1、INTERNATIONAL STANDARD IS0 12491 First edition 1997-05-01 Statistical methods for quality control of building materials and components Mkthodes statistiques de contrble de la qualit des matkiaux et a=400net; p=iso; o=isocs; s=central Printed in Switzerland ii Q IS0 IS0 12491:1997(E) Foreword IS0 (th
2、e 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 committ
3、ee 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 electrotech
4、nical 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 T
5、echnical Committee ISOflC 98, Bases for design of Wuctures. Subcommittee SC 2, Re/iaMfy of structures. Annex A of this International Standard is for information only. IS0 12491:1997(E) Introduction Quality control of building materials and components is, according to IS0 2394, an indispensable part
6、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 effici
7、ent, 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 engineerin
8、g works. Described techniques consist predominantly of classical statistical methods of common interest for all the participants in the building process. For other more sophisticated techniques and specific problems, existing statistical standards listed in annex A should be applied. INTERNATIONAL S
9、TANDARD 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 safe
10、ty 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
11、 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 ar
12、e 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. IS0 2394:-l, General principles on reliability for structures. IS0 3534-1:1993, Statistics - Vocabu
13、lary and symbols - Part 1: Probability and general statistical terms. IS0 3534-2:1993, Statistics - Vocabulary and symbols - Part 2: Statistical quality control. 3 Definitions For the purposes of this International Standard, the definitions given in IS0 3534-l and IS0 3534-2, and the following defin
14、itions, 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 ac
15、tivities 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) Q IS0 3
16、.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
17、 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) dist
18、ribution: 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
19、 variable X is less than or equal to r: I-I(x) = P, (XI x) 3.8 (probability) density function, +): The derivative (when it exists) of the distribution function: f(.+ d =(4 dx 3.9 (population) parameter: Quantity used in describing the distribution of a random variable in a population. 3.10 fkactile.
20、 xP: 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 zP is a p-fractile if P,(X 5 x*=p 3.11 (population) mean, p: For a continuous variable X having the probability density fix), th
21、e 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, c?: For a continuous variable X having the probability density function fix), the variance, if it exists, is given by the integral being extended over the in
22、terval(s) of variation of the variable X. IS0 12491: 1997(E) 3.13 (population) standard deviation, cr: Positive square root of the population variance a2. 3.14 standardized variable: A random variable, the mean of which equals zero and the standard deviation of which equals 1. If the variable X has
23、a mean equal to p and a standard deviation equal to CT, 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 densi
24、ty function of which is 3.16 log-normal distribution: Probability distribution of a continuous variable X which can take any value from x, to +w, or from - to x,. In the former, more frequent, case the probability density function is given as where x 2 x0 cly and CT, are, respectively, the mean and
25、the standard deviation of the new variable; Y = In (X-x,) In the latter, less frequent, case the sign of the brackets (X-x0) 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 ea
26、ch unit of the population has the same probability of being taken. 3.18 3.19 n: (sample) size, n: Number of sampling units in the sample. sample mean, Z: Sum of n values xi of sampling units divided by the sample size 1 X=-CXi n 3 IS0 12491: 1997(E) 3.20 sample variance, s2: Sum of n squared deviati
27、ons from the sample mean Z divided by the sample size n minus 1: 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 m
28、odel 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 ass
29、ociated with a confidence interval. NOTE - In IS0 3534-1, it is designated (1 -IX ). 3.26 two-sided confidence interval: When Z, and Z, are two functions of the observed values such that, 8 being a parameter to be estimated, the probability Pr (T, I 8 I !Z,) is at least equal to the confidence level
30、 y (where y is a fured number, positive and less than l), the interval between Z, and T, is a two-sided y confidence interval for 8. 3.27 one-sided confidence interval: When 2 is a function of the observed values such that, 0 being a population parameter to be estimated, the probability Pr (5” 2 9)
31、or the probability P, (2 I 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 2 (or the interval from the T up to the largest possible value of 9) is a one-sided y confidence interval for 8. 3
32、.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 rejec
33、ted. 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 th
34、is 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. 0 IS0 IS0 12491:1997(E) 3.33 x 2-distribution: Probability distribution of a continuous variable x which can take any value from 0 to 00 , t
35、he probability density function of which is dx 2-V ( x 2 (v/2)-1 2 )= p/2) qv/4 exp -5 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 t-distribution: Probability distribution of a continuous variable f which can take any value from - to
36、+=, the probability density function of which is f(t;v)=f r(v +1) /2 1 XV r(v /2) ( 1+t2 Iv (v+l) /2 where - t += 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
37、any value from - to +m, the probability density function of which is where - t += with two parameters; i.e. number of degrees of freedom v and noncentrality parameter 6. 3.36 Fclistribution: Probability distribution of a continuous variable P which can take any value from 0 to + 00, the probability
38、density function of which is f(o5,v,) = qv,+v2vq I+, /2)r(v, /2) w“2 (v2Y2 (v F:;:+“*),2 1 2 IS0 12491:1997(E) where F 2 0 with parameters (numbers of degrees of freedom) v1 ,v2 = 1, 2, 3, .; r is the gamma function. 3.37 lot: Definite quantity of units, manufactured or produced under conditions whi
39、ch are presumed uniform. NOTE - In statistical quality control in building, a lot is usually equivalent to a “batch” and is considered as a “population”. 3.38 isolated lot: A lot separated from the sequence of lots in which it was produced or collected, and not forming part of a current sequence of
40、inspection lots. NOTE - In statistical quality control in building, lots are usually considered as “isolated lots”. 3.39 conforming unit: Unit which satisfies all the specified requirements. 3.40 nonconforming unit: Unit containing at least one nonconformity which causes the unit not to satisfy spec
41、ified requirements. 3.41 sampling inspection: Inspection in which decisions are made to accept or not accept a lot, based on results of a sample selected from that lot. 3.42 sampling inspection by variables: Method of sampling inspection which consists of measuring a quantitative variable X for each
42、 unit of a sample. 3.43 sampling inspection by attributes: Method of sampling inspection which consists of distinguishing between conforming and nonconforming units of a sample. 3.44 sampling plan: A plan according to which one or more samples are taken in order to obtain information and the possibi
43、lity of reaching a decision concerning the acceptance of the lot. NOTE - It includes the sample size n and the acceptance constants K, , KS ( in sampling inspection by variables), or the sample size n and the acceptance number AC (in sampling inspection by attributes). 3.45 operating characteristic
44、curve (OC curve): Curve showing, for a given sampling plan, the probability that an acceptance criterion is satisfied, as a function of the lot quality level. 3.46 producer: Any participant of the building process supplying a lot for further procedure or use. 3.47 consumer: Any participant of the bu
45、ilding process purchasing a lot for further procedure or use. 3.48 producer% risk point (PRP): A point on the operating characteristic curve corresponding to a predetermined and usually low probability of non-acceptance. NOTE - This probability is the producers risk (PR) when an isolated lot is considered.
