Process Capability Analysis

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University of Hail College of Engineering

ME 418 – Quality in ManufacturingISE 320 - Quality Control and Industrial Statistics

CHAPTER 05

PROCESS CAPABILITY ANALYSIS

Professor Mohamed Aichouni

Process Capability AnalysisProcess capability analysis is performed to answer the Process capability analysis is performed to answer the fundamental question: “Is our process capable to meet customer requirements or specifications?”Before this analysis can be done, we must ensure that the process is in a state of statistical control.Tolerances : Specifications Limits

design specifications reflecting product requirementsProcess capability

range of natural variability in a process what we measure with control charts.

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Process CapabilityDesign

Specifications

Design Specifications

(a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time.

Process

4-3

(b) Design specifications and natural variation the same; process is capable of meeting specifications most of the time.

Process

Process Capability (cont.)Design

Specifications

(c) Design specifications greater than natural variation; process is capable of always conforming to specifications.

ProcessDesign

Specifications

4-4

(d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification.

Process

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Improvement in Capability

Cp less than 1.0

σ̂6LSLUSLCp

−=

Cp ~ 1.0

Cp > 1.0

Sigma levels in Processes

μ

Process operating at sigma level

6

USLTLSL

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Process Capability Indices

Cp < Cp < 1 1 the Process is not capable the Process is not capable

Cp ≥ Cp ≥ 1 1 : Capable Process: Capable Process

Process Capability Indices ‐ Cp

+3σ-3σ

8

USLUSLLSLLSL

Spec Width (door*) USL Spec Width (door*) USL -- LSLLSLCCpp = =

Mfg Capability (car) Mfg Capability (car) = =

66σσ

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Process Capability Indices ‐ Cp

CUSL - LSL

LSL USL

Cp =6σ

Cp < 1 - not capableCp = 1 - marginally capable

Cp > 1 - capable

9

The average is not part of the formula.target.-process capability if stable and onpotential "best case"A measure of

Can be misleading if process is unstable or off target.Must have both a LSL and USL to calculate.

Visualizing Process Capability

0.4

0.3

Lower Spec. Limit

Upper Spec. Limit

Cust. Tolerance0.4

0.3

Lower SpecLimit

Upper Spec.Limit

Cust. Tolerance

43210-1-2-3-4

0.2

0.1

0.0

Process Capability

86420-2-4-6-8

0.2

0.1

0.0

Process Capability

10

Cp=1 Cp=2

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What if Process is Off‐Target?

Lower UpperCust Tolerance

Cp = 1.33

Cpk = 11..33335.334.02.671.33-1.33-2.67-4.0-5.33 0

0.4

0.3

0.2

0.1

0.0

Lower Spec. Limit

Upper Spec. Limit

Cust. Tolerance

110

0.4

0.3

0.2

0.1

0.05.334.02.671.33-1.33-2.67-4.0-5.33

Lower Spec. Limit

Upper Spec. Limit

Cust. Tolerance

Cp = 1.33

Cpk = 00..8383

Process Capability Indices ‐ Cpk

Cpk =Min (USL - avg, avg - LSL)

3σST

Cpk < 1 - not capableCpk = 1 - marginally capable

LSL USL

12

Cpk 1 marginally capableCpk > 1 - capable

Cp = Cpk if process is on target.capability if the process is stable.potentialStill a measure of

Can be used for 1-sided specs. (Cpu, Cpl)A negative Cpk is possible if the average is outside specifications.

avg

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Process Capability ExampleSuppose the specifications on a piston ring are:

And the standard deviation is : 0.0099 mm.

mm05.0000.74 ±

68195.7305.74 −− LSLUSLC

Capable Process

68.1)0099.0(66

≈==σ

C p

Process Capability Using Minitab (Example 5.1)

In a car manufacturing process, data were recorded for a quality characteristic

sample X1 X2 X3 X41 6.2 6.7 7.1 7.92 7.5 4.9 7.5 10.23 6.9 7.7 7.8 9.54 11.5 4.7 10 10.9quality characteristic

(tightening force on nuts) on the table;

the design specifications were:Target = 8 kgf/cmUSL = 9 kgf/cm

5 7.4 7.4 9.2 116 10.1 7.2 11.6 87 9.3 10 10.2 148 4.6 6.4 10 1.99 8.2 3.8 8.6 7.3

10 4.4 6.6 10.5 811 6 9 13 9.612 12.9 6.6 8.3 12.813 10 5.9 7.3 9.914 6 7.5 9.4 12.315 9.9 8.2 7.8 7.516 5.9 5.5 4.9 3.7

LSL = 7 kgf/cm

Is the process capable to meet the specifications ?

16 5.9 5.5 4.9 3.717 5.9 8.2 8.7 6.818 12.6 6.7 9.6 10.619 11.2 8.2 8.7 11.920 10.7 9.2 9.7 8.921 9.4 10 6.1 10.322 9.2 7.7 7.1 8.323 8.7 8.3 10 5.124 7.5 8.7 8 7.825 8 7.6 7.7 10.9

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Process Capability Using Minitab

Select StatMenu; Menu; Quality Tools; Capability Analysis then Normal


In the dialogue box enter the specifications andselect data X1 – X4

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ResultsClear Incapable ProcessShould be improved

Capability Sixpack in MINITAB

18

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Applications in Asphalt Production

LSL Target USL

Product

LSL Target USL

Product not

meeting specificati

ons

Production Plant A Production Plant BProduction Plant A

Incapable ProcessPoor QualityHigh Losses

Production Plant B

Capable ProcessGood Quality

Applications in Asphalt ProductionComparison of # Processes

CP ≥ 1 Process Capability is acceptable ;CP ≥ 1 Process Capability is acceptable ; CP ≥ 1.3 Process Capability excellent.

Expected level of quality : highCP < 1 : Big problem with the process and the product

quality . Process Not Capable to meet Customer

Specifications

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Example 5.2

In a manufacturing process the length of the work piece is considered as the quality

241.6 238.6 239.1241.3 239.2 239.5239.7 240.4 241.5241.0 242.5 238.1

3X2 X1 XSample1234

characteristic to be monitored .20 samples were gathered from the process at regular intervals to study the capability of the process to meet the design specifications.

Specifications : L = 240 ± 2 mm

239.8 238.3 238.7240.3 240.4 241.6239.4 240.9 239.6239.5 238.7 240.4240.1 241.1 239.8240.3 238.7 240.3239.0 240.2 239.8239.9 238.7 237.6

5678910111213

Is the process capable to meet the specifications ?

240.3 239.8 239.8240.9 238.9 238.8240.2 238.5 238.0239.8 240.5 236.5238.4 239.1 237.8239.4 239.5 236.9238.5 241.0 238.1240.9 239.7 236.8

1314151617181920

Example 5.3

In a manufacturing plant we want to compare 2 production lines (A) and (B) ; 60 parts are taken from each line and the quality

Production Line (A)

150.4150.5150.3150.2150.3150.1150.4149.9150.4150.3150.3150.1149.9150.2150.1150.0150.2150.1150.2150.2150.3150.3150.3150.2150 2150 3150 5150 0150 1150 0q y

characteristic measured and recorded on the table. The design Specifications are : L = (150 ± 0.5) mm

Make a comparison between the two production lines.

Which one is better ? And Why?

150.2150.3150.5150.0150.1150.0150.5150.0150.2150.3150.3150.0150.0149.9150.4150.2150.4149.9150.7150.1150.4150.1150.1150.2150.4150.1150.3150.5150.5150.4150.6150.3150.2149.8150.3150.4

Production Line (B)

150.0149.9149.8149.6150.1149.9149.9149.8149.9150.3150.2149.5Which one is better ? And Why?

If there is shift of the process, what can be the possible reasons for that ?

What recommendations would you make to the manufacturer?

149.4150.1150.0150.2150.0150.0149.8150.0150.1149.7150.0149.7150.2149.8149.6150.0150.1150.0149.8150.1149.7149.9150.0149.9150.2149.9150.0150.1150.1149.9149.4150.3149.7149.8149.5150.0149.8149.8149.9149.6149.9150.2149.7150.1150.0149.7149.9149.6

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Process Capability Analysis