PROCESS CAPABILITY

Parul Institute of Management, Vadodara

BySachin Modgil

Friday, April 7, 2023

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Contents

1. Process Capability

2. Control Limits Vs Specification Limits

3. Tolerance

4. Example

5. Things to Remember

6. ConclusionFriday, April 7, 2023

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Process Capability

Even when the process operates under the influence of chance causes, certain amount of variation is inherent. This inherent variability of a process in a machine or equipment is referred to as the process or machine or equipment capability

Or Process Capability measures the extent to which

the voice of the process is aligned with the voice of the customer

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Introduction

Control Limits (Manufacturer) Vs Specification Limits (Customer)

Type of Specifications (USL & LSL)

Tolerance: USL-LSL

Natural tolerance range is the range of three standard deviations from the mean on either side.

Standard indexes are used: Cp, Cpk, Pp and Ppk. These can be converted into ppm. Friday, April 7, 2023

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Example

Cp is capability index Cp= T/6σ Pp is performance Index

Example: 30 Samples of size 4 each were taken. Sample average (X bar) as deviation from 100 microns and sample range (R) values in microns are given

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Sample No X Bar R

1 9.5 15

2 18.25 10

3 20.75 8

4 21.25 9

5 24.25 10

6 25.25 15

7 26.50 19

8 28.25 22

9 22.75 6

10 28.75 20

11 33.00 10

12 15.00 17

13 22.50 11

14 18.75 10

15 21.75 23

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Sample No. X bar (Microns) R (Microns)

16 12.50 10

17 22.75 14

18 21.50 18

19 15.75 20

20 17.00 7

21 20.75 12

22 17.50 7

23 20.25 15

24 18.25 14

25 20.50 24

26 28.75 5

27 15.50 20

28 14.50 3

29 22.75 23

30 30.50 16

Total 608.25 413

Example

If the Specification for land width is 0.120±0.020 mm from the above data, compute process capability (6σ), measure of precision(Cp) and measure of Accuracy (Cpk) and interpret them.

Now 608.25/30= 20.3 , Hence X double Bar= 0.1203

Average Range= 413/30=13.77 We have D4 R bar= (2.28)(13.77)=31.4 microns Also D3 R bar= (0) (13.77)=0

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Example…

Since all the ranges are in limits, we compute process capability

6σ= 6(Rbar/d2)=(6 X13.77)/2.059=40 microns Tolerance (T) = USL-LSL= 0.140-0.100= 0.04mm=

40 microns Cp=T/6σ= 40/40=1.0, which means process is just

able to meet the tolerance Hence 6σ= Tolerance (T)

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Example

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Cpk= min(X double bar-LSL/3σ ,USL- X double bar/3σ)

Min (0.1203-0.1000/0.02 ,0.1400-0.1203/0.02) Min (1.015,0.985) 0.985~ 1.0 Indicates process is fairly centered

Meaning of Cp, Cpk, Pp and Ppk

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1 2

CAPABILITY PERFORMANCEShort Term Long TermIn Control Not in Control

Pooled std dev Total / overall std dev

aHow much

variability

compares spec range (tolerance) to process

width

Cp Pp

bHow

centred

how close process

centre is to nearest

spec limit

Cpk Ppk

Remember

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Cp Cpk Pp Ppk Sigma

Red (Bad) < 1.00 < 1.00 < 1.33 < 1.33 < 4.5

Yellow (OK) 1.00 - 1.33 1.00 - 1.33 1.33 - 1.67 1.33 - 1.67 4.5 - 5.5

Green (Good) > 1.33 > 1.33 > 1.67 > 1.67 > 5.5

( Cpk x 3 ) +1.5 = sigma

The following chart is used as a rule of thumb

Conclusuion

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A Process Capability study is the end result of the analysis done on process output data.

A Process Capability study reflects what our customer sees.

It indicates what our short term and long term situation looks like.

Recognise however that our processes need to be stable (in statistical control) as well as capable.

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Questions ?