# ISO TR 5307-1991

BRITISH STANDARD BS 5551-2.6 1992 ISO/TR 5307 1991 Fertilizers Part 2 Sampling Section 2.6 Guide to derivation of a sampling plan for the uation of a large delivery of solid fertilizerBS5551-2.61992 This British Standard, having been prepared under the directionof the Chemicals Standards Policy Committee, waspublished under the authorityof the Standards Boardand comes into effect on 15 May1992 © BSI 10-1999 The following BSI references relate to the work on this standard Committee reference CIC/37 Draft for comment 91/57860 DC ISBN 0 580 20877 X Committees responsible for this British Standard The preparation of this British Standard was entrusted by the Chemicals Standards Policy Committee CIC/- to Technical Committee CIC/37, upon which the following bodies were represented Association of Public Analysts British Aggregate Construction Materials Industries British Coal Corporation Chemical Industries’ Association Consumers’ Association Department of Trade and Industry Laboratory of the Government Chemist Fertiliser Manufacturers’ Association Ltd. Institute of Trading Standards Administration Ministry of Agriculture, Fisheries and Food Ministry of Defence Amendments issued since publication Amd. No. Date CommentsBS5551-2.61992 © BSI 10-1999 i Contents Page Committees responsible Inside front cover National foreword ii Introduction 1 1 Scope 2 2 References 2 3 Notation and symbols 2 4 Preliminary hypotheses 3 5 Principle of the sampling plan 4 5.1 General 4 5.2 Ination 4 5.3 What is determined by the proposed 6 6 Theory of the sampling plan 7 6.1 Definitions 7 6.2 Determination of limits 7 6.3 Use of two non-central t distribution 8 6.4 Determination of N and N‰ 9 7 Practical procedure for the determination of N and N ‰ 11 7.1 Basic ination 11 7.2 Calculation 11 7.3 Simplified calculation when N‰ 30 12 8 Examples of calculations 13 8.1 Calculation by the complete process 13 8.2 Simplified calculation 15 9 Effect of the values of the various parameters on N and K 16 10 uation of a delivery 17 Annex A 19 Annex B 20 Figure 1 The relationship between D, L and r a 5 Table 1 12 Table 2 13 Table 3 13 Table 4 15 Table 5 15 Table 6 16 Table 7 17 Table 8 Effect of the various parameters on the values of N, N‰ and K 17 Table A.1 Values of the standardized normal variable u as a function of P 19 Table B.1 Values of 1 – a 2 /a 2 20 List of references Inside back coverBS5551-2.61992 ii © BSI 10-1999 National foreword This Section of BS 5551 has been prepared under the direction of the Chemicals Standards Policy Committee in order to provide a derivation of a sampling plan for the uation of a large delivery of solid fertilizer. For some years the United Kingdom has participated in the standardization of s of sampling fertilizers through Subcommittee2, Sampling, of Technical Committee134, Fertilizers and soil conditioners, of the International Organization for Standardization ISO. As international agreement is reached on the s, it is proposed to publish them as Sections of BS5551. BS 5551 is published in four Parts, each Part being subdivided into Sections and, where appropriate, Subsections. The four Parts are Part 1 Terminology and labelling; Part 2 Sampling; Part 3 Physical properties; Part 4 Chemical analysis. This Section of Part2 is identical with ISO/TR53071991 Solid fertilizers Derivation of a sampling plan for the uation of a large delivery. This document has been published by ISO as a type 3 technical report, which is a document containing ination in a different from that usually published in International Standards. In this case the document contains the theoretical background to the derivation of the sampling plan given in ISO8634. This document complements other standards for sampling fertilizers, both published and in course of preparation. A British Standard does not purport to include all the necessary provisions of a contract. Users 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 81571984 BS 5551 Fertilizers Section 1.21986 Glossary of terms Identical ISO 86341991 a Section 2.91991 Sampling plan for the uation of a large delivery of solid fertilizer Identical a Referred to in the text as unpublished. Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, pages 1 to 20, an inside back cover and a back cover. This standard has been updated see copyright date and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover.BS5551-2.61992 © BSI 10-1999 1 Introduction Within the framework of its work on sampling, Technical Committee 134 “Fertilizers and Soil Conditioners” has, through its subcommittee 2, carried out statistical studies on various sampling plans which may be used to assess large deliveries of fertilizers. This work complements other standards for fertilizers, currently under preparation, and provides the theoretical background necessary to appreciate fully the requirements of those standards. This technical report type 3, which is different from the International Standards usually produced by ISO/TC134/SC4, is intended to act as a complement to them, as a basis for the sampling of fertilizer deliveries. Each country has its own regulations applicable to the fertilizer trade; an official department is responsible for carrying out checks regarding application of the regulations. If these regulations are violated, sanctions may be taken against those responsible for placing the fertilizer on the market in that country. In the case of an imported delivery, it is the representative of the manufacturing company in the country, or the importer who is considered by the relevant authorities to be responsible for the declared contents shown on labels or other documentation accompanying the fertilizers. ISO 8634 concerns the case of an importer who resells, on his own responsibility, a large amount of fertilizer received from abroad. After unloading, this delivery is resold in smaller lots to traders dealers or farmer cooperatives who will themselves be direct suppliers to farmers. In the case in question, it is the importer whose name is associated with the fertilizer; and it is therefore he who will be considered by the retailers and users to be responsible for the declared contents. ISO 8634 is designed for acceptance inspection. It determines the rules for a sampling i.e. the sampling plan; b acceptance the acceptance or rejection of the delivery; and both apply to the bulk delivery imported. The location of the acceptance inspection, as defined in ISO8634, in the chain of transactions can be represented by the following diagramBS5551-2.61992 2 © BSI 10-1999 1 Scope This Technical Report presents the sampling theory which has resulted in the definition of the sampling plan described in ISO8634 1 . The sampling plan is applicable to a large delivery of more than250 t of fertilizer supplied to another party, for resale, on his own responsibility, in small lots, each of which would be subject to legislation. By large amount is understood, for example, a full boat-load 5,000t, 10,000t or more thus corresponding to a relatively long period of manufacture, but the theory applies to any delivery of250t or more. 2 References ISO 81571984, Fertilizers and soil conditioners Vocabulary. ISO 8634, Solid fertilizers Sampling plan for the uation of a large delivery 1 . 3 Notation and symbols The following symbols appear in this Technical Report and have the meanings assigned to them below. 1 To be published. ¨, Actual mean value and standard deviation between sampling units in the delivery. ¨ a , Mean value and standard deviation between sampling units in a delivery of just acceptable quality. ¨ r , Mean value and standard deviation between sampling units in a delivery of just unacceptable quality. ¨ e , , ¨ f , Mean and standard deviation, respectively, of two lots which can be considered by the importer to be of the same quality. U Number of sampling units in the delivery. N Number of sampling units to be selected during the sampling of the delivery. Increments. N‰ Number of analyses to be carried out on the N increments during the inspection of the delivery. N R Number of sampling units contained in the smallest lot presented for resale. k Number of increments to be combined into each aggregate sample for analysis. n Number of sampling units which will be mandatorily selected during the official sampling of a lot of N Rsampling units. Mean value found by analysis after the selection of n sampling units from a lot of sampling units. s Estimate ofwith the aid of the N‰ analyses, whereis the standard deviation between the sampling units in the delivery. X i Analytical result obtained on the sample of rank i. Estimate of the mean value of the delivery with the aid of the N‰ analyses. D Declared value e.g.of a plant nutrient in the fertilizer delivery. L Official inspection limit value which depends on the declared value D. It may be equal to D or less than D by a prescribed tolerance which may depend on the size of the lot sold. r a Probability that the mean value of n sampling units is lower than the official limit value L, just acceptable by the importer. B B a B r B e B f x B XBS5551-2.61992 © BSI 10-1999 3 4 Preliminary hypotheses The sampling plan has been drawn up on the assumption that there is no serial correlation between the successive units of the delivery. The N units inspected are selected at random from the delivery, each unit having the same chance of being selected, and the N groups of k units made up at random from the N. It is also understood that the lots made up by the importer represent a random sample from among the U bags of the delivery and that the increments taken from a lot by the authorities responsible for the inspection are taken at random from the lot. In the subsequent theory, it is assumed that a single plant nutrient is of interest or that, if this is not the case, each plant nutrient is considered separately. It is also assumed that the fertilizer is packaged. although similar arguments will also apply to products in bulk. The analytical error is considered to be negligible in relation to the sampling error. Finally, it is assumed once and for all, as has been shown by the studies of data from production and dispatch inspection carried out in various countries a that the mean concentration of a certain component or value in the sampling units e.g. bag constituting a definite lot of fertilizer shall be considered as a random quantity which obeys a normal distribution; b that the distribution of this random quantity does not depend, at least for sufficiently large lots, on their size. r r Probability that the mean value of n sampling units is lower than the official limit value L, just unacceptable by the importer. Probability of rejection of a delivery of just acceptable quality seller’s or producer’s risk. Probability of acceptance of a delivery of just unacceptable quality importer’s or consumer’s risk. Value of the standardized normal variable such thatequals r a . Value of the standardized normal variable such thatequals r r . Value of the standardized normal variable such thatequals . Value of the standardized normal variable such thatequals . Non-centrality parameter. K Calculation coefficient which is dependent on n, the risk levelsandand the probability levels r aand r r . a Constant factor dependent on N‰ which represents the uncertainty associated with the estimate of the standard deviation. t 0 Value of the non-central Student ratio corresponding to the level of probability for a non-centrality parameter equal to B 0 Limit value of the estimate calculated from t 0 . A, B Calculation intermediates used during the estimation of the lot after analysis. F Calculation intermediate used to facilitate the calculation of k and N. “ u 1 r a – u 1 r r – u 1 – u 1 “ – “ “BS5551-2.61992 4 © BSI 10-1999 5 Principle of the sampling plan 5.1 General The sampling plan described in ISO8634 defines a pair of numbers, N and N‰, which depend on a the legal requirements of the importing country acceptable limit for the value and the size of the smallest lot which can be inspected; b the risks which the importer accepts. NOTEIt should be remembered that it is intended for the inspection of the delivery received by the importer, and not for the lots resold by the same importer. N is the number of increments which are to be taken from the delivery and N‰ the number of analyses to be carried out on these N increments. The N increments are combined and mixed k by k k is a whole number, thus resulting in N‰ aggregate samples N kN‰ and an analysis is carried out on each of these N‰ aggregate samples. This procedure is explained by the relatively long and costly nature for the analyses for determining the content of the various fertilizer nutrients. The sampling plan adopted is based on the use of two non-central Student distributions. As the standard deviation of the population is only known through N‰ analyses and the corresponding estimate s, the confidence intervals to be used should draw on Student’s distribution and not Gaussian distribution. Moreover, in the present case, the two central values of the limit distributions which the buyer’s and seller’s risks should cover, will be defined on the basis of a fixed value L by a shift based on the standard deviationof the population. In this case, the reduced value of the interval between the value L and the confidence interval limits obeys a non-central Student distribution, which has been tabulated in particular by Neyman and Tokarska. It depends only on the shift of the central value in relative value in relation to the standard deviationof the population. Given that in each non-central Student test one linked to the seller’s risk, and the other to the buyer’s risk the same standard deviation i.e.or arose in the non-centrality parameter and in the dispersion of the mean of the N sample values, then the determination of N and N‰ is independent of the value of the actual standard deviation of the lot. 5.2 Ination This is of two types. The first type is derived from the national regulations of the importing country. That is The second type can be fixed by mutual agreement between the two contracting parties the supplier and the importer, taking into account the conditions of application of the regulations in the importing country frequency and stringency of inspections, punitive sanctions, etc. That is n The number of sampling units from which, in accordance with the regulations, partial