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Process capability

Process

A combination of equipment, materials, people, methods and

environment that act together to produce an output. The

quality of the process is judged by the quality ( characteristic )

of the output.

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Process capability

Process capability

The inherent variability of a quality characteristic that the

process is capable of maintaining, when in a state of statistical

control under a given set of conditions.

Assuming normal distribution of the quality characteristic

Process Capability = +/- 3 SD = Total spread of 6 SD.

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Process capability

Process capability is judged by comparing process

performance with process requirements. Since meeting

specification limits is one of the most basic requirements of

a process capability study, it is extremely important to

accurately verify and define the specification limits.

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Need for process capability

For meeting customer requirements/ specifications.

To compare actual performance of equipment with

manufacturer’s claim.

To compare the performance of two processes.

To provide more realistic tolerances for component

dimensions.

Provide a basis for process control.

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Factors influencing process capability

1. Condition of machine/ equipment.

2. Type of operation and operational conditions.

3. Raw materials.

4. Skill of operators.

5. Measurement method / instruments.

6. Inspector’s skill.

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Estimation of process capability

• Visual from run chart.

• Frequency distribution and histogram.

• Control charts.

• Analysis of variances.

• Probability papers.

Note : Reduction of variability can be achieved through use of SPC

tools and Design of Experiments.

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The empirical rule

We have seen in the earlier chapter that almost all (to be

accurate 99.73%) the process output from a normally

distributed process lies between (process mean - 3 SD)

and (process mean+ 3 SD).

The total spread of the process can thus be described as 6 SD

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99.73% population between process mean +/- 3 SD

LSL USL

- 3 SD + 3 SD

2 3 4 5 6 7 8 9 12 10 16 15 14 13 11 1

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Process capability indices : The Cp index

A major reason for quantifying process capability is to

compute the ability of a process to hold product tolerances.

A measure of this relationship is process capability ratio or

Cp. Process capability is also known as potential capability.

The Cp index is given by:-

Cp = Tolerance

6 SD

Where Tolerance = USL - LSL

SD = Standard Deviation

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Process capability indices : The Cp index

Interpretations of Cp

Cp > 1 : The process is quite capable

Cp = 1 : The process is just capable

Cp < 1 : The process is incapable

The recommended value of Cp is 1.33 ( minimum)

In order to achieve Six Sigma quality in the organization, we

must reduce the variation in the process so as to achieve the

value of Cp=2.

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Calculating defective PPM at various levels of sigma.

Refer normal distribution table for finding defective parts per

million ( PPM ) for corresponding z values.

Quality level Cp z Defective PPM

2 Sigma 0.67 2 22750

3 Sigma 1.00 3 1350

4 Sigma 1.33 4 32

5 Sigma 1.67 5 0.3

6 Sigma 2.00 6 0.001

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Impact of process capability

For individual parts, the ideal design is Cp = 2; in other words,

the design specification is twice as “wide” as the true capability

of the process. This is where the phrase “Six Sigma Quality”

originated. Since the process capability is +/- 3SD, a design

specification twice as wide would be +/- 6 SD.

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Impact of process capability

However, it is learnt from the industry experience across the

world, that the processes rarely stay centered on their targeted

nominals, shifts of 1.5 SD to either side of the mean are

common, even in well controlled processes.

Therefore in practice, an ultimate z-value of 4.5 is considered

Six Sigma Quality. Consulting the z-table, we find that the

probability of producing non conformities associated with a z-

value of 4.5 is 0.0000034. If this value is obtained, then only

3.4 out of every million parts manufactured will be defective.

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Calculating defective PPM with permissible shift of 1.5 SD

at various levels of sigma. ( practical situation )

Refer normal distribution table for finding defective PPM for

corresponding z values.

Quality level Cp z Defective PPM

2 Sigma 0.17 0.5 308538

3 Sigma 0.50 1.5 66807

4 Sigma 0.83 2.5 6210

5 Sigma 1.17 3.5 233

6 Sigma 1.50 4.5 3.4

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Drawbacks of Cp

Cp however is not a very reliable measure as it does not tell us

all.

Consider the following four processes producing the same

output X with specification 20+/- 4. Each of these processes

have the Standard deviation of 1.

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LSL USL

X=20

SD=1

Cp=1.33

Process 1

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LSL USL

X=22

SD=1

Cp=1.33

Process 2

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LSL USL

X=15

SD=1

Cp=1.33

Process 3

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LSL USL

X=25

SD=1

Cp=1.33

Process 4

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Calculation of Cpk index

Cpk = Min [ USL - x , x - LSL ]

3SD 3SD

Cpk is a measure of process performance capability

The process performance index Cpk is given by:-

Example :

Specification : 20 +/- 4, SD = 1

Cp = Tolerance/6SD = 8/6 = 1.33

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x = 20, Cpk = Cp = 1.33

x = 22, Cpk = 0.67

x = 15, Cpk = -0.33

x = 25, Cpk = -0.33

Example :

Specification : 20 +/- 4, SD = 1

Cp = Tol/6 SD = 8/6 = 1.33

Calculation of Cpk index - Example

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In the previous slide we observe that, although the Cp

value = 1.33 in all the four cases, but because of the shift

in the process setting level we are getting Cpk values as

0.67 in 2nd case and hence the non conformities. Similar

observations are noticed in 3rd and 4th case where we get

the Cpk as -0.33.

Calculation of Cpk index

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The Cpk index

Thus Cpk = Cp means the process is centered.

Cpk < 1 means non- conformances are being produced.

Cpk < 0 indicates that the process has been set beyond either of

the two specification limits.

Note : Cpk is always less than or equal to Cp.

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Therefore, the first step is to bring Cpk=Cp by proper

centering of the process. The second step should be to

improve the Cp value by decreasing the variation.

Cp and Cpk indices

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One-sided Tolerances - The Cp and Cpk indexes are used

for characteristics with two-sided tolerances - that is,

processes with both upper and lower specification limits.

Since many characteristics have only one-sided

specifications, it is also convenient to have one-sided

capability indexes.

Process capability indexes for one sided tolerances

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For processes that have only a Lower specification limit, LSL,

the lower capability index Cpl is defined by:-

Correspondingly, when only an Upper specification exists,

we define an upper capability index by:-

Process capability indexes for one sided tolerances

Cpl = x - LSL

3 SD

Cpu = USL - x

3 SD