advanced process capability

8/10/2019 Advanced Process Capability

1/11

Process Capability

v1.ppt

1

Process Capability

What it is Process Capability looks at short term capability and long term

performance of a process with regard to customer specifications.

Standard indexesare used: Cp, Cpk, Ppand Ppk. These can be

converted into ppm.

A simple view of Process Control and Process Capability

process control- refers only to the voice of the process - looking at

the process using an agreed performance measure to see whether

the process forms a stable distribution over time.

process capability- measures the goodness of a process-

comparing the voice of the process with the voice of the customer.

The voice of the customer here is the specification range (tolerance)and/or the nearest customer specification limit.

The objectiveis to get as close to the theoretical best that your process

can achieve by eliminating special causesof variation, so that only

common (natural) causesare acting on the process, and then to reduce

these to a minimum, whenever possible.


2/11

Process Capability

v1.ppt

2

Process Capability

Process Control

Out of Control

(Special Causes Present)

In Control

(Special Causes Eliminated)

Note - no reference to

specs !

In Control but not Capable

(Variation from Common Causes

Excessive)

In Control and Capable

(Variation from Common

Causes Reduced)Lower Spec Limit

Upper Spec Limit

Process Capability

What it is


3/11

Process Capability

v1.ppt

3

Process Capability

What it is

Cpor ENTITLEMENT is the theoretical best

hat a process can achieve.

1 2

CAPABILITY PERFORMANCEShort Term Long Term

In Control Not in Control

Pooled std dev Total / overall std dev

aHowmuch

variability

compares

spec range(tolerance)

to process

width

Cp Pp

bHow

centred

how close

process

centre is to

nearest

spec limit

Cpk Ppk


4/11

Process Capability

v1.ppt

4

Process Capability

The 4 capability Capability Indexes: explaining the terms . . .

1 2



Pooled std dev Total / overal l s td dev

a

How

much

variability

compares

spec range

(tolerance)

to process

width

Cp Pp

bHow

centred

how close

processcentre is to

nearest

spec limit

Cpk Ppk

300

350

400

450

500

550

600

Time

short term

long term

Not (necessarily) in Control:common

causes and special causes acting

(possible drifts or shifts in the process)

In Control:only common causes acting (no

sudden drifts or shifts in the process)

What it is


5/11

Process Capability

v1.ppt

5

Process Capability


1 2




a

How

much

variability

compares

spec range

(tolerance)

to process

width

Cp Pp

bHow

centred

how close

processcentre is to

nearest

spec limit

Cpk Ppk

300

350

400

450

500

550

600

Time

Pooled ortotal standard deviation- used in manual calculations:

Pooled (or combined): sP= sqrt [ sum (d.f. *s2) / sum (d.f.) ]

Total (or overall): sT= sqrt [ sum (x - x)2/ (n-1) ]

What it is


6/11

Process Capability

v1.ppt

6


1 2




a

How

much

variability

compares

spec range

(tolerance)

to process

width

Cp Pp

bHow

centred

how close

process

centre is to

nearestspec limit

Cpk Ppk

Process Capability

Cp= USL-LSL6sP

Pp= USL-LSL6sT

sP =pooled standard deviation sT =total standard deviation

USLLSL

Cp, Ppcompares specification range (tolerance)to process width

regardless of where the process is centred.

It is the ratio of the specification width to 6 x process standard

deviation.

What it is


7/11

Process Capability

v1.ppt

7


Process Capability

Cpk, Ppkmeasure how close the process centre is to the nearest customer

spec.

It is (difference between the process average and the nearest specification)

(3 x the process standard deviation).

Cpk= min {Cpkl, Cpku}Cpkl = X-LSL

3sP

Cpku= USL-X

3sP

Ppkl= X-LSL

3sT

Ppku= USL-X

3sT

Ppk= min {Ppkl, Ppku}

1 2




a

How

much

variability

compares

spec range

(tolerance)

to process

width

Cp Pp

bHow

centred

how close

process

centre is to

nearest

spec limitCpk Ppk

X

USLLSL

What it is


8/11

Process Capability

v1.ppt

8

How to use it

Process Capability

Use Minitab output whenever possible, since it combines the indexes

with a graphical representation of the process: actual sample, estimated

short term capability and estimated long term performance

Also use as a ru le of thumbthe following chart

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

Caution:

Cpk is an index much misused: It is only applicable to normally

distributed variable data that is measured in the short term.

Conversions from Cpk to ppm and sigma assume that all defectives are

occurring at one tail of the distribution with an average sigma shift of

1.5 sigma. (industry standard).

Cpk MUST be seen as part of a package of information.

Capability studies for non-normal data (Weibull) do not give Cpk

values


9/11

Process Capability

v1.ppt

9

Process Capability

Example

Using Minitab:

250 350 450 550 650

LSL USL

Process Capability Analysis for Data

USL

Target

LSL

Mean

Sample N

StDev (ST)

StDev (LT)

Cp

CPU

CPL

Cpk

Cpm

Pp

PPU

PPL

Ppk

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

520.000

*

420.000

435.833

30

10.7176

59.6888

1.56

2.62

0.49

0.49

*

0.28

0.47

0.09

0.09

366666.67

100000.00

466666.67

69795.44

0.00

69795.44

395402.81

79256.43

474659.24

Process Data

Potential (ST) Capability

Overall (LT) Capability Observed Performance Expected ST Performance Expected LT Performance

ST

LT


10/11

Process Capability

v1.ppt

10

Process Capability

Example

Using Minitab, with non-normal data

0 5 10 15 20 25

LSL USL

Process Capability Analysis for Weibull

Calculations Based on Weibull Distribution Model

USL

Target

LSL

Mean

Sample N

Shape

Scale

Pp

PPU

PPL

Ppk

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

6.00000

*

2.00000

5.65406

50

1.58256

6.29977

0.19

0.09

0.35

0.09

120000.00

400000.00

520000.00

150164.01

396235.71

546399.72

Process Data

Overall (LT) Capability

Observed LT Performance

Expected LT Performance

Note:For Weibull Capability Analysis, data must have positive values, andLONG TERM metrics only are given.

NO values for Cpk are given, because the data is non-normal


11/11

advanced process capability

Documents