then Cpk = Cp. Otherwise, Cpk < Cp.

• For a process to be at the 6s quality level, it must have a Cp ≥ 2.0

and a Cpk ≥ 1.5.

3σ

LSLx,

3σ

xUSLminCpk

2.7. Definition of Cpk

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• Background: – Data collected during a capability study of the wire pull force for a

wire bond process (in gram)

– The specification limits are 8.0 to 50.0 gram.

– Use file ‘wire pull simple’ in folder Data 15.

• Tasks: • Use JMP to calculate process capability indices.

• Is the process capable of manufacturing can openers with the specs provided?

• What can you say about the sigma level of the process?

2.8. Example : Process Capability

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• The Cp and Cpk capability indices require the data to be

normally distributed.

• Often attribute data is not normally distributed.

• Examples:

– Cell phone defect rates.

– Number of calls waiting to be answered in a call center.

3.1. Capability Indices for Attribute Data

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• Percentile Capability Indices:

– Used when the attributed data has counts.

– Example: Number of calls in a call center waiting to be answered.

– NOTE: This technique can also be used for non-normal, variable

data.

– YB needs to consult to a MBB/BB for doing capability calculations for

non-normal data. It is covered here for completeness purposes.

• DPMO (Defects per Million Opportunities):

– Used when the attributed data has two values: good and bad. GB is

expected to be able to do this capability calculation

– Example: Number of defective phones produced.

3.2. Capability Indices for Non-Normal Distributions

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3.3. Percentile Capability Indices

• Similar to the Cp and Cpk calculations.

– The mean is replaced by the median.

– Percentiles are used instead of sigma.

– NOTE: Need a minimum sample size of 100.

• * The “n” in Cnp and Cnpk stands for nonparametric

005.0995.0 PP

LSLUSLCnp

005.050.0

50.0

50.0995.0

50.0 ,minPP

LSLP

PP

PUSLCnpk

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3.4. DPMO based Capability Indices

• By examining the raw data, we can count the number of

defects that do not meet customer requirements and

translate that directly into a defect calculation referred to

as Defects Per Million Opportunities, or DPMO.

• Based on the DPMO, look up the sigma quality level.

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3.5. DPMO Defined

• DPMO = Defects Per Million Opportunities

= 1 Million * [ D / ( N * O ) ]

where:

– D* = total number of defects counted in the sample:

a defect defined as failure to meet a Critical Customer Requirement or CCR

– N = number of units of product or service

– O = number of opportunities per unit of product or service for a customer defect to occur

– M = million

• There must be at least 5 defects and 5 non-defects to use the

DPMO formula.

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3.6. Opportunity

• People often get confused in determining the number of opportunities for

defects. The basis for the defects and the opportunities must match.

• Example: A die has 28 leads requiring 28 wires and 56 bonds (one on each

end of the wire).

Defect Opportunity

Number of die with at least one bad

wire bond.

1 (Only count one possible defect per

die)

Number of bad wires per die 28 (There are 28 wires per die)

Number of bad bonds per die 56 (There are 56 bonds per die)

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3.7. DPMO/PPM Based Capability Indices

Sigma DPMO Cp Cpk

2 308770 0.67 0.17

2.25 226716 0.75 0.25

2.5 158687 0.83 0.33

2.75 105660 0.92 0.42

3 66811 1.00 0.50

3.25 40060 1.08 0.58

3.5 22750 1.17 0.67

3.75 12225 1.25 0.75

4 6210 1.33 0.83

4.25 2980 1.42 0.92

4.5 1350 1.50 1.00

4.75 577 1.58 1.08

5 233 1.67 1.17

5.25 88 1.75 1.25

5.5 32 1.83 1.33

5.75 11 1.92 1.42

6 3.4 2.00 1.50

Compute the defects per million

opportunities and then look up

on the table for the Cp and Cpk.

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• Scenario:

• A hotel provides room service meals to its guests.

• Hotel policy is that the meal must be delivered at the time scheduled by the customer.

• The hotel six sigma team has found from the Voice of the Customer that a too early breakfast delivery will inconvenience the guest as well as a too late delivery.

• Guest research indicates that customers require that the breakfast meal be delivered within 10 minutes of the scheduled delivery time.

• 725 deliveries were monitored and 53 of those arrived outside the +/- 10 minute window.

• What is the capability of the meal delivery service?

3.8.a. Example: DPMO Based Capability Indices

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For this example:

D = 53 Early or late deliveries

N = 725 Number of deliveries monitored

O = 1 Each delivery had one opportunity for

a defect

DPMO = 1,000,000 * [53 / (725*1)]

= 73,103 DPMO

Using the Sigma Calculation table, enter the DPMO column and look up the

process sigma directly.

Sigma Quality Level Approximately 2.9

3.8.b. Example: DPMO Based Capability Indices

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Thank You