ISO 12491:1997

IS0
INTERNATIONAL
STANDARD
First edition
1997-05-01
Statistical methods for quality control of
building materials and components
M&hodes sta tistiques de con tr6le de la qua/it6 des ma tkiaux et &ments
de construction
Reference number
IS0 12491:1997(E)
IS0 12491:1997(E)
Page
Contents
........................................................................................
Scope
Normative references .
.................................................................................. 1
Definitions
a
Population and sample .
............................................................................. a
4.1 General
a
4.2 Normal distribution .
...................................................... 9
4.3 Log-normal distribution
.................................................................. 9
4.4 Normality tests
Methods of statistical quality control .
......................................................... 9
5.1 Quality requirements
..................................................
5.2 Basic statistical methods
5.3 Bayesian approach .
...........................................................
5.4 Additional methods
........................................... 12
Estimation and tests of parameters
..................................... 12
6.1 Principles of estimation and tests
6.2 Estimation of the mean .
.................................................. 13
6.3 Estimation of the variance
.......................................................
6.4 Comparison of means
.................................................. 15
6.5 Comparison of variances
......................................................... 15
6.6 Estimation of fractiles
......... 16
6.7 Prediction of fractiles using the Bayesian approach
ia
Sampling inspection .
ia
....................................................
7.1 Variables and attributes
.............................................. ia
7.2 Inspection of an isolated lot
..................... 19
7.3 Sampling inspection by variables: CJ known.
Sampling inspection by variables: o unknown . 20
7.4
..................................... 20
7.5 Sampling inspection by attributes
Annex
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Bibliography
. . . . . . .~.~.
Alphabetical index
0 IS0 1997
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ii
IS0 12491 :1997(E)
@ IS0
Foreword
IS0 (the International Organization for Standardization) is a worldwide
federation of national standards bodies (IS0 member bodies). The work of
preparing International Standards is normally carried out through IS0
technical committees. Each member body interested in a subject for which
a technical committee has been established has the right to be represented
on that committee. International organizations, governmental and non-
governmental, in liaison with ISO, also take part in the work. IS0
collaborates closely with the International Electrotechnical Commission
(IEC) on all matters of electrotechnical standardization.
Draft International Standards adopted by the technical committees are
circulated to the member bodies for voting. Publication as an International
Standard requires approval by at least 75 % of the member bodies casting
a vote.
International Standard IS0 12491 was prepared by Technical Committee
ISOmC 98, Bases for design of structures, Subcommittee SC 2, Reliability
of structures.
Annex A of this International Standard is for information only.

IS0 12491:1997(E) @ IS0
Introduction
Quality control of building materials and components is, according to
IS0 2394, an indispensable part of an overall concept of structural
reliability. As quality control is generally a time-consuming and expensive
task, various operational techniques and activities have been developed to
fulfil quality requirements in building. It appears that properly employed
statistical methods can provide efficient, economic and effective means of
quality control, particularly when expensive and destructive tests are to be
performed. The purpose of this International Standard is to provide general
techniques for quality control of building materials and components used in
building or other civil engineering works.
statistical methods .
Described techniques consist predominantly of classical
of common interest for all the participants in the building process. For other
statistical
more sophisticated techniques and specific problems, existing
standards listed in annex A should be applied.
iv
INTERNATIONAL STANDARD 0 IS0 IS0 12491:1997(E)
Statistical methods for quality control of building
materials and components
1 Scope
This International Standard gives general principles for the application of statistical
methods in the quality control of building materials and components in compliance with
the safety and serviceability requirements of IS0 2394.
This International Standard is applicable to all buildings and other civil engineering
work, existing or under construction, whatever the nature or combination of the
materials used, for example concrete, steel, wood, bricks.
2 Normative references
The following standards contain provisions which, through reference in this text,
constitute provisions of this International Standard. At the time of publication, the
editions indicated were valid. All standards are subject to revision, and parties to
agreements based on this International Standard are encouraged to investigate the
possibility of applying the most recent editions of the standards indicated below.
Members of IEC and IS0 maintain registers of currently valid International Standards.
General principles on reliability for structures.
IS0 2394:---l,
IS0 3534~19993, Statistics - Vocabulary and symbols - Part 1: Probability and
general statistical terms.
IS0 35342:1993, Statistics - Vocabulary and symbols - Part 2: Statistical quality
control.
3 Definitions
For the purposes of this International Standard, the definitions given in IS0 3534-1 and
IS0 3534-2, and the following definitions, apply.
NOTE - The terms and their definitions are listed in the order corresponding to their appearance
in the main text. An alphabetic list of these terms with numerical references to subclauses where
the terms appear is given in the index.
3.1 quality control: Operational techniques and activities that are used to fulfill
requirements for quality.
3.2 statistical quality control: That part of quality control in which statistical
methods are used (such as estimation and tests of parameters and sampling inspection).
’ To be published. (Revision of IS0 2394:1986)

IS0 12491:1997(E)
3.3 unit: Defined quantity of building material, component or element of a building or
other civil engineering work that can be individually considered and separately tested.
3.4 population: Totality of units under consideration.
3.5 (random) variable, X A variable which may take any of the values of a specified
set of values and with which is associated a probability distribution.
NOTE - A random variable that may take only isolated values is said to be “discrete ”. A random
variable which may take any value within a finite of infinite interval is said to be “continuous ”.
3.6 (probability) distribution: A function which gives the probability that a variable
X takes any given value (in the case of a discrete variable) or belongs to a given set of
values (in the case of a continuous variable).
3.7 distribution function, n(x): A function giving, for every value of x, the probability
that the variable X is less than or equal to x:
n(x) = Pr (XI x)
3.8 (probability) density function, f(x): The derivative (when it exists) of the
distribution function:
d=(x)
X=
f( >
dx
3.9 (population) parameter: Quantity used in describing the distribution of a random
variable in a population.
3.10 fractile, x : If X is a continuous variable and p is a real number between 0 and 1,
the p-fractile is the value of the variable X for which the distribution function equals p.
Thus x is a p-fractile if
P
PJX I x )=p
P
3.11 (population) mean, p: For a continuous variable X having the probability
density f(x), the mean, if it exists, is given by
the integral being extended over the interval(s) of variation of the variable X.
3.12 (population) variance, 02: For a continuous variable X having the probability
density function f(x), the variance, if it exists, is given by
02= ,(x-p)” f(x)&
the integral being extended over the interval(s) of variation of the variable X.
IS0 12491:1997(E)
3.13 (population) standard deviation, 0: Positive square root of the population
variance GL.
3J4 standardized variable: A random variable, the mean of which equals zero and
the standard deviation of which equals f. If the variable X has a mean equal to p and a
standard deviation equal to 0, the corresponding standardized variable is given as
NOTE - The distribution of the standardized variable is called “standardized distribution ”.
3.15 normal distribution: Probability distribution of a continuous variable X, the
probability density function of which is
oJ% 2 0
f( x > =- 1 exp H -- 1 - x-p 11
3.16 log-normal distribution: Probability distribution of a continuous variable X
which can take any value from x, to +m, or from - to x,.
In the former, more frequent, case the probability density function is given as
x 2 x0
pr and CJ, are, respectively, the mean and the standard deviation of the new variable;
Y = In (X-x0)
In the latter, less frequent, case the sign of the brackets (X-x,) and (x -x0) is to be
changed. Note that the variable Y has a normal distribution.
3.17 (random) sample: One or more sampling units taken from a population in such a
way that each unit of the population has the same probability of being taken.
3.18 (sample) size, n: Number of sampling units in the sample.
3.19 sample mean, T: Sum of n values Xi of sampling units divided by the sample size
n:
X=--CXi
n
IS0 12491:1997(E)
3.20 sample variance, s2: Sum of n squared deviations from the sample mean Z
divided by the sample size n minus 1:
=-
s2 Xi - -
c( x>
n-l
3.21 sample standard deviation, s: Positive square root of the sample variance s2.
3.22 estimation: Operation of assigning, from observations on a sample, numerical
values to the parameters of a distribution chosen as the statistical model of the
population from which this sample was taken.
3.23 estimator: Function of a set of the sample random variables used to estimate a
population parameter.
3.24 estimate: Value of an estimator obtained as a result of an estimation.
3.25 confidence level, y : Given value of the probability associated with a confidence
interval.
NOTE - In IS0 3534-1, it is designated (1 -OC ).
3.26 two-sided confidence interval: When Tl and T, are two functions of the
observed values such that, 8 being a parameter to be estimated, the probability Pr (T,
5 8 5 T,) is at least equal to the confidence level y (where y is a fixed number, positive
and less than 1), the interval between Tl and T, is a two-sided y confidence interval for 8.
3.27 one-sided confidence interval: When T is a function of the observed values
such that, 0 being a population parameter to be estimated, the probability Pr (T 2 8)
or the probability Pr (T 5 0) is at least equal to the confidence level y (where y is a fixed
number, positive and less than l), the interval from the smallest possible value of 8 up
to T (or the interval from the T up to the largest possible value of 0) is a one-sided y
confidence interval for 8.
3.28 outliers: Observations in a sample, so far separated in value from the remainder
as to suggest that they may be from a different population.
3.29 (statistical) test: Statistical procedure to decide whether a hypothesis about the
distribution of one or more populations should be accepted or rejected.
3.30 (statistical) hypothesis: Hypothesis, concerning the population, which is to be
accepted or rejected as the outcome of the test using sample observations.
3.31 significance level, a: Given value, which is the upper limit of the probability of
a statistical hypothesis being rejected when this hypothesis is true.
3.32 number of degrees of freedom, v : In general, the number of terms in a sum
minus the number of constraints on the terms of the sum.

@ IS0
IS0 12491:1997(E)
3.33 x 2-distribution: Probability distribution of a continuous variable x 2 which can
take any value from 0 to = , the probability density function of which is
2 (v/2)-1
X
( 1
X
f(X2;v) =
exp -2
2(v'2) r(v/2)
c 1
where
x 2 - > 0 with a parameter (number of degrees of freedom) v = 1, 2, 3,. . .;
I? is the gamma function.
3.34 tdistribution: Probability distribution of a continuous variable t which can take
any value from - to +w, the probability density function of which is
1 qv + 1> 121
f(t;v)=-
r(v /2)
n:V
Al-
(l+ t2 lv)"'"'2
where
- c t c -em with a parameter (number of degrees of freedom) v = 1, 2, 3,. ;
r is the gamma function.
3.35 noncentral t-distribution: Probability distribution of a continuous variable t
which can take any value from - to +=, the probability density function of which is
1 1 1
K
f (t;v ’s)=F 2(v-1)/2
72 exp
where
.
I
- c t c += with two
parameters; 1.e. number of degrees of freedom v and
noncentrality parameter 6.
3.36 F-distribution: Probab
...