iso 22514-2: 2013 - q-das · pdf fileiso 22514-2: 2013 ‒ changes to iso 21747: 2006 2/17...

ISO 22514-2: 2013

Changes to ISO 21747: 2006

ISO 22514-2: 2013 ‒ Changes to ISO 21747: 2006 1/17

Version: A © 2015 Q-DAS GmbH & Co. KG, 69469 Weinheim ISO_22514_2_main_topics_eb.docx

Content

Purpose of the document ........................................................................................................................ 2

Part I - main content of ISO 22514-2: 2013 ............................................................................................. 3

Time-dependent distribution models ................................................................................................. 3

Process performance indices .............................................................................................................. 4

Process performance index Pp ......................................................................................................... 4

Upper process performance index PpkU ........................................................................................... 5

Lower process performance index PpkL ........................................................................................... 6

Minimum process performance index Ppk ....................................................................................... 7

Process capability indices .................................................................................................................... 8

Process capability index Cp .............................................................................................................. 8

Upper process capability index CpkL ................................................................................................. 9

Lower process capability index CpkU .............................................................................................. 10

Minimum process capability index Cpk .......................................................................................... 11

Calculation methods of location (See ISO 22514-2: 2013, table 3) ............................................... 12

Calculation methods of dispersion (See ISO 22514-2: 2013, table 4) ........................................... 13

Application of different calculation methods ............................................................................... 14

Reporting performance and capability indices ............................................................................. 14

Part II - calculation methods for location and dispersion in Q-DAS products ....................................... 15

Calculation method settings in Q-DAS software products ................................................................ 16

Settings for stable processes ......................................................................................................... 16

Settings for instable processes ...................................................................................................... 17



Purpose of the document

The international standard ISO 21747: 2003 has been withdrawn and replaced by the standard ISO 22514-2: 2013. In order to avoid confusion regarding compliance with ISO 22514-2 we provide information about the key content of ISO 22514-2: 2013.

This document is divided into two parts. Part I shows key content elements of ISO 22514-2: 2013 with the main focus on calculation methods of process performance/capability indices.

Part II provides recommendations regarding the settings for the evaluation strategy of Q-DAS software for compliance with ISO 22514-2: 2013. These settings are related to:

qs-STAT: Process Capability module

destra: Process Capability module

procella: Process Capability module



Part I - main content of ISO 22514-2: 2013

Time-dependent distribution models

The following table lists all time-dependent distribution models in compliance with ISO 22514-2: 2013.

Characteristic Time-dependent distribution models (ISO 22514-2: 2013)

A1 A2 B C1 C2 C3 C4 D

Location c c c r r s s s

Dispersion c c s/r c c c c s/r

Short time distribution

nd 1m nd nd nd as as as

Resulting distribution

nd 1m as nd 1m as as as

Table 1: Time dependent distribution models (See ISO 22514-2: 2013, table 2)

c parameter remains constant s parameter only changes systematically r parameter only changes randomly nd normally distributed as any shape 1m not normally distributed, one mode only



Process performance indices

If a process is not considered to be in a state of statistical control, a process performance index can be assigned.

Process performance index Pp

Figure 1: Process performance index Pp

Δ dispersion of the distribution of the product characteristic

L lower specification limit

Pp process performance index

U upper specification limit

X0,135 % 0,135 % distribution quantile


Xmid distribution midpoint

variable

L UX0.135 % Xmid X99.865 %

Specification = U ‒ L

D = X99.865 % ‒ X0.135 %

den

sity



Upper process performance index PpkU

Figure 2: Upper process performance index PpkU

ΔU difference between X99,865 % and Xmid of the distribution of the product characteristic


PpkU upper process performance index





variable

L UX0.135 % Xmid X99.865 %

U – Xmid

DU = X99.865 % ‒ Xmid

den

sity



Lower process performance index PpkL

Figure 3: Lower process performance index PpkL

ΔL difference between Xmid and X0,135 % of the distribution of the product characteristic


PpkL lower process performance index





variable

L UX0.135 % Xmid X99.865 %

Xmid ‒ L

DL = Xmid ‒ X0.135 %

den

sity



Minimum process performance index Ppk

Figure 4: Minimum process performance index Ppk




Ppk minimum process performance index


PpkU upper process performance index





variable

L UX0.135 % Xmid X99.865 %

Xmid ‒ L

DL = Xmid ‒ X0.135 %

den

sity

U – Xmid

DU = X99.865 % ‒ Xmid



Process capability indices

If a process is considered to be in the state of statistical control, a capability index can be assigned.

Process capability index Cp

Figure 5: Process capability index Cp

Cp process capability index

Δ dispersion of the distribution of the product characteristic






variable

L UX0.135 % Xmid X99.865 %

D = X99.865 % ‒ X0.135 %

den

sity

Specification U – L



Upper process capability index CpkL

Figure 6: Upper capability index CpkL

CpkU upper process capability index







variable

L UX0.135 % Xmid X99.865 %

den

sity

U – Xmid

DU = X99.865 % ‒ Xmid



Lower process capability index CpkU

Figure 7: Lower process capability index CpkU

CpkL lower process capability index








variable

L UX0.135 % Xmid X99.865 %

Xmid ‒ L

DL = Xmid ‒ X0.135 %

den

sity



Minimum process capability index Cpk

Figure 8: Minimum capability index Cpk

Cpk minimum process capability index

CpkL lower process capability index

CpkU upper process capability index








variable

L UX0.135 % Xmid X99.865 %

Xmid ‒ L

den

sity

DL = Xmid ‒ X0.135 %

U – Xmid

DU = X99.865 % ‒ Xmid



Calculation methods of location (See ISO 22514-2: 2013, table 3)

Location method label, l

Calculation method of location / formula Ml,d

1 �̂�𝑚𝑖𝑑 = �̅� =1

𝑘𝑛∑ 𝑥𝑖

𝑘𝑛

𝑖=1

2 �̂�𝑚𝑖𝑑 = �̃� = {

𝑥(𝑛+12 ) ; 𝑛 𝑜𝑑𝑑

1

2[𝑥

(𝑛2

)+𝑥

(𝑛2

+1)] ; 𝑛 𝑒𝑣𝑒𝑛

3 �̂�𝑚𝑖𝑑 = �̿� =1

𝑘∑ �̅�𝑖

𝑘

𝑖=1

4 �̂�𝑚𝑖𝑑 = �̅̃� =1

𝑘∑ �̃�𝑖

𝑘

𝑖=1

Table 2: Calculation methods of process location (See ISO 22514-2: 2013, table 3)

k number of subgroups

n size of the i-th subgroup (same size for each subgroup)

Ml,d Calculation methods with location method label l and dispersion method label d

𝑥(𝑛+12

) sample value of rank [(n+1)/2] using n as the number of all individuals

𝑥(𝑛2

) sample value of rank (n/2) using n as the number of all individuals

𝑥(𝑛2

+1) sample value of rank (n/2+1) using n as the number of all individuals

𝑥𝑖 individual value of a subroup

�̅̃� average of all subgroup medians

�̃�𝑖 median of the i-th subgroup

�̅̅� average of all subgroup averages

�̅�𝑖 average of the i-th subgroup


Note: The calculation formulas for location estimators #3 and #4 given in ISO 22514-2: 2013 were incorrect. We use the corrected versions of these formulas in this document.



Calculation methods of dispersion (See ISO 22514-2: 2013, table 4)

Dispersion method label, d

Calculation method of dispersion / formula Ml,d

1 �̂� = 𝑋99.865 % − 𝑋0.135 %

�̂�𝑈 = 𝑋99.865 % − 𝑋𝑚𝑖𝑑; �̂�𝐿 = 𝑋𝑚𝑖𝑑 − 𝑋0.135 %

2 �̂� = 6�̂�; �̂�𝑈 = 3�̂�; �̂�𝐿 = 3�̂� where �̂� = √1

𝑘∑ 𝑠𝑖

2𝑘𝑖=1

3 �̂� = 6�̂�; �̂�𝑈 = 3�̂�; �̂�𝐿 = 3�̂� where �̂� =∑ 𝑠𝑖

𝑘𝑖=1

𝑘𝑐4

4 �̂� = 6�̂�; �̂�𝑈 = 3�̂�; �̂�𝐿 = 3�̂� where �̂� =∑ 𝑅𝑖

𝑘𝑖=1

𝑘𝑑2

5 �̂� = 6�̂�; �̂�𝑈 = 3�̂�; �̂�𝐿 = 3�̂� where �̂� = √ 1

𝑛−1∑ (𝑥𝑖−�̅�)2𝑛

𝑖=1

Table 3: Calculation methods of process dispersion (See ISO 22514-2: 2013, table 4)

c4 constant based on subgroup size n

Δ dispersion of the process



d2 constant based on subgroup size n

k number of subgroups of the same size n

Ml,d Calculation methods with location method label l and dispersion method label d

Ri range of the i-th subgroup

si standard deviation of the i-th subgroup

𝑠𝑖2 variance of the i-th subgroup

σ standard deviation, population

�̅� average of sample distribution






Application of different calculation methods

The following table provides information about the calculation methods for the respective time-dependent distribution model.

Calculation method

Time model

A1 A2 B C1 C2 C3 C4 D

Location

1 a a

2 a a a a a a a a

3 a

4 a a a

Dispersion

1 a a a a a a a a

2 a

3 a

4 a

5 a a a a a

Table 4: Calculation methods for process location and dispersion (See ISO 22514-2: 2013, table 5)

a = applicable

Note #1: Dispersion estimators based on the inner dispersion of subgroups (dispersion estimators #2, #3 and #4) are only available for the time distribution model A1.

Note #2: Location estimator #2 and dispersion estimator #1 are the most general estimators. For this reason, they should be used preferably.

Note #3: Dispersion calculation method #1 can also be applied to the empirical cumulative distribution function if the amount of data is large, e.g. 1000 individuals.

Reporting performance and capability indices

If process performance/capability statistics are used for process qualification, they shall be reported in relation to ISO 22514-2: 2013.

Typical contents of such a report:

Process performance/capability index

Minimum process performance/capability index

Applied calculation method

Number of values included in the calculation

Measurement uncertainty

Time distribution model



Part II - calculation methods for location and dispersion in Q-DAS products

The following table shows the changes of labels for calculation methods.

Location and dispersion calculation methods

Location parameter

l

ISO 21747: 2006 ISO 22514-2: 2013 distribution model

1 1 A1, B

2 2 A1, A2, B, C1, C2, C3, C4, D

3 2 A1, A2, B, C1, C2, C3, C4, D

4 3 A1

5 4 A1, A2, B

Dispersion parameter

d

1 2 A1

2 3 A1

3 4 A1

4 5 A1, A2, B, C1, D

5 -- --

6 1 A1, A2, B, C1, C2, C3, C4, D

Table 5: Comparison of ISO 22514 and ISO 21747 labels for process location and dispersion estimators



Calculation method settings in Q-DAS software products

Settings for stable processes

The following figure shows all methods complying with ISO 22514-2 in a red frame. All other calculation methods are not defined in ISO 22514-2 and should therefore not be used if compliance to ISO 22514-2 is important.

All labels of the calculation methods have been changed in ISO 22514-2. The following table shows what the new labels refer to.

Label of Calculation Method Applicable to time dependent distribution model ISO 21747: 2006 ISO 22514-2: 2013

M14,1 M3,2 A1

M14,2 M3,3 A1

M14,3 M3,4 A1

M14,4 M3,5 A1

M11,5 -- --

M12,5 -- --

M11,6 M1,1 A1, B

M13,6 M2,1 A1, A2, B, C1, C2, C3, C4, D

Table 6: Comparison of ISO 21747 and ISO 22514 labels for calculation methods of location and dispersion (stable)



Settings for instable processes

The following shows all methods complying with ISO 22514-2 in a red frame. All other calculation methods are not defined in ISO 22514-2 and should therefore not be used if compliance to ISO 22514-2 is important.

All labels of the calculation methods have been changed in ISO 22514-2. The following table shows what the new labels refer to.

Label of Calculation Method Applicable to time dependent distribution model ISO 21747: 2006 ISO 22514: 2013

M14,4 M3,5 A1*

M11,6 M1,1 A1*, B

M13,6 M2,1 (A1*, A2*), B, C1, C2, C3, C4, D

Table 7: Comparison of ISO 21747 and ISO 22514 labels for calculation methods of location and dispersion (not stable)

* If a process is not considered to be in a state of statistical control, this time distribution model should not be applied

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