1、TECHNICAL REPORT IS0 TR 5307 First edition 1991-12-01 Solid fertilizers - Derivation of a sampling plan for the evaluation of a large delivery Matitkes fertilisantes solides - Fondements theoriques du plan dkchantillonnage destine B Ibvaluation dune grosse livraison Reference number ISOITR 5307:1991
2、(E) ISOITR 5307:1991 (E) Contents Page 1 Scope 1 2 References 1 3 Notation and symbols 1 4 Preliminary hypotheses . 4 5 Principle of the sampling plan 4 5.1 General 4 5.2 Information 5 5.3 What is determined by the proposed method . 8 6 Theory of the sampling plan 8 6.1 Definitions . 8 6.2 Determina
3、tion of limits 9 6.3 Use of two non-central t distributions 10 6.4 Determination of N and N 11 7 Practical procedure for the determination of N and N . 15 7.1 Basic information 15 7.2 Calculation 15 7.3 Simplified calculation when N 30 . 16 8 Examples of calculations . 17 8.1 Calculation by the comp
4、lete process . 17 8.2 Simplified calculation . 20 9 Effect of the values of the various parameters on N and K . 20 10 Evaluation of a delivery 22 Annexes A Table of values of the standardized normal variable u as a function of P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 B Table of values of (1 - u2)/a2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 0 IS0 1991 All rights reserved. No part of this publ
6、ication may be reproduced or utilized In any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from the publisher. International Organization for Standardlzatlon Case Postale 56 l CH-1211 Geneve 20 l Switzerland Printed In Switzerland
7、 ii ISOlTR 5307:1991(E) 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 t,hrough IS0 technical committees. Each member body interested i
8、n a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, govern- mental and non-governmental, in liaison with ISO, also take part in the work. IS0 collaborates closely with the International Electrotechnical Comm
9、ission (IEC) on all matters of eiectrotechnical standardization. The main task of technical committees is to prepare International Stan- dards, but in exceptional circumstances a technical committee may propose the publication of a Technical Report of one of the. following types: - type 1, when the
10、required support cannot be obtained for the publi- cation of an International Standard, despite repeated efforts; - type 2, when the subject is still under technical development or where for any other reason there is the future but not immediate possibility of an agreement on an International Standa
11、rd; - type 3, when a technical committee has collected data of a different kind from that which is normally published as an International Stan- dard (“state of the art”, for example). Technical Reports of types 1 and 2 are subject to review within three years of publication, to decide whether they c
12、an be transformed into International Standards. Technical Reports of type 3 do not necessarily have to be reviewed until the data they provide are considered to be no longer valid or useful. ISO/TR 5307, which is a Technical Report of type 3, was prepared by Technical Committee ISO/TC 134, Fertilize
13、rs and soil conditioners. This document is a type 3 Technical Report. It is not envisaged that it will be published as an International Standard. It gives the mathematical derivation of the sampling plan specified in IS0 8634. Annexes A and B are for information only. iii ISOlTR 5307:1991 (E) Introd
14、uction 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 standar
15、ds 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/TC 134/SC4, is intended to act as a
16、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
17、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 con
18、tents shown on labels or other documentation accompanying the fertilizers. IS0 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 coope
19、ratives) 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. IS0 8634 is designed for accept
20、ance 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. iv ISOlTR 5307:1991 (E) The location of the acceptance inspection, as defined in IS0 8634, in the chain of tr
21、ansactions can be represented by the following diagram: Country of manufacture Importing country Selle- Importer _+ Retailers -Farmers Acceptance inspection in accordance with IS0 8634 (no loading or unloading) . . . TECHNICAL REPORT ISOlTR 5307:1991(E) Solid fertilizers - Derivation of a sampling p
22、lan for the evaluation of a large delivery 1 Scope This Technical Report presents the sampling theory which h s resulted in the definition of the sampling plan described in IS0 8634 17 . . The sampling plan is applicable to a large delivery of more than 250 t of fertilizer supplied to another party,
23、 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 (5,000 t, 10,000 t or more) thus corresponding to a relatively long period of manufacture, but the theory applies to any delivery of 250
24、t or more. 2 References IS0 8157: 1984, Fertilizers and soil conditioners - Vocabulary. IS0 8634:-l), Solid fertilizers - Sampling plan for the evaluation of a large delivery. 3 Notation and symbols The following symbols appear in this Technical Report and have the meanings assigned to them below. A
25、ctual mean value and standard deviation between sampling units in the delivery. P a %i Mean value and standard deviation between sampling units in a delivery of just acceptable quality. 1) To be published. 1 ISOlTR 5307:1991 (E) u N N NR k n X s xi x D L Mean value and standard deviation between sam
26、pling units in a delivery of just unacceptable quality. Mean and standard deviation, respectively, of two lots which can be considered by the importer to be of the same quality. Number of sampling units in the delivery. Number of sampling units to be selected during the sampling of the delivery. (In
27、crements). Number of analyses to be carried out on the N increments during the inspection of the delivery. Number of sampling units contained in the smallest lot presented for resale. Number of increments to be combined into each aggregate sample for analysis. Number of sampling units which will be
28、mandatorily selected during the official sampling of a lot of NR sampling units. Mean value found by analysis after the selection of n sampling units from a lot of sampling units. Estimate of g./ hi- with the aid of the N analyses, where (I is the standard deviation between b) that the distribution
29、of this random quantity does not depend, at least for sufficiently large lots, on their size. 5 Principle of the sampling plan 5.1 General The sampling plan described in IS0 8634 defines a pair of numbers, N and N, which depend on: a) the legal requirements of the importing country (acceptable limit
30、 for the value and the size of the smallest lot which can be inspected); b) the risks which the importer accepts. NOTE - It 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. b ISOlTR 5307:1991(E) N
31、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 the
32、se 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 popu
33、lation is only known through N analyses and the corresponding estimate s, the confidence intervals to be used should draw on Students distribution and not Gaussian distribution. Moreover, in the present case, the two central values of the limit distributions which the buyers and sellers risks should
34、 cover, will be defined on the basis of a fixed value (L) by a shift based on the standard deviation d of 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 parti
35、cular by Neyman and Tokarska. It depends only on the shift of the central value (in relative value) in relation to the standard deviation o of the population. Given that in each non-central Student test (one linked to the sellers risk, and the other to the buyers risk) the same standard deviation (i
36、.e. s or s) 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 Information This is of two types. The first type is derived from the national reg
37、ulations of the importing country. That is: n The number of sampling units from which, in accordance with the regulations, partial samples are to be taken, in the case of the smallest lot that can be inspected. L The official inspection limit; if the declared value is D, it can be equal to D or less
38、 than D by a permitted tolerance which may or may not be a function of the number of lots inspected. (L = D - T, if T = tolerance). The second type can be fixed by mutual agreement between the two contracting parties (the supplier and the importer), taking into account 5 ISOlTR 5307:1991 (E) the con
39、ditions of application of the regulations in the importing country (frequency and stringency of inspections, punitive sanctions, etc.): That is: ra This is the fundamental parameter as it defines the “level of quality“ which shall be the minimum objective of the manufacturer in production, in order
40、to give satisfaction to the importer (see figure 1 and 7.1). Production will normally be centred upon the declared value D; but it is not sufficient for it to fulfil this condition. What is required by the importer, and it should be noted that he is not the user, is to be able to resell small lots w
41、ithout being penalised by the official inspection service. He therefore wishes it to be impossible to draw from the overall delivery small lots which, after sampling, reveal average contents less than L, under official inspection conditions. The ideal would be for the production to contain no small
42、lot likely to appear on inspection to have a value less than L; but this ideal is impossible to attain under practical manufacturing conditions and would only be verifiable by a full inspection, at a proh.ibitive cost. The importer therefore accepts a certain percentage of incorrect units (i.e. bags
43、, if the bag is a sampling unit) defining the quality level of the overall delivery which he considers acceptable; this percentageis expressed by the parameter r, which can be defined as 1(the probability, which is just acceptable to the importer, that the average value of n sampling units is less than the official limit L”. Distribution of the delivery (sample average of n increments) Contents Minimum quality defining an acceptable delivery Figure 1 - The relationship between D, L and ra 6
