E4136110r b en

© RENAULT 2011 Origin : PEGI - Renault Page : 1 / 22
Approval of measurement facility capability /
Specific inspection facility
E41.36.110.R /B
________________________________________
Standard
________________________________________
Status Enforceable
TRANSLATION ADVISORY NOTICE: This document has been translated from French. In the event of any
dispute, only the French version is referred to as the reference text and is binding on the parties
Object Define the capability approval procedure for any specific inspection facility,
whatever its characteristics, used for dimensional measurement.
It applies to all specific inspection facilities defined above, for example inspection
fixtures, specific automatic inspection machines, inspection stations built into
machine tools, etc.
It is possible to apply this procedure for checking of a specific characteristic of an
all-purpose measurement facility, according to predetermined instructions, after
conventional geometric acceptance testing of the facility.
By analogy, application of this standard can be extended to inspection facilities for other
measurable variables.
Scope Renault Group
Issued by 66140 - Profession and Upstream Process department
Confidentiality Not confidential
Approved by Function Signature Application Date
Patrice Duhaut Leader of the UET Innovation &
transverse expertise
06/2011

E41.36.110.R /B
History of versions
Version Up date Object of main modifications Author
A 09/2010 Creation Slawomir Indyk
B 06/2011 Deletion of the xls given file.
Annex 2, § 2.2.2 : Deletion of the drawing: " Graph of risk of error
of judgement R for CMC of 2.3 and 4"
Slawomir Indyk
Supersedes E41.36.110.R /A of 09/2010
Availability Inside Renault, on the Intranet: http://gdxpegi.ava.tcr.renault.fr
Outside Renault, on the Internet: www.cnomo.com
E-mail : norminfo.moyens@renault.com
Documents cited Regulations :
International :
European :
French :
CNOMO :
Renault :
Other internal doc :
Other external doc :
Coding ICS : 03.100.50 ; 03.120.30 ; 17.020
Class E41
Key words capabilite, aptitude, statistique, cmc, mesure, controle dimensionnel, capability, ability,
measurement, statistics, dimensional check
Language English
(1) Have participated in writing the document
Site Department Name Site Department Name
CTR 66140 Goncalves T

E41.36.110.R /B
Contents
Page
1 General ......................................................................................................................................3
2 Definitions .................................................................................................................................4
3 Acceptance of facility geometry - Methodology....................................................................5
3.1 Precautions................................................................................................................................................. 5
3.2 Repeatability of calibration measurements on the inspection facility......................................................... 5
3.3 Repeatability of measurement of a part on the inspection facility.............................................................. 5
3.4 Measuring several parts on the inspection facility...................................................................................... 5
3.5 Metrology measurement of parts................................................................................................................ 6
4 Calculation of inspection machine capability coefficient (CMC) .........................................7
4.1 Notation ...................................................................................................................................................... 7
4.2 Calculating average values ........................................................................................................................ 7
4.3 Calculation of variances ............................................................................................................................. 8
4.4 Calculation of average precision error ....................................................................................................... 8
4.5 Calculation of inspection facility global uncertainty.................................................................................... 8
4.6 Calculation of inspection facility capability coefficient................................................................................ 8
5 Machine capability approval....................................................................................................9
6 Simplified acceptance..............................................................................................................9
7 List of reference documents....................................................................................................9
Annex 1: Analysis of causes of uncertainty ......................................................................................10
Annex 2: Methodological supplement................................................................................................15
Annex 3: Example of CMC calculation ...............................................................................................21
1 General
A specific inspection facility, whether manual or automatic, is a facility only able to check the
characteristics for which it has been designed (e.g.: multidimension check).
The purpose of capability approval is to:
 Provide a practical check that the equipment and the process are able to carry out the
operation for which they have been designed (functional aptitude),
 Check that the degree of uncertainty in measurement is compatible with the tolerances for the
parts to be inspected (accuracy of measurement).
This type of check makes it possible to evaluate both uncertainties due to manufacture and those due to
design.
It is also used to check that the utilisation and calibration instructions are of operational standard.
Le The principal consists in measuring one or several parts first using metrological means and then using
the specific inspection facility, and then comparing the results.

E41.36.110.R /B
2 Definitions
Calibration master (for specific inspection facility)
Measurement made on a part with dimensions generally close to those of parts to be checked and
with faults in form and temporal stability of dimensions compatible with the degree of precision
required, this being better than of the facility as s whole.
Average accuracy error
J = systematic component, average error for a measuring instrument in the measurement range
studied.
Repeatability
Dispersion of measurement results for a part, repeated in identical conditions and without
recalibration, over a short period:
Repeatability of calibration master measurements is equal to ± Ie where :
 le = 2 se
 and "se" is the experimental standard deviation over several calibration measurements
taken on the measurement facility.
Repeatability of measurements for a parts equal to ± Ir where :
 Ir = 2 sr
 and "sr" is the experimental standard deviation over several measurements of a part taken
on the measurement facility.
Overall uncertainty for inspection facility
lg = Overall uncertainty in measurements made on the inspection facility, calculated from the values
read.
Uncertainty of metrology measurements
lmetro = Uncertainty of metrology measurements.
Tolerance bracket
lT = TB= upper and lower limits of tolerance on the characteristics checked on the facility.
Inspection machine capability coefficient
The inspection machine capability coefficient (CMC) is the relationship which characterizes the ability
of the inspection machine to measure a given characteristic with the required degree of precision.
A coefficient takes account of all of the errors in measurement due to the measuring method, the
design of facility, to its manufacture, to the part to be measured (faults in for, deformations) and to the
calibration master.
gI2
IT
=CMC

E41.36.110.R /B
3 Acceptance of facility geometry - Methodology
3.1 Precautions
The finalised inspection facility is to be installed under the normal utilisation conditions specified by the
instructions for utilizations at stations.
3.2 Repeatability of calibration measurements on the inspection facility
Calibration measurement must have been carried out less than six months ago. Its theoretical
value and degree of uncertainty of measurement are known.
Calibrate the inspection facility using the calibration master provided for this purpose and following
the instructions in the operating manual.
Measure the calibration 5 times on the inspection facility being tested, without altering calibration.
Remove the calibration master from the facility after each measurement.
Measurements are made on the inspection facility in strict accordance with the instruction in the
instruction manual for the inspection facility.
 Calculate the experimental calibration standard deviation (se) on the inspection facility.
Repeatability of measurements on the inspection facility is equal to ± Ie where le = 2 se.
If le is greater than the value specified in paragraph 5, the inspection facility must be reviewed.
Note: If the nature of the clause checked does not require a calibration master, take se = 0.
3.3 Repeatability of measurement of a part on the inspection facility
Take a typical series production part,
Measure this part at least 5 times on the inspection facility, removing the part after each
measurement and without recalibrating.
Calculate the standard deviation (sr) over the 5 measurements.
Repeatability of measurements on the measurement facility is equal ± Ir where Ir = 2 sr.
If Ir is greater than the value specified in paragraph 5, the inspection facility must be reviewed before
carrying on with the acceptance procedure.
This check makes it possible to avoid complete acceptance if the inspection facility has a serious fault.
If no serious fault is encountered, go to the next operation.
3.4 Measuring several parts on the inspection facility
Selecting sample parts:
Chose a minimum of 5 parts, representative of series production, and with characteristics as well
distributed over a tolerance bracket greater than 0,6 lT (TB) as is possible.
At least parts must fall within the tolerance bracket.
To gain better knowledge of the inspection facility, it is useful to take a second sample. The values for all
of the parts must be close the operating range. The values are to be obtained by supplementary
machining if required.
Measure the parts on the inspection facility by circular permutation until each part has been measured
5 times, without recalibrating and over a short period of time.

E41.36.110.R /B
3.5 Metrology measurement of parts
Give the conventional true value, obtained in metrology, with the corresponding degree of uncertainty of
measurement. In order to reduce the uncertainty in repeatability of the measuring instrument, it is
recommended to take as the conventionally true value the average of n measurements made on the
same part.
In this case, the metrology uncertainty of repeatability is divided by n.
Precautions:
The uncertainty for metrology measurement must be equal to or less than half of the theoretical degree of
uncertainty of measurement on the inspection facility
It is possible that geometrical faults in machining origins or deformation of a part may introduce e degree
of dispersion of measurement making it possible to fulfil the condition described above
Two cases must then be considered:
a) Inspection facility for a characteristic of machining instruction (non functional dimension)
The metrology measurement must be made under the same conditions as on the specific
inspection facility, i.e. using:
 the same supports,
 the same measurement points,
 and in so far is possible, the same clamping apparatus.
If the uncertainty of metrology measurement is greater than lT/16 (due to defects of form in
machining origins or a deformable part, etc.) proceed as follows:
1. bring the measurement facility to be checked to the metrology measurement facility,
2. check that the inspection facility support points are similar to those for the machining
facility,
3. as reference, take the part support points on the facility to be checked,
4. measure the part installed on this inspection facility.
If is not possible to bring the inspection fixture to the metrology measurement facility or to use
the same clamping as on the inspection facility, the part must be measured free standing, on
condition that a check is made to ensure that deformation due to clamping is constant pr
negligible.
If metrology measurement cannot be made with a sufficient degree of precision, the case must
be studied in collaboration with the central Metrology Department.
b) Inspection facility for a functional characteristic
The purpose of this type of facility is to check compliance of functional dimensions of parts in
relation to their design drawings.
Metrology measurements are then made on the part free standing, unless particular
requirements for measurement are specified by Design departments. The existing machining
origins are not used as measurement references
Remark: Certain characteristics in machining instructions are also functional. In such cases,
part must be measured free standing.

E41.36.110.R /B
4 Calculation of inspection machine capability coefficient (CMC)
An example of calculation is given in appendix 3.
4.1 Notation
p = number of parts
i = part index (from 1 to p)
m = number of measurement on a part or on calibration master on the inspection facility
j = measurement index (from 1 to m)
x = value obtained in metrology
y = value obtained on inspection facility
xi = conventional true value for part no i, measured in metrology
yij = value measured on inspection facility, on part no. i, during measurement no. j
J = average precision error for inspection facility
V = variance
s = experimental standard deviation = V
l = measurement uncertainty
Indices affecting these 3 variables:
a = amplification
l = linearity
r = repeatability
g = global
e = calibration master
metro = metrology
lT = tolerance bracket (TB) for the characteristic to be checked.
4.2 Calculating average values
∑
p
1=i ix
p
1
=x = average of measurement on all parts in metrology
∑
m
1=j iji y
m
1
=y = average of m measurements on part No I on inspection facility
∑
p
1=i iy
p
1
=y = average of all measurement on all parts on inspection facility

E41.36.110.R /B
4.3 Calculation of variances
Principle of calculation
The results of the (n) of the measurements (z) are considered as having the same distribution law.
Estimation of variance V (z) is given by the formula:
∑
n
1=i
2
i )z-(z
1-n
1
=V(z)
Practical calculation: it is preferable to use the equivalent formula:













∑ ∑
n
1=i
2
n
1=i i
2
i
z
n
1
-z
1-n
1
=V(z)
Calculation of overall variance of inspection facility
Vg = variance of (yij - xi).
To simplify the notation, we write:
∑ ∑∑
p
1=
m
1=iijij =:etx-y=d i j
( ) 





∑ ∑
2
ij
2
ij d
pm
1
-d
1-pm
1
=gV
Calculation of calibration master variance on inspection facility
Ve = variance of (yei)'s, values of the calibration master measured on the inspection facility
y
m
1
-y
1-m
1
=
m
1=j
2
m
1=j ej
2
ej













∑ ∑eV
4.4 Calculation of average precision error
x-y=J
4.5 Calculation of inspection facility global uncertainty
This is equal to ± Ig where:
egg V+V2+J=i
4.6 Calculation of inspection facility capability coefficient
gI2
IT
=CMC

E41.36.110.R /B
5 Machine capability approval
Unless otherwise specified in the specifications, the facility shall be accepted if the conditions of the table
below are fulfilled (see details of calculations in paragraph 4).
Table 1
IT > 16 µm and Q > 5 ≤ 16 µm and Q ≤ 5
Facility resolution ≤ IT/20 ≤ IT/10
± Ie ≤ ± IT/20 ≤ ± IT/10
± Ir ≤ ± IT/8 ≤ ± IT/4
± Imetro ≤ ± IT/16 ≤ ± IT/8
± Ig ≤ ± IT/8 ≤ ± IT/4
CMC ≥ 4 ≥ 2
Q: basic tolerance quality index.
Remarks: The indicated resolution is only necessary for calculation of CMC.
The limit values for Ig comply with standard ISO 14253-1.
If these conditions are nor fulfilled, it is recommended to analyse the possible causes
using the detailed calculations and the graphic representation provided in annex 1.
6 Simplified acceptance
This procedure only applies in cases where it is impossible to apply the acceptance procedure
described in the paragraph above. (For example, if typical parts are missing on delivery on inspection
facility)
The procedure makes it possible to refuse a facility which fails to comply, but acceptance can only be
pronounced after the full acceptance procedure.
The method is identical to that for complete acceptance, but here only on part is measured (instead of
the minimum 5).
This part is measured in metrology, then 5 times on the inspection facility without modifying the
calibration, and lifting the part after each measurement.
7 List of reference documents
NOTE : For undated documents, the latest version shall apply
ISO 14253-1 : Geometrical product specification (GPS). Inspection by measurement of workpieces
and measuring equipments. Part 1 : decision rules for proving conformance or non-
conformance with specifications

E41.36.110.R /B Annex 1 Normative
Annex 1: Analysis of causes of uncertainty
The graphs and calculations described, in this annex are optional. They allow you to analyse the various
causes of uncertainty and to arrive at a "diagnosis" of them.
For example, it is possible to discern a predominant fault. If there is no predominant fault, results must be
interpreted with caution.
1 Calculation of regression curve
(See graphs, paragraph 4 of annex)
y = ax + b is the equation for the curve showing regression of y in relation to x, calculated for all points
(xi, yij).
Remark: the curve passes through the point y,x .
To simplify writing, we can use the following form of notation:
∑ ∑ p
1=i
=
where n = m . p (Number of xi, yij points)
( )∑ ∑
∑∑∑
2
i
2
i
iiii
x-xn
y.x-yxn
=a
.
x.a-y=b
To determine whether this curve is significantly different from the y = x curve, it is possible to apply the
following statistical test:
The quantity: 



 2
a
2
y
t+t
2
1
=F
Follows a Snédécor law with 2 and (p - 2) degrees of freedom (see table, paragraph 3 of annex) where:
( )
l
2
2
y V
x-yp
=t
( ) ( )
V
x-x1-a
=t
l
2
i
p
1=i
2
2
a
∑
(for Vl calculation see paragraph 2.2 of annex).
In Snédécor table (see paragraph 3 of annex), read the value for Flimit for γ1 = 2.
γ2 = p - 2 and p = 0.05 :
 Si F ≤ Flimit the regression curve is not significantly different from y = x.
 Si F > Flimit the regression curve is significantly different from y = x.
To determine whether this is due to the slope of the curve or to precision error, use the Student-Ficher
test: tandt ya according to a Student-Ficher law with (p - 2) degrees of freedom.
In the Student-Ficher table (see paragraph 3 of annex), read the value of t for γ = p - 2 and P = 0.05.
 If at > t is read in the table, the difference is due to the slope of the curve (amplification error).
 If yt > t is read in the table, the difference arises from precision error.
If one of the 2 tests is significant, it is possible to correct, by modifying:
 Either the gain for amplification error,
 Or the calibration curve for precision error.
Re-measure the parts on the inspection machine and re-calculate the CMC. If not, these two components
are considered to be random and included in the overall uncertainty.

2 Calculation of variances
2.1 Calculation of variance due to repeatability error (Vr)
Vr = common repeatability variance
Suppose that: ( )iijij y-y=e













∑ ∑∑
2
m
1=j
m
1=j ij
2
ij
p
1=ir e
m
1
-e
1)-(mp
1
=V
The uncertainty due to repeatability is equal to ± Ir where:
rr V2=I
2.2 Calculation of variance due to linearity error (Vl)
Vl = variance of: ei = b)ax(y ii +=













∑ ∑
2
p
1=i
p
1=i i
2
il e
p
1
-e
2-p
1
=V
Uncertainty due to linearity error is equal to ± Il where:
2.3 Calculation of variance due amplication error (Va)
Va = variance of : (axi + b) - (xi + J) = (a = 1)2
. variance of xi
Va = 





− ∑∑ =+
− P
1I
2
i
P
1I
2
I
1a
2
)x..(
P
1
....X
p
.)(
Uncertainty due to amplification error is equal to ± Ia where:
2.4 Remark
The relationship of one of these three variances to overall variance Vg gives an order of magnitude for the
percentage of variability explained by the variance chosen. However, this relationship is only an indication
as the sum of (Vr + Vl + Va) is not exactly equal to Vg, the third variance not being totally independent of
the first two. The aim of the calculation of these variances is simply to give an orientation for diagnosis.

3 Distribution tables
Figure 1
γ1= 2γ2
P =005
1 199.5
2 19.5
3 9.55
4 6.94
5 5.79
6 5.14
7 4.74
8 4.46
9 4.26
10 4.10
11 3.98
12 3.88
13 3.80
14 3.74
15 3.68
16 3.63
17 3.59
18 3.55
19 3.52
20 3.49
P
γ
0.05
1 12.706
2 4.303
3 3.182
4 2.776
5 2.571
6 2.447
7 2.365
8 2.306
9 2.262
10 2.228
11 2.201
12 2.179
13 2.160
14 2.145
15 2.131
16 2.120
17 2.110
18 2.101
19 2.093
20 2.086
DISTRIBUTION TABLE FOR F
(Snédécor Variable)
Value for F with probability P being exceeded
(F = SS 2
2
2
1 / )
DISTRIBUTION TABLE FOR t
(Student law)
Values for t with probability P of being exceeded for absolute
valued'être dépassée en valeur absolue

4 Graphic representation of main causes of errors
Figure 2
y
x
INSPECTION
FACILITY
METROLOGY
PRECISION ERROR
x
x
x
x
x
J
x
REPEATABILITY ERROR
y
x
INSPECTION
FACILITY
METROLOGY
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
LINEARITY ERROR
y
x
INSPECTION
FACILITY
METROLOGY
+
+
+
+
++
+
+
+
+
+
+
AMPLIFICATION ERROR
x
INSPECTION
FACILITY
METROLOGY
x
x
x
x
x
y

Uncertainty of measurement = yij – xi
REPEATABILITY LINEARITY AMPLIFICATION AVEARGE PRECISION
= [yij –yi] + [yi – (axi + b)] + [(axi + b) – (xi + J)] + (xi + J) – xi]
METROLOGY
INSPECTION
FACILITY
y
=
x
+
J
y
=
x
REGRESSION
LINE
Y
= ax + b
J
x1 x1 xx
yij
yy
yiyi
REPEATABILITY
LINEARITY
AMPLIFICATION
PRECISION
METROLOGY
INSPECTION
FACILITY
y
=
x
+
J
y
=
x
REGRESSION
LINE
Y
= ax + b
J
x1 x1 xx
yij
yy
yiyi
REPEATABILITY
LINEARITY
AMPLIFICATION
PRECISION

E41.36.110.R /B Annex 2 Informative
Annex 2: Methodological supplement
This annex gives:
 Additional methodological data for certain aspects of application,
 Evaluation of risk of error of judgement for an inspection facility during measurement.
1. Methodological supplement for approval of capability of specific
inspection facility capability
The (non-exhaustive) list of points given below may be completed to deal with other particular cases
encountered, by various departments concerned during application of the standard.
1.1 Choice or representative characteristics
Which dimensions to use to calculate CMC?
All of the characteristics checked must be covered by a CMC calculation. In practice, a decision may be
taken not to calculate the CMC for every characteristic, subject to an agreement between the designer,
the plant where the facility will be used and the department responsible for acceptance; however, the
CMC must be calculated for all the characteristics subject to production facility capability measurement,
and for all functional dimensions.
1.2 Parts samples
When it is not possible to obtain parts distributed over more than 0,6 TB (IT):
The parts must have an optimum distribution of their characteristics over a bracket 0.6 TB: a parts
sample aiming at this optimum objective is necessary in order to evaluate errors of accuracy, linearity
and amplification across the entire operating range of the inspection facility.
Ideally range should extend beyond the TB.
For practical reasons, this type of sample is not always possible at first reception of the facility; in this
case it is possible to refuse the facility if the CMC is outside of tolerances for a single part or for parts
extending avec less than 0.6 TB, but final acceptance can only be given for series production parts with
adequate dispersion.

2. Evaluation of risk of error of judgement due to use of an inspection
facility
The process described below makes it possible to evaluate the risk of making an erroneous judgement
due to the use of an inspection facility of known capability for the value to be measured.
2.1 Principle of evaluation
The capability of an inspection facility, as specified by this standard defines uncertainty of measurement
as the sum of the average precision error and the uncertainty due to errors of linearity, amplification and
repeatability of the facility.
This uncertainty of measurement brought, on both sides, to the value to be measured, represents the
bracket in which the true value of a measurement is situated.
Thus, for any measurement of characteristics aiming to compare a measured value Yi to a specified limit
Ls, it is possible to estimate a risk error of judgement which is relative to the probable part of true values
which would not correspond to the judgement of the value measured.
This part is determined in relation to the absolute error between the value read Yi and the specified limit
Ls with the degree of uncertainty Ig.
2.2 Interpretation of CMC
2.2.1 Evaluation of risk applied to a measurement value
The CMC characterizes uncertainty by:
CMC2
IT
Ig
×
=
From which the relationship determining the risk of error of judgement.
IT
LY
Kwhere
CMCKCMC
IT
LY
I
LY
si
si
g
si
−
=
××=××
−
=
−
22
Thus to evaluate the risk of error of judgment R applying to a value from a facility, we calculate for each
K, the normal density of probability of risk, which can be determined from the table below.
This table, which characterizes the function of distribution of the reduced normal variable, determines the
probability P from the expression 4 x K x CMC, which allows us to evaluate the risk R from the statement
R = 1 - P.

Table 1: Table determining P as a function of (4 x K x CMC)
4xKxCMC 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.52.39 0.5279 0.5319 0.5359
0.1 0.5395 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7923 0.7852
0.9 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8455 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9046 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.6515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
2.0 0.9772 0.9798 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.2 0.9861 0.9864 0.9668 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3 0.9863 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
3.1 0.93
03 0.93
06 0.93
10 0.93
13 0.93
16 0.93
18 0.93
21 0.93
24 0.93
26 0.93
29
3.2 0.93
31 0.93
34 0.93
36 0.93
38 0.93
40 0.93
42 0.93
44 0.93
46 0.93
48 0.93
50
3.3 0.93
52 0.93
53 0.93
55 0.93
57 0.93
58 0.93
60 0.93
61 0.93
62 0.93
64 0.93
65
3.4 0.93
66 0.93
68 0.93
69 0.93
70 0.93
71 0.93
72 0.93
73 0.93
74 0.93
75 0.93
76
3.5 0.93
77 0.93
78 0.93
78 0.93
79 0.93
80 0.93
81 0.93
81 0.93
82 0.93
83 0.93
83
3.6 0.93
84 0.93
85 0.93
85 0.93
86 0.93
86 0.93
87 0.93
87 0.93
88 0.93
88 0.93
89
3.7 0.93
89 0.93
90 0.94
00 0.94
04 0.94
08 0.94
12 0.94
15 0.94
18 0.94
22 0.94
25
3.8 0.94
28 0.94
31 0.94
33 0.94
36 0.94
38 0.94
41 0.94
43 0.94
46 0.94
48 0.94
50
3.9 0.94
52 0.94
54 0.94
56 0.94
58 0.94
59 0.94
61 0.94
63 0.94
64 0.94
66 0.94
67
NOTE 1 : For example: notation 0.93
03, equals 0.99903 (Revue de statistiques Appliquées, Tables
statistiques, CERESTA)
Example of calculation of risk or error of judgment
 Characteristic to be checked: 10 ± 0.05
mm
 CMC of facility : 3.5
 Value measured : 10.04 mm
a) Risk of error of judgement brought to upper limit
1,0
1,0
05,1004,10
=
−
=K
and 4 x K x CMC = 1.4
→ P = 0.9192
→ R = 1 - P = 0.08 i.e. 8 %
This value therefore has an 8 % risk of being greater than 10.05 mm, i.e. not acceptable.
Nota: In the case of a CMC of 4, this risk will be 5 %,

b) Risk of error of judgement brought to lower limit
0,9
0,1
10,049,95
K =
−
=
and 4 x K x CMC =12.6
→ P ~ 1
→ R ~ 0
This value therefore has a 0 % risk being less than 9.95 mm, i.e. not acceptable.
2.2.2 Evolution of judgement risk
Iit can be seen that:
 The lower the CMC, the higher the risk of error of judgement,
 The more the measurement value tends towards the specified limit, (K → 0), the more the error
tends towards 50 %,
2.2.3 Characterizing the range of measurement for a given risk
Applying a principle identical to that for paragraph 2.2.1, it is possible to determine the range of
measurements for which the risk of error of judgement is greater than a specified risk.
This range is characterized by two limits which are determined in relation to K, corresponding to the
specified risk.
Thus, for a specified risk Rs, we first calculate the probability Ps from the equation
Ps = 1 - Rs,
When Ps is known, we can determine the result corresponding to the expression 4 x K x CMC, from the
table of fractiles for the reduced normal law given below
Using the result, and knowing the CMC for the facility, it then remains to calculate the relationship K
which characterizes the range of measurement corresponding to the specified risk.

Table 2: table for determination of (4 x K x CMC) as a function of Ps
Ps 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 -
0.00 ∞ 3.0902 2.8782 2.7478 2.6521 2.5758 2.5121 2.4573 2.4089 2.3656 2.3263 0.99
0.01 2.3263 2.2904 2.2571 2.2262 2.1973 2.1701 2.1444 2.1201 2.0969 2.0749 2.0537 0.98
0.02 2.0537 2.0335 2.0141 1.9954 1.9774 1.9600 1.9431 1.9268 1.9110 1.8957 1.8808 0.97
0.03 1.8808 1.8663 1.8522 1.8384 1.8250 1.8119 1.7991 1.7866 1.7744 1.7624 1.7507 0.96
0.04 1.7507 1.7392 1.7279 1.7169 1.7060 1.6954 1.6849 1.6747 1.6646 1.6546 1.6449 0.95
0.05 1.6449 1.6352 1.6258 1.6164 1.6072 1.5982 1.5893 1.5805 1.5718 1.5632 1.5548 0.94
0.06 1.5548 1.5464 1.5382 1.5301 1.5220 1.5141 1.5063 1.4985 1.4909 1.4833 1.4758 0.93
0.07 1.4758 1.4684 1.4611 1.4538 1.4466 1.4395 1.4325 1.4255 1.4187 1.4118 1.4051 0.92
0.08 1.4051 1.3984 1.3917 1.3852 1.3787 1.3722 1.3658 1.3595 1.3532 1.3469 1.3408 0.91
0.09 1.3408 1.3346 1.3285 1.3225 1.3165 1.3106 1.3047 1.2988 1.2930 1.2873 1.2816 0.90
0.10 1.2816 1.2759 1.2702 1.2646 1.2591 1.2536 1.2481 1.2426 1.2372 1.2319 1.2265 0.89
0.11 1.2265 1.2212 1.2160 1.2107 1.2055 1.2004 1.1952 1.1901 1.1850 1.1800 1.1750 0.88
0.12 1.1750 1.1700 1.1650 1.1601 1.1552 1.1503 1.1455 1.1407 1.1359 1.1311 1.1264 0.87
0.13 1.1264 1.1217 1.1170 1.1123 1.1077 1.1031 1.0985 1.0939 1.0893 1.0848 1.0803 0.86
0.14 1.0803 1.0758 1.0714 1.0669 1.0625 1.0581 1.0537 1.0494 1.0450 1.0407 1.0364 0.85
0.15 1.0364 1.0322 1.0279 1.0237 1.0194 1.0152 1.0110 1.0069 1.0027 0.9986 0.9945 0.84
0.16 0.9945 0.9904 0.9863 0.9822 0.9782 0.9741 0.9701 0.9661 0.9621 0.9581 0.9542 0.83
0.17 0.9542 0.9502 0.9463 0.9424 0.9385 0.9346 0.9307 0.9269 0.9230 0.9192 0.9154 0.82
0.18 0.9154 0.9116 0.9078 0.9040 0.9002 0.8965 0.8927 0.8890 0.8853 0.8816 0.8779 0.81
0.19 0.8779 0.8742 0.8705 0.8669 0.8633 0.8596 0.8560 0.8524 0.8488 0.8452 0.8416 0.80
0.20 0.8416 0.8381 0.8345 0.8310 0.8274 0.8239 0.8204 0.8169 0.8134 0.8099 0.8064 0.79
0.21 0.8064 0.8030 0.7995 0.7961 0.7926 0.7892 0.7858 0.7824 0.7790 0.7756 0.7722 0.78
0.22 0.7722 0.7688 0.7655 0.7621 0.7588 0.7554 0.7521 0.7488 0.7454. 0.7421 0.7388 0.77
0.23 0.7388 0.7356 0.7323 0.7290 0.7257 0.7225 0.7192 0.7160 0.7128 0.7095 0.7063 0.76
0.24 0.7063 0.7031 0.6999 0.6967 0.6935 0.6903 0.6871 0.6840 0.6808 0.6776 0.6745 0.75
0.25 0.6745 0.6713 0.6682 0.6651 0.6620 0.6588 0.6557 0.6526 0.6495 0.6464 0.6433 0.74
0.26 0.6433 0.6403 0.6372 0.6341 0.6311 0.6280 0.6250 0.6219 0.6189 0.6158 0.6128 0.73
0.27 0.6128 0.6098 0.6068 0.6038 0.6008 0.5978 0.5948 .05918 0.5888 0.5858 0.5828 0.72
0.28 0.5828 0.5799 0.5769 0.5740 0.5710 0.5681 0.5651 0.5622 0.5592 0.5563 0.5534 0.71
0.29 0.5534 0.5505 0.5476 0.5446 0.5417 0.5388 0.5359 0.5330 0.5302 0.5273 0.5244 0.70
0.30 0.5244 0.5215 0.5187 0.5158 0.5129 0.5101 0.5072 0.5044 0.5015 0.4987 0.4959 0.69
0.31 0.4959 0.4930 0.4902 0.4874 0.4845 0.4817 0.4789 0.4761 0.4733 0.4705 0.4677 0.68
0.32 0.4677 0.4649 0.4621 0.4593 0.4565 0.4538 0.4510 0.4482 0.4454 0.4427 0.4399 0.67
0.33 0.4399 0.4372 0.4344 0.4316 0.4289 0.4261 0.4234 0.4207 0.4179 0.4152 0.4125 0.66
0.34 0.4125 0.4097 0.4070 0.4043 0.4016 0.3989 0.3961 0.3934 0.3907 0.3880 0.3853 0.65
0.35 0.3853 0.3826 0.3799 0.3772 0.3745 0.3719 0.3792 0.3665 0.3638 0.3611 0.3585 0.64
0.36 0.3585 0.3558 0.3531 0.3505 0.3478 0.3451 0.3425 0.3398 0.3372 0.3345 0.3319 0.63
0.37 0.3319 0.3292 0.3266 0.3239 0.3213 0.3186 0.3160 0.3134 0.3107 0.3081 0.3055 0.62
0.38 0.3055 0.3029 0.3002 0.2976 0.2950 0.2924 0.2898 0.2871 0.2845 0.2819 0.2793 0.61
0.39 0.2793 0.2767 0.2741 0.2715 0.2689 0.2663 0.2637 0.2611 0.2585 0.2559 0.2533 0.60
0.40 1.2533 0.2508 0.2482 0.2456 0.2430. 0.2404 0.2378 0.2353 0.2327 0.2301 0.2275 0.59
0.41 0.2275 0.2250 0.2224 0.2198 0.2173 0.2147 0.2121 0.2096 0.2070 0.2045 0.2019 0.58
0.42 0.2019 0.1993 0.1968 0.1942 0.1917 0.1891 0.1866 0.1840 0.1815 0.1789 0.1764 0.57
0.43 0.1764 0.1738 0.1713 0.1687 0.1662 0.1637 1.1611 0.1586 0.1560 0.1535 0.1510 0.56
0.44 1.1510 0.1484 0.1459 0.1434 0.1408 0.1383 0.1358 0.1332 0.1307 0.1282 0.1257 0.55
0.45 0.1257 0.1231 0.1206 0.1181 0.1156 0.1130 0.1105 0.1080 0.1055 0.1030 0.1004 054
0.46 0.1004 0.0979 0.0954 0.0929 0.0904 0.0878 0.0853 0.0828 0.0803 0.0778 0.0753 0.53
0.47 0.0753 0.0728 0.0702 0.0677 0.0652 0.0627 0.0602 0.0577 0.0552 0.0527 0.0502 0.52
0.48 0.0502 0.0476 0.0451 0.0426 0.0401 0.0376 0.0351 0.0326 0.0301 0.0276 0.0251 0.51
0.49 0.0251 0.0226 0.0201 0.0175 0.0150 0.0125 0.0100 0.0075 0.0050 0.0025 0.0000 0.50
- 0.010 0.009 0.008 0.007 0.006 0.005 0.04 0.003 0.002 0.001 0.000 Ps
Revue de Statistiques Appliquées, Tables statistiques, CERESTA,

Example of determination of measurement range
 Checked characteristic : 10 ± 0.05
mm
 CMC of facility : 3.5
 Specified risk : 5 %
Calculation of K
Ps = 1 - Rs = 0.95 (i.e. 95 %)
→ 4 x K x CMC = 1.64
→ K = 0.12
0.1ITwhere0.012LY0.12
IT
LY
K si
si
==−→=
−
=
Thus the limits of the measurement range brought to a low limit and having a risk level greater than
5% are:
9.938 mm and 9.962 mm
And the limits for the measurement range with a risk greater than 5 % brought to the upper limit are:
10.038 mm and 10.062 mm
Graphic representation of range of measurement with risk factor
greater than specified limits by 5 %

Annex 3: Example of CMC calculation
Nominal dimension : 10 Max. : 10.0250 Min. : 9.9750
For reasons of accuracy and if possible, express measurement as errors with respect to the nominal dimension,
and in the smallest unit, as well as the l'IT (TB)
IT : 50 (TB) Used unit: Micrometer
PRELIMINARY STEPS :
REPEATABILITY OF CALIBRATION ON FACILITY
Measurement N° 1 2 3 4 5
Value yej 2 1 2 1 1
Average
5
y
y
ej
e
∑= = 1.4000
Repeatability variance
∑= )-( yy
4
1
V eej
2
e = 0.3000
Uncertainty
V2I ee = = 1.0954
DECISION (1) Ie > IT/20 (2) Facility to be reviewed
IT/20 (2) 2.5000 Ie ≤ IT/20 (2) Acceptable
REPEATABILITY OF MEASUREMT OF A PART ON THE FACILITY
Value yj 50 49 48 50 49
Value yj 48 50 47 49 50
Average
m
y
y j∑
= = 49.000
Repeatability variance ∑= )-( yy
1)-(m
1
V j
2
r = 1.1111
Uncertainty
V2I rr =
m : number of measurement and
5 ≤ m ≤ 10
= 2.1082
DECISION (1) Ir > IT/8 (2) Facility to be reviewed
IT/8 (3) IT = TB 6.2500 Ir ≤ IT/8 (2) Acceptable
(1) strike out as appropriate (3) IT/8 for IT (TB) ≥ 16 µm
(2) IT/20 for IT (TB) ≥ 16 µm IT/4 for IT (TB) <16 µm
IT/10 for IT(TB) <16 µm j Measurement index

PARTS 1 TO 5 MEASURED ON FACILITY
Measurement N° Part N° 1
y1J
Part N° 2
y2J
Part N° 3
y3J
Part N° 4
y4J
Part N° 5
y5J
1 yi1 -10 0 20 -5 2
2 yi2 -11 1 22 -3 3
3 yi3 -9 2 20 -2 4
4 yi4 -8 0 18 -3 2
5 yi5 -10 1 21 -3 5
METROLOGY VALUE : (METROLOGY MEASUREMENT UNCERTAINTY : Imetro = 2)
xi -13 2 19 -1 2
di1 = yi1 - xi 3 -2 1 -4 0
di2 = yi2 - xi 2 -1 3 -2 1
di3 = yi3 - xi 4 0 1 -1 2
di4 = yi4 - xi 5 -2 -1 -2 0
di5 = yi5 - xi 3 -1 2 -2 3
Average of difference averages:
pm
J
dij∑∑= = 0.4800
Difference overall variance:
1-pm
V
J)-d( ij
2
g
∑∑
= = 5.2600
Difference overall calibration master
deviation
Vs gg = = 2.2935
Repeatability variance on calibration
master
Ve = 0.3000
Repeatability standard deviation on
calibration master Vs ee = = 0.5477
Measurement uncertainty VVI eg2Jg ++= = 5.1959
CAPABILITY OF INSPECTION FACILITY : CMC = IT/2 Ig = 4.8115
RESULT (1)
CMC cdc : ≥ 4
CMC < CMC cdc
NON
UNACCEPTABLE
CMC > CMC cdc
ACCEPTABLE
i = Measurement N° index
j = part N° index
p = Number of parts
m = Number of measurement
(1) Unless otherwise specified: IT ≤ 16 µm when Q ≤ 5 CMC ≥ 2
IT > 16 µm and Q > 5 CMC ≥ 4

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