Lecture 8-Process Capability.pdf

�Process capability is defined as 6σ

Three ways process capability can be obtained are :

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Defining process capability

 Process capability refers to the ability of the

process to meet the specifications set by the customer or designer.

 A critical performance measure which addresses

A process must be in statistical control before its

capability is measured.

Processes out of control fluctuate and thus are

unpredictable; trying to measure their

capability would lead to misleading

conclusions.

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Caution !

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Evaluation of process capability

 It is critical to understand that:

1. Process specification pertain to individual item

quality characteristics

2. Capability indices pertain to population of

individual items

3. Subgroup based control chart limits pertain to

only the population of the subgroup NOT to the population of individual items.

�Objective is to determine how well the output

from a process meets specification limits

�Compare total process variation and

tolerance.

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Process capability analysis

LSL USL

-3 +3

�The capability index measures whether the process or machine can produce pieces which conform to the

specifications.

• The larger the index, the more likely the process will generate conforming parts or pieces provided that the process is centred at the nominal or target value. (CP >= 1.33)

� CAUTION : The capability index does not indicate process performance in terms of the nominal or target value.

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Process Capability Index (Cp)

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Process Capability Index

 The Process Capability Index (Cpk) differs from the Cp in that it indicates if the

process mean has shifted away from the design target, and in which direction it has shifted – that is, if it is off center.

 If the Cpk index is greater than 1.00 then process is capable of meeting

design specifications. If Cpk is less than 1.00 then process mean has moved

closer to either upper or lower design specifications, and generate defects. When Cpk equals Cp, this indicates that the process mean is centered on the design (nominal) target.

where

• x-bar is the mean of the process

• sigma is the standard deviation of the process

• UTL is the customer’s upper tolerance limit (specification) • and LTL is the customer’s lower tolerance limit

      _   3 X -UTL or 3 LTL X min = C_pk

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Calculating process capability

indices

 Process capability indices: ratios that quantify

the ability of a process to produce within specifications

 Two common indices are:

 The Cp index

-the inherent or potential inherent measure of capability  The Cpk index

Three situations:

�1. 6 0 σ =USL−LSL Case I

�2. 6 0 σ >USL−LSL Case II

�3. 6 0 σ <USL−LSL Case III

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Relationship of Process

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Interpreting the Process Capability Index

 Cpk < 1 Not Capable

 Cpk > 1 Capable at 3

 Cpk > 1.33 Capable at 4

 Cpk > 1.67 Capable at 5

Process Capability and the specification limits (i.e., tolerances) are combined to form a Capability Index:

Cp = USL- LSL 6 σ0 � If Cp < 1.00 Case III � If Cp = 1.00 Case II � If Cp > 1.00 Case I 12

Process Capability Index (Cp)

(Process Potential Index --Text)

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Process Capability Index

(Example)

A process has a mean of 45.5 and a standard deviation of 0.9. The product has a specification of 45.0 ± 3.0. Find the Cpk .

 = min { (45.5 – 42.0)/3(0.9) or (48.0-45.5)/3(0.9) }

 = min { (3.5/2.7) or (2.5/2.7) }

 = min { 1.30 or 0.93 } = 0.93 (Not capable!)

 However, by adjusting the mean, the process can become capable.

         3 X -UTL or 3 LTL X min = C_pk

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Individual values compared with

averages

 When distributions of averages are compared to

distributions of individual values, the averages are grouped closer to the center value than are the individual values, as described by the central limit theorem.

 What does this imply for averages in control

limits versus individual values in specification limits?

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To simplify calculation

 If the process can be assumed to be normal, the

population standard deviation can be estimated from either the standard deviation associated

with the sample standard deviation or the range:

d

R





c

S





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Control limits and specification

limits

 X-bar charts do not reflect how widely the

individual values composing the plotting averages spread.

 The spread can only be seen by observing what is

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The Six sigma spread versus

specification limits

 Case I: 6 < USL - LSL

 Most desirable; individual values fall within specification

limits

 Case II: 6 = USL - LSL

 Okay, as long as the process remains in control

 Case III: 6 > USL - LSL

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Potential capability (C

index)

 Measure inherent capability of production

process

 Defined as

Cp =Upper Spec limit – Lower Spec Limit

6 σ

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Actual Capability (C

 Measure realized capability relative to actual

production (assuming process is stable)

 Define as:

This measure takes into account the centring of the process. We first obtain two one-sided indexes, then select the minimum of the two.

 This measure takes into account the centring of the process.

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Another measure of process capability (Cpk)

�Case I: 6



< USL - LSL

�Most desirable; individual values fall within specification limits

�Case II: 6



= USL - LSL

�Okay, as long as the process remains in control

�Case III: 6



> USL - LSL

�Undesirable; process incapable of meeting specifications

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The Six sigma spread versus

specification limits

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Illustration

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Illustration cont’d

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Illustration cont’d

Two sided specification One sided specification Existing process 1.33 1.25 New process 1.50 1.45 Safety , strength or critical parameters

for existing process

1.50 1.45 Safety , strength or critical parameters

for new process

1.67 1.60

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Recommended minimum value of

Process Capability Ratio

Motorola’s “Six Sigma” Concept

With the process centred exactly in the middle (nominal dimension), only 2 defectives out of one billion are expected.

If the process mean shifts ± 1.5 sigma, the expected number of defectives will be 3.4 per million.

�What is the key to achieving six-sigma

capability?