1、Guidance on the application of statistical methods for determining the properties of masonry productsPD CEN/TR 16886:2016BSI Standards PublicationNational forewordThis Published Document is the UK implementation of CEN/TR 16886:2016.The UK participation in its preparation was entrusted to TechnicalC
2、ommittee B/519, Masonry and associated testing.A list of organizations represented on this committee can be obtained onrequest to its secretary.This publication does not purport to include all the necessary provisions ofa contract. Users are responsible for its correct application. The British Stand
3、ards Institution 201.Published by BSI Standards Limited 201ISBN 978 0 580 87711 7ICS 03.120.30; 91.100.25Compliance with a British Standard cannot confer immunity fromlegal obligations.This Published Document was published under the authority of theStandards Policy and Strategy Committee on 31 +BOVB
4、SZ 201.Amendments/corrigenda issued since publicationDate Text affectedPUBLISHED DOCUMENTPD CEN/TR 16886:2016g3g3g3g23g8g6g11g17g12g6g4g15g3g21g8g19g18g21g23g3g21g4g19g19g18g21g23g3g23g8g6g11g17g12g20g24g8g3g23g8g6g11g17g12g22g6g11g8g21g3g5g8g21g12g6g11g23g3CEN/TR 16886 g3 g3g3 g17g145g152g135g143g1
5、32g135g148g3g884g882g883g888g3g12g6g22g3g882g885g484g883g884g882g484g885g882g482g3g891g883g484g883g882g882g484g884g887g3g8g144g137g142g139g149g138g3g25g135g148g149g139g145g144g3g3g10g151g139g134g131g144g133g135g3g145g144g3g150g138g135g3g131g146g146g142g139g133g131g150g139g145g144g3g145g136g3g149g150
6、g131g150g139g149g150g139g133g131g142g3g143g135g150g138g145g134g149g3g136g145g148g3g134g135g150g135g148g143g139g144g139g144g137g3g150g138g135g3g146g148g145g146g135g148g150g139g135g149g3g145g136g3g143g131g149g145g144g148g155g3g146g148g145g134g151g133g150g149g3g10g151g139g134g135g3g146g145g151g148g3g14
7、2g821g131g146g146g142g139g133g131g150g139g145g144g3g134g135g3g143g177g150g138g145g134g135g149g3g149g150g131g150g139g149g150g139g147g151g135g149g3g146g145g151g148g3g142g131g3g134g177g150g135g148g143g139g144g131g150g139g145g144g3g134g135g149g3g146g148g145g146g148g139g177g150g177g149g3g134g135g149g3g17
8、7g142g177g143g135g144g150g149g3g134g135g3g143g131g173g145g144g144g135g148g139g135g3g3 g15g135g139g150g136g131g134g135g144g3g136g242g148g3g134g139g135g3g4g144g153g135g144g134g151g144g137g3g149g150g131g150g139g149g150g139g149g133g138g135g148g3g16g135g150g138g145g134g135g144g3g156g151g148g3g5g135g149g1
9、50g139g143g143g151g144g137g3g134g135g148g3g8g139g137g135g144g149g133g138g131g136g150g135g144g3g152g145g144g3g16g131g151g135g148g153g135g148g141g3g19g148g145g134g151g141g150g135g144g3g3g3g23g138g139g149g3g23g135g133g138g144g139g133g131g142g3g21g135g146g145g148g150g3g153g131g149g3g131g146g146g148g145g
10、152g135g134g3g132g155g3g6g8g17g3g145g144g3g884g886g3g4g151g137g151g149g150g3g884g882g883g887g484g3g12g150g3g138g131g149g3g132g135g135g144g3g134g148g131g153g144g3g151g146g3g132g155g3g150g138g135g3g23g135g133g138g144g139g133g131g142g3g6g145g143g143g139g150g150g135g135g3g6g8g17g512g23g6g3g883g884g887g4
11、84g3g3g6g8g17g3g143g135g143g132g135g148g149g3g131g148g135g3g150g138g135g3g144g131g150g139g145g144g131g142g3g149g150g131g144g134g131g148g134g149g3g132g145g134g139g135g149g3g145g136g3g4g151g149g150g148g139g131g481g3g5g135g142g137g139g151g143g481g3g5g151g142g137g131g148g139g131g481g3g6g148g145g131g150g
12、139g131g481g3g6g155g146g148g151g149g481g3g6g156g135g133g138g3g21g135g146g151g132g142g139g133g481g3g7g135g144g143g131g148g141g481g3g8g149g150g145g144g139g131g481g3g9g139g144g142g131g144g134g481g3g9g145g148g143g135g148g3g28g151g137g145g149g142g131g152g3g21g135g146g151g132g142g139g133g3g145g136g3g16g13
13、1g133g135g134g145g144g139g131g481g3g9g148g131g144g133g135g481g3g10g135g148g143g131g144g155g481g3g10g148g135g135g133g135g481g3g11g151g144g137g131g148g155g481g3g12g133g135g142g131g144g134g481g3g12g148g135g142g131g144g134g481g3g12g150g131g142g155g481g3g15g131g150g152g139g131g481g3g15g139g150g138g151g13
14、1g144g139g131g481g3g15g151g154g135g143g132g145g151g148g137g481g3g16g131g142g150g131g481g3g17g135g150g138g135g148g142g131g144g134g149g481g3g17g145g148g153g131g155g481g3g19g145g142g131g144g134g481g3g19g145g148g150g151g137g131g142g481g3g21g145g143g131g144g139g131g481g3g22g142g145g152g131g141g139g131g48
15、1g3g22g142g145g152g135g144g139g131g481g3g22g146g131g139g144g481g3g22g153g135g134g135g144g481g3g22g153g139g150g156g135g148g142g131g144g134g481g3g23g151g148g141g135g155g3g131g144g134g24g144g139g150g135g134g3g14g139g144g137g134g145g143g484g3g3g3g3g3g8g24g21g18g19g8g4g17g3g6g18g16g16g12g23g23g8g8g3g9g18
16、g21g3g22g23g4g17g7g4g21g7g12g29g4g23g12g18g17g3g6g18g16g12g23g50g3g8g24g21g18g19g50g8g17g3g7g8g3g17g18g21g16g4g15g12g22g4g23g12g18g17g3g8g24g21g18g19g34g12g22g6g11g8g22g3g14g18g16g12g23g8g8g3g9g111g21g3g17g18g21g16g24g17g10g3g3g3g3CEN-CENELECg3Management Centre: Avenue Marnix 17, B-1000 Brussels g82
17、5g3g884g882g883g888g3g6g8g17g3 g4g142g142g3g148g139g137g138g150g149g3g145g136g3g135g154g146g142g145g139g150g131g150g139g145g144g3g139g144g3g131g144g155g3g136g145g148g143g3g131g144g134g3g132g155g3g131g144g155g3g143g135g131g144g149g3g148g135g149g135g148g152g135g134g3g153g145g148g142g134g153g139g134g13
18、5g3g136g145g148g3g6g8g17g3g144g131g150g139g145g144g131g142g3g16g135g143g132g135g148g149g484g3g21g135g136g484g3g17g145g484g3g6g8g17g512g23g21g3g883g888g890g890g888g483g884g882g883g888g3g8PD CEN/TR 16886:2016CEN/TR 16886:2016 (E) 2 Contents PageEuropean Foreword 3 Introduction .4 1 Scope 5 2 Normative
19、 references 5 3 Terms, definitions and symbols .5 3.1 Terms and definitions 5 3.2 Symbols .8 4 General 9 5 Statistical evaluation . 10 5.1 Factory production control . 10 5.2 Finished product testing 10 5.2.1 General . 10 5.2.2 Inspection lot 11 5.2.3 Spot sampling and sample sizes 11 5.2.4 Producti
20、on types . 12 5.2.5 Control method A: Batch control . 12 5.2.6 Control method B:Rolling inspection 13 5.2.7 Evaluation of test results . 15 5.2.8 How to come from unknown to known standard deviation? 18 5.2.9 Conformity 18 5.2.10 Simple and conservative approach 19 5.2.11 Non-conforming products . 1
21、9 5.2.12 Guidance 19 6 Product type determination . 22 Annex A (informative) Normal distribution (Laplace-Gauss distribution) . 23 Annex B (informative) Tables for acceptance coefficient kndepending on the used fractile p and confidence level g576 (taken from ISO 16269-6:2005) 24 Annex C (informativ
22、e) Examples of statistical evaluation . 40 C.1 Example 1 40 C.2 Example 2 42 C.3 Example 3 44 C.4 Example 4 45 C.5 Example 5 47 Annex D (informative) Normality test of SHAPIRO WILK 50 D.1 General . 50 D.2 Normality test of SHAPIRO-WILK 50 Bibliography . 54 PD CEN/TR 16886:20162g6g8g17g512g23g21g3g88
23、3g888g890g890g888g483g884g882g883g888g3g525g8g526CEN/TR 16886:2016 (E) 3 European Foreword This document (CEN/TR 16886:2016) has been prepared by Technical Committee CEN/TC 125 “Masonry”, the secretariat of which is held by BSI. Attention is drawn to the possibility that some of the elements of this
24、 document may be the subject of patent rights. CEN shall not be held responsible for identifying any or all such patent rights This document has been prepared under a mandate given to CEN by the European Commission and the European Free Trade Association. PD CEN/TR 16886:20163g6g8g17g512g23g21g3g883
25、g888g890g890g888g483g884g882g883g888g3g525g8g526CEN/TR 16886:2016 (E) 4 Introduction This document is informative for the guidance of manufacturers and Notified Bodies (NBs), who want to use statistical methods for the evaluation of conformity and Factory Production Control of masonry products. Its
26、use is optional. Other statistical methods and non-statistical methods may be used. Quality control of building materials and components is an indispensable part of an overall concept of structural reliability. As quality control is generally a time-consuming and expensive task, various operational
27、techniques and activities have been developed to fulfil safety requirements in buildings. Properly employed statistical methods are one way to provide efficient, economic and effective means of quality control. Background: “The terms and definitions in EN 1990 (Eurocode: Basis of structural design)
28、are derived from ISO 2394 (General principles on reliability for structures). For the design of structures, EN 1996-1-1 (Eurocode 6: Design of masonry structures Part 1-1: General rules for reinforced and unreinforced masonry structures) is intended to be used together with EN 1990. ISO 12491 (Stati
29、stical methods for quality control of building materials and components) gives general principles for the application of statistical methods for the quality control of building materials and components, in compliance with the safety and serviceability requirements of ISO 2394. ISO 12491 is applicabl
30、e to all buildings and other civil engineering works, existing or under construction, whatever nature or combination of materials used, e.g. concrete, steel, wood, bricks. The EN 771 series specifies that one method of satisfying the conformity criterion laid down in these product standards is to us
31、e the approach given in ISO 12491.” This Technical Report gives guidance on how a statistical evaluation can be put into practice based on the background of ISO 12491. A simplified method is also given based on information obtained from practice about the possible distribution in production for spec
32、ific product characteristics. The method may also be used for the evaluation of different properties at the different stages of the factory production control (FPC) with the aim to minimize testing costs for the manufacturer and to ensure that the requirements are fulfilled. Detailed examples are gi
33、ven in Annex C. For other more sophisticated techniques and specific problems, other international standards can be applied. The initial draft of this document was prepared by the joint working group CEN/TC 125/TG 5 and the Sector Group 10 of Notified Bodies under the Construction Products Directive
34、. The CEN/TR is a tool available for manufacturers and Notified Bodies. It is laid down in the hENs of masonry products that the manufacturer should demonstrate compliance for his product with the requirements of the harmonized product standards. The purpose of this Technical Report is to put statis
35、tical evaluation into practice. Detailed examples are given in the annexes. PD CEN/TR 16886:20164g6g8g17g512g23g21g3g883g888g890g890g888g483g884g882g883g888g3g525g8g526CEN/TR 16886:2016 (E) 5 1 Scope In the masonry unit standards and in national legislation, some properties need to be declared based
36、 on a certain fractile and confidence level. To demonstrate compliance with that a statistical tool can be used. The purpose of this Technical Report is to exemplify how a statistical tool can be used in practice. This document should not contradict nor extend the scope of the work and role of a Not
37、ified Body, nor impose additional burdens on the manufacturer, beyond those laid down in the Construction Products Regulation and the product standards. Mechanical and other properties of building materials and components are in the report described by random variables with a certain type of probabi
38、lity distribution. The popular normal distribution (Laplace-Gauss distribution) is given in Annex A. Normal distribution may be used to approximate many actual symmetrical distributions. When a remarkable asymmetry is observed, then another type of distribution reflecting this asymmetry should be co
39、nsidered, leading to a more complex method to demonstrate compliance with the product standard. More information on the normality test of Shapiro-Wilk is given in Annex D. 2 Normative references The following documents, in whole or in part, are normatively referenced in this document and are indispe
40、nsable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. EN 1990, Eurocode - Basis of structural design EN 1996 (all parts), Eurocode 6 Design of masonry structures 3 Te
41、rms, definitions and symbols For the purposes of this document, the following terms, definitions and symbols apply. 3.1 Terms and definitions 3.1.1 unit defined quantity of building material, component or element that can be individually considered and separately tested 3.1.2 population totality of
42、units under consideration 3.1.3 variable X variable which can take any of the values of a specified set of values and with which is associated a probability distribution 3.1.4 probability distribution function which gives the probability that a variable X takes any given value (in the case of a disc
43、rete variable) or belongs to a given set of values (in the case of a continuous variable) PD CEN/TR 16886:20165g6g8g17g512g23g21g3g883g888g890g890g888g483g884g882g883g888g3g525g8g526CEN/TR 16886:2016 (E) 6 3.1.5 distribution function g555g523x) function giving, for every value of x, the probability
44、that the variable X is less than or equal to x: () ,( )xPXxg51g32 g100 3.1.6 (probability) density function f(x) derivative (when it exists) of the distribution function 3.1.7 parameter (population) quantity used in describing the distribution of a random variable in a population 3.1.8 fractile x if
45、 X is a continuous variable and p is a real number between 0 and 1, the p-fractile is the value of a variable X for which the distribution function equals p Note 1 to entry: Thus xpis a fractile if g19g481g523g27g3g954g3g154p) = p 3.1.9 population mean g586 for a continuous variable X having the pro
46、bability density f(x), the mean, if it exists, is given by: ()fxdxg80 g32g117g179the integral being extended over the interval(s) of variation of the variable X 3.1.10 population variance g5922for a continuous variable X having the probability density function f(x), the variance, if it exists, is gi
47、ven by 22()()xfxdxg86g80g32g16g179the integral being extended over the interval(s) of variation of the variable X 3.1.11 population standard deviation g592 positive square root of the population variance g5922PD CEN/TR 16886:20166g6g8g17g512g23g21g3g883g888g890g890g888g483g884g882g883g888g3g525g8g52
48、6CEN/TR 16886:2016 (E) 7 3.1.12 normal distribution probability distribution of a continuous variable X, the probability density function of which is 211() exp22xfxg80g86g86g83g170g186g16g167g183g32g16g171g187g168g184g169g185g171g187g172g1883.1.13 random sample one or more sampling units taken from
49、a population in such a way that each unit of the population has the same probability of being taken 3.1.14 sample size n number of sampling units in the sample 3.1.15 sample mean xmsum of n values xiof sampling units divided by the sample size n Ximxng32g1663.1.16 sample variance s2sum of n squared deviations from the sample mean xmdivided by the sample size n minus 1 2Xi m2()sn1xg54g16g32g163.1.17 sample standard deviation s positive square root of the sample variance s23.1.18 estimation operation of assigning, from observations on a sample, numerical va
