Lecture 8-Process Capability.pdf

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PROCESS CAPABILITY �Process capability is defined as 6σ0 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 process result w.r.t. product specification.

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Caution ! 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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Evaluation of process capability 

1.

2.

3.

It is critical to understand that: Process specification pertain to individual item quality characteristics Capability indices pertain to population of individual items Subgroup based control chart limits pertain to only the population of the subgroup NOT to the population of individual items.

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Process capability analysis �Objective is to determine how well the output from a process meets specification limits �Compare total process variation and tolerance. LSL

USL

-3

Target

+3 6

Process Capability Index (Cp) �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  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.

C pk

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

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 8

Calculating process capability indices 

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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 - a realizes or actual measure of capability 

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Relationship of Process Capability to Specification Limits

Three situations: �1. 6 0 σ =USL−LSL Case I �2. 6 0 σ >USL−LSL Case II �3. 6 0 σ 1

Capable at 3

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Cpk > 1.33

Capable at 4

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Cpk > 1.67

Capable at 5

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Cpk > 2

Capable at 6

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Process Capability Index (Cp) (Process Potential Index --Text) 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

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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 .

C pk

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

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

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= min { (3.5/2.7) or (2.5/2.7) }

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

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However, by adjusting the mean, the process can become capable. 13

Individual values compared with averages 

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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:





R

d

2



or



S

c

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Control limits and specification limits 

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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 happening on the s or r chart.

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The Six sigma spread versus specification limits 

Case I: 6 < USL - LSL 

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Case II: 6 = USL - LSL 

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Most desirable; individual values fall within specification limits Okay, as long as the process remains in control

Case III: 6 > USL - LSL 

Undesirable; process incapable of meeting specifications

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Potential capability (Cp index) Measure inherent capability of production process  Defined as Cp =Upper Spec limit – Lower Spec Limit 

6 σ The estimated index= ^Cp

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Actual Capability (Cpk index) 

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Measure realized capability relative to actual production (assuming process is stable) Define as:

Cpk =minimum { (μ- LSL)/3σ , (USL -μ)/3σ }

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Another measure of process capability (Cpk) (Process Performance Index 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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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 �Undesirable; process incapable of meeting specifications

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Illustration

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Illustration cont’d

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Illustration cont’d

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compiled by amir Yazid

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Recommended minimum value of Process Capability Ratio Two sided specification Existing process 1.33 New process 1.50 Safety , strength or critical parameters 1.50 for existing process Safety , strength or critical parameters 1.67 for new process

One sided specification 1.25 1.45 1.45 1.60

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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.

In-class exercise (ICE) �What is the key to achieving six-sigma capability?