1、BRITISH STANDARD BS 6954-2: 1988 ISO 3443-2: 1979 Tolerances for building Part 2: Recommendations for statistical basis for predicting fit between components having a normal distribution of sizes UDC 624 + 69:31:519.213.216.219BS6954-2:1988 This British Standard, having beenprepared under the direct
2、ionof the Basic Data andPerformance Criteria for CivilEngineering and BuildingStructures, was published under the authority ofthe Board of BSI and comesintoeffect on 29 February 1988 BSI 06-1999 The following BSI references relate to the work on this standard: Committee reference BDB/4 Draftfor comm
3、ent 77/14297 DC ISBN 0 580 16505 1 Committees responsible for this British Standard The preparation of this British Standard was entrusted by the Basic Data and Performance Criteria for Civil Engineering and Building Structures Standards Committee (BDB/-) to Technical Committee BDB/4, upon which the
4、 following bodies were represented: Association of County Councils British Standards Society Building Employers Confederation Chartered Institution of Building Services Engineers Concrete Society Department of Education and Science Department of the Environment (Building Research Establishment) Depa
5、rtment of the Environment (Property Services Agency) Incorporated Association of Architects and Surveyors Institute of Building Control Institute of Clerks of Works of Great Britain Inc. Institution of Civil Engineers Institution of Structural Engineers Institution of Water and Environmental Managem
6、ent (IWEM) National Council of Building Materials Producers Royal Institute of British Architects Royal Institution of Chartered Surveyors Amendments issued since publication Amd. No. Date of issue CommentsBS6954-2:1988 BSI 06-1999 i Contents Page Committees responsible Inside front cover National f
7、oreword ii 1 Scope 1 2 Field of application 1 3 Reference 1 4 General 1 5 Probability and induced deviations 1 6 Combination of random variables 2 Annex A Sampling and the calculation of the standard deviation 4 Figure 1 Gaussian curves (normal distribution for different standarddeviations) 1 Figure
8、 2 Limits corresponding to 1, 2 and 3 times the standard deviation 2 Figure 3 Distribution of values a) and distribution of deviations b), withillustration of limits c) 3 Publications referred to Inside back cover BS6954-2:1988 ii BSI 06-1999 National foreword This Part of BS 6954 has been prepared
9、under the direction of the Basic Data and Performance Criteria for Civil Engineering and Building Structures Standards Committee. This Part of BS 6954 together with Parts 1 and 3 form a revision of DD 22:1972. BS 6954-1, BS 6954-2 and BS 6954-3 supersede DD 22:1972, which is withdrawn. This Part of
10、BS 6954 is identical with ISO 3443/2-1979 “Tolerances for building Part 2: Statistical basis for predicting fit between components having a normal distribution of sizes”, published by the International Organization for Standardization (ISO). BS 6954 comprises three Parts as follows: Part 1: Recommen
11、dations for basic principles for evaluation and specification; Part 2: Recommendations for statistical basis for predicting fit between components having a normal distribution of sizes; Part 3: Recommendations for selecting target size and predicting fit. BS 6954 enables the nature of deviations fro
12、m intended sizes to be taken into account when designing to achieve satisfactory fit. This Part of BS 6954 shows how inaccuracies can be treated as both random and systematic, with the random variability following a normal distribution. Terminology and conventions. The text of the international stan
13、dard has been approved as suitable for publication as a British Standard without deviation. Some terminology and certain conventions are not identical with those used in British Standards; attention is drawn especially to the following. The comma has been used as a decimal marker. In British Standar
14、ds it is current practice to use a full point on the baseline as the decimal marker. Wherever the words “International Standard” appear, referring to this standard, they should be read as “British Standard”. A British Standard does not purport to include all the necessary provisions of a contract. U
15、sers of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Cross-references International standard Corresponding British Standard ISO 3207:1975 BS 2846 Guide to statistical interpretation of d
16、ata Part 3:1975 Determination of a statistical tolerance interval (Identical) Summary of pages This document comprises a front cover, an inside front cover, pagesi andii, pages1 to6, an inside back cover and a back cover. This standard has been updated (see copyright date) and may have had amendment
17、s incorporated. This will be indicated in the amendment table on theinside front cover.BS6954-2:1988 BSI 06-1999 1 1 Scope This International Standard describes the fundamental characteristics of dimensional variability in building and of the particular case of combination of random unrelated variab
18、les; it sets out the need to relate dimensional variability to the limits imposed on joint widths by the need for satisfactory functioning. 2 Field of application This International Standard applies to all forms of building construction that have predictable variability which follows a Gaussian dist
19、ribution. 3 Reference ISO 3207, Statistical interpretation of data Determination of a statistical tolerance interval. 4 General Although this International Standard does not deal in detail with the design of joints between components, it recognises that a given joint design will have certain associa
20、ted limits within which the required joint width must lie if it is to function satisfactorily. The joint width achieved in a given assembly of components will be determined by the dimensional variability (deviations, errors, inaccuracies) in that assembly. The calculation of “fit” is essentially a p
21、rocess of reconciling the required joint width range with the joint width that is predicted to result from dimensional variability. Thus, the dimensional flexibility of a jointing technique is expressed in terms of its maximum and minimum clearance capabilities, i.e. the limits of clearance within w
22、hich performance can be maintained. Exceeding either limit results in a “misfit”. The design or selection of a jointing technique should therefore include the aim of matching its clearance capability with the clearance predicted to occur. The calculation of “fit” is relevant both to the derivation o
23、f a suitable work size for a component and to proposed uses of an existing component, of known work size, in a known situation. 5 Probability and induced deviations In many production and erection processes, the achieved sizes in a sufficient number of attempts follow the so-called normal distributi
24、on, the density function of which is depicted by the Gaussian curve (see Figure 1). Figure 1 Gaussian curves (Normal distribution for different standard deviations)BS6954-2:1988 2 BSI 06-1999 A normal distribution has two parameters, the mean and the standard deviation. The probability density curve
25、 is symmetrical about the mean, at which point the peak occurs. The standard deviation is a quantity that represents the spread of the curve (see Figure 2). If the mean value is displaced in relation to the specified value B, there is said to be a systematic deviation see Figure 3b). If the values a
26、pply to sizes which are distributed normally with the parameters mean sand standard deviation s , then the deviations are distributed normally with parameters d= s B and d= s . A systematic deviation implies that dis different from zero. If the parameters are known, the probability of failure (defec
27、ts) corresponding to given limits is the sum of the two probabilities of either limit being infringed see Figure 3c). These two parameters for populations of types of construction or components cannot be precisely known and have to be estimated from samples, since by definition population data relat
28、e to infinite populations. The parameters can be estimated with sufficient precision from samples of adequate size (see ISO 3207) of such construction or components. The data so obtained relate to “populations” and the question of representativeness of small samples of construction such as occur on
29、site does not arise. 6 Combination of random variables In any assembly of components in building, a number of dimensional variabilities combine to produce the total variability operating (for example, variability in size and variability in position). In most cases these are the result of quite separ
30、ate operations and can therefore be considered as occurring independently and at random. The occurrence of an extreme deviation value in any operation is infrequent. The simultaneous occurrence of two or more extreme values is many times more infrequent. This aspect of probability, together with the
31、 chance that different deviations may compensate for each other, is taken into account in the statistical theory of random accumulated errors. The effect of so combining independent variables is that the probability of exceeding a given multiple of standard deviation remains the same for the combine
32、d variability as it had been for each constituent. This theory relies upon the measurement of all variability in terms of the standard deviation, as described above. It states that the standard deviation of the total variability (combined effect of several variables) is equal to the square root of t
33、he sum of the squares of the individual standard deviations of the separate variables: The standard deviation has been shown to correspond to the limit that is exceeded by approximately one item in three. If the standard deviation of the variability in joint width due to component deviations is calc
34、ulated by the above formula, it can be multiplied by a suitable factor to give the limits on joint width corresponding to any appropriate risk of misfit. This assumes that component deviations follow a normal distribution, without finite limits being imposed. If limits are applied, for example, in m
35、anufacture, and the few units whose sizes exceed them are rejected and do not reach the site, the risk of misfit is marginally better than calculated. Thus the effect of the total of all the variabilities in any assembly upon the joints in that assembly can be assessed in terms of the probability of
36、 either joint limit (required minimum width or required maximum width) being exceeded. By this means a basis is provided for the selection of target dimensions (for example work sizes), for the selection of jointing techniques (i.e. joint width ranges) and for the control of variability. Figure 2 Li
37、mits corresponding to 1, 2 and3times the standard deviationBS6954-2:1988 BSI 06-1999 3 Figure 3 Distribution of values a) and distribution of deviations b), with illustration of limitsc)BS6954-2:1988 4 BSI 06-1999 Annex A Sampling and the calculation of the standard deviation A.1 General The measure
38、ment of samples is generally a routine process in which no thought is given to the individual significance of the values found. The primary need is for the sample to be gathered at random, so that it can be regarded as representative of the body of items from which it was drawn 1) . The patterns ass
39、ociated with probability emerge only when statistical processes are applied to the resultant data, and the properties of the distribution are calculated. The two characteristics most commonly required are the arithmetic mean of the values, and the standard deviation as a measure of their variability
40、 or dispersion. The techniques described in this annex apply only to variable processes having a normal distribution of deviation. The normal distribution of values described in clause 5 is the pattern that appears when a sufficient number of random attempts to achieve a target are measured assuming
41、 the values to be unbiased. The more observations that are made, the closer the pattern resembles that predicted by theory. A similar relationship applies when a sample is used to estimate the properties of the population from which it was drawn. The information from a sample that contains only a fe
42、w items is unreliable. This means that in such cases the population parameters can be surmised only as broad limiting values, i.e. the population mean and standard deviation can be predicted as being likely to lie within a certain range around the calculated sample mean and standard deviation. As th
43、e sample size increases, so the range of likely positions for the true value of the population attribute diminishes. These ranges of values are defined by confidence limits applied to the mean and standard deviation calculated from a sample. They are, for example, derived for 95 % confidence, meanin
44、g that there is a5 % chance that the true values for the population lie beyond the limits. Lower confidence levels may prove to be more economic for the building industry. Confidence limits for the mean and standard deviation are tabulated for various sample sizes in ISO 3207. A.2 Estimation of the
45、mean and standard deviation of a population from a series of observed values The following symbols apply: The basic expressions are as follows: However, the calculation of the standard deviation from this expression is laborious if a large number of observations is involved. The arithmetic can be si
46、mplified by using the following short cuts. a) In calculating the mean and standard deviation of a series of observations, a constant may be subtracted from every observation for the purpose of computation, provided that this constant is added to the computed mean. This procedure is known as changin
47、g the origin, and after the computations have been completed the constant must be added to the computed mean to refer it again to the former origin; the standard deviation is unaffected by the change of origin. b) The observations may all be multiplied (or divided) by the same factor, provided that
48、the computed mean and the standard deviation are divided (or multiplied) by the same factor. The units in which the computations are carried out are usually known as working units. c) The expressionis the sum of the squares of the deviations of the observed values from their mean value. The computat
49、ion of this expression may be performed more simply as follows. 1) Sum the squares of the observations in the new units if adjustments have been made as described in a) and b). 2) Subtract from this: the square of the sum of the observations (in new units, if adjusted). 1) Under certain circumstances, precautions may be needed to ensure randomness. It may be necessary to select items according to tables of random numbers, and techniques exist for examining abnormal results and rejecting them if genuinely unrepresentative. Further gui
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