{"id":356921,"date":"2024-10-20T01:14:33","date_gmt":"2024-10-20T01:14:33","guid":{"rendered":"https:\/\/pdfstandards.shop\/product\/uncategorized\/bs-iso-3951-22013\/"},"modified":"2024-10-26T01:39:48","modified_gmt":"2024-10-26T01:39:48","slug":"bs-iso-3951-22013","status":"publish","type":"product","link":"https:\/\/pdfstandards.shop\/product\/publishers\/bsi\/bs-iso-3951-22013\/","title":{"rendered":"BS ISO 3951-2:2013"},"content":{"rendered":"<p>This part of ISO&nbsp;3951 is primarily designed for use under the following conditions:<\/p>\n<ol style=\"list-style-type:lower-alpha\">\n<li>\n<p>where the inspection procedure is to be applied to a <b>continuing series of lots<\/b> of discrete products all supplied by one producer using one production process. If there are different producers or production processes, this part of ISO&nbsp;3951 shall be applied to each one separately;<\/p>\n<\/li>\n<li>\n<p>where the <b>quality characteristics<\/b> of the items of product are <b>measurable on a continuous scale<\/b>;<\/p>\n<\/li>\n<li>\n<p>where the measurement error is negligible (i.e. with a standard deviation no more than 10&nbsp;% of the corresponding process standard deviation). However, procedures are also provided in Clause&nbsp;9 and Annex&nbsp;P for accommodating measurement error when it has a non-negligible standard deviation;<\/p>\n<\/li>\n<li>\n<p>where production is stable (under statistical control) and the quality characteristics are distributed, at least to a close approximation, according to <b>normal distributions<\/b>;<\/p>\n<\/li>\n<li>\n<p>where, in the case of multiple quality characteristics, the characteristics are independent, or almost independent, of one another;<\/p>\n<\/li>\n<li>\n<p>where a contract or standard defines <b>a lower specification limit<\/b>, <i>L<\/i>, <b>an upper specification limit<\/b>, <i>U<\/i>, <b>or both<\/b> on each of the quality characteristics. If there is only one quality characteristic, an item is qualified as conforming if its measured quality characteristic <i>x<\/i> satisfies the appropriate one of the following inequalities:<\/p>\n<ol style=\"list-style-type:decimal\">\n<li><label>1)<\/label>\n<p><i>x<\/i> \u2265 <i>L<\/i> (i.e. the lower specification limit is not violated);<\/p>\n<\/li>\n<li><label>2)<\/label>\n<p><i>x<\/i> \u2264 <i>U<\/i> (i.e. the upper specification limit is not violated);<\/p>\n<\/li>\n<li><label>3)<\/label>\n<p><i>x<\/i> \u2265 <i>L<\/i> and <i>x<\/i> \u2264 <i>U<\/i> (i.e. neither the lower nor the upper specification limit is violated).<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<p>If there are two or more, say <i>m<\/i>, quality characteristics, then, designating the lower and upper limits for the <i>i<\/i><sup>th<\/sup> quality characteristic by <i>L<sub>i<\/sub><\/i> and <i>U<sub>i<\/sub><\/i> respectively, an item of product is qualified as nonconforming if one or more of its <i>m<\/i> measured quality characteristics, <i>x<sub>i<\/sub><\/i>, fails to satisfy the appropriate one of the following inequalities:<\/p>\n<ol style=\"list-style-type:decimal\">\n<li><label>4)<\/label>\n<p><i>x<sub>i<\/sub><\/i> \u2265 <i>L<sub>i<\/sub><\/i>;<\/p>\n<\/li>\n<li><label>5)<\/label>\n<p><i>x<sub>i<\/sub><\/i> \u2264 <i>U<sub>i<\/sub><\/i>;<\/p>\n<\/li>\n<li><label>6)<\/label>\n<p><i>x<sub>i<\/sub><\/i> \u2265 <i>L<sub>i<\/sub><\/i> and <i>x<sub>i<\/sub><\/i> \u2264 <i>U<sub>i<\/sub><\/i>.<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>Inequalities 1), 2), 4), and 5) are called cases with a <b>single specification limit<\/b> while 3) and 6) are called cases with <b>double specification limits<\/b>. For double specification limits, a further distinction is made between combined control, separate control, and complex control. If there is only one quality characteristic, then<\/p>\n<ul>\n<li>\n<p>combined control is where a single AQL applies to nonconformity beyond both limits,<\/p>\n<\/li>\n<li>\n<p>separate control is where separate AQLs apply to nonconformity beyond each of the limits, and<\/p>\n<\/li>\n<li>\n<p>complex control is where one AQL applies to nonconformity beyond the limit that is of greater seriousness and a larger AQL applies to the total nonconformity beyond both limits.<\/p>\n<\/li>\n<\/ul>\n<p>If there are two or more quality characteristics, this generalizes as follows:<\/p>\n<ul>\n<li>\n<p>combined control is where nonconformity beyond both limits on a variable belongs to the same class, to which a single AQL applies;<\/p>\n<\/li>\n<li>\n<p>separate control is where nonconformity beyond the two limits on a variable belongs to separate classes, to each of which a single AQL applies;<\/p>\n<\/li>\n<li>\n<p>complex control is where nonconformity beyond the limit that is of greater seriousness belongs to one class to which a single AQL applies, and the total nonconformity beyond both limits belongs to another class to which a larger AQL applies.<\/p>\n<\/li>\n<\/ul>\n<p>Note that, in the case of two or more quality characteristics, nonconformity on more than one quality characteristic may belong to the same class.<\/p>\n<h4>PDF Catalog<\/h4>\n<table border=\"1px\" class=\"des-table\">\n<tr>\n<th>PDF Pages<\/th>\n<th>PDF Title<\/th>\n<\/tr>\n<tr>\n<td><b>2<b><\/td>\n<td>undefined  <\/td>\n<\/tr>\n<tr>\n<td><b>8<b><\/td>\n<td>Foreword  <\/td>\n<\/tr>\n<tr>\n<td><b>10<b><\/td>\n<td>Introduction  <\/td>\n<\/tr>\n<tr>\n<td><b>13<b><\/td>\n<td>1 Scope  <\/td>\n<\/tr>\n<tr>\n<td><b>14<b><\/td>\n<td>2 Normative references <br \/> 3 Terms and definitions  <\/td>\n<\/tr>\n<tr>\n<td><b>18<b><\/td>\n<td>4 Symbols <br \/> 4.1 Univariate symbols  <\/td>\n<\/tr>\n<tr>\n<td><b>20<b><\/td>\n<td>4.2 Multivariate symbols <br \/> 5 Acceptance quality limit (AQL) <br \/> 5.1 Concept <br \/> 5.2 Use <br \/> 5.3 Specifying AQLs  <\/td>\n<\/tr>\n<tr>\n<td><b>21<b><\/td>\n<td>5.4 Preferred AQLs <br \/> 5.5 Caution <br \/> 5.6 Limitation <br \/> 6 Switching rules for normal, tightened, and reduced inspection  <\/td>\n<\/tr>\n<tr>\n<td><b>22<b><\/td>\n<td>7 Relation to ISO 2859-1 and ISO 3951-1 <br \/> 7.1 Relation to ISO 2859-1 <br \/> 7.1.1 Similarities to ISO 2859-1 <br \/> 7.1.2 Differences from ISO 2859-1  <\/td>\n<\/tr>\n<tr>\n<td><b>23<b><\/td>\n<td>7.2 Relation to ISO 3951-1 <br \/> 7.2.1 Similarities to ISO 3951-1 <br \/> 7.2.2 Differences from ISO 3951-1  <\/td>\n<\/tr>\n<tr>\n<td><b>24<b><\/td>\n<td>8 Consumer protection <br \/> 8.1 Use of individual plans <br \/> 8.2 Consumer\u2019s risk quality (CRQ) tables <br \/> 8.3 Producer\u2019s risk tables <br \/> 8.4 Operating characteristic (OC) curves <br \/> 9 Accommodating measurement variability  <\/td>\n<\/tr>\n<tr>\n<td><b>25<b><\/td>\n<td>10 Planning <br \/> 11 Choice between variables and attributes  <\/td>\n<\/tr>\n<tr>\n<td><b>26<b><\/td>\n<td>12 Choice between the s-method and \u03c3-method <br \/> 13 Choice of inspection level and AQL <br \/> 14 Choice of sampling scheme <br \/> 14.1 Standard plans  <\/td>\n<\/tr>\n<tr>\n<td><b>27<b><\/td>\n<td>14.2 Special plans <br \/> 15 Preliminary operations  <\/td>\n<\/tr>\n<tr>\n<td><b>28<b><\/td>\n<td>16 Standard procedures for the univariate s-method <br \/> 16.1 Obtaining a plan, sampling, and preliminary calculations <br \/> 16.2 Form k acceptability criterion for the s-method  <\/td>\n<\/tr>\n<tr>\n<td><b>30<b><\/td>\n<td>16.3 Form p* acceptability criterion for the s-method <br \/> 16.3.1 Introduction <br \/> 16.3.2 Combined control for the s-method  <\/td>\n<\/tr>\n<tr>\n<td><b>36<b><\/td>\n<td>16.3.3 Separate control for the s-method <br \/> 16.3.4 Complex control for the s-method <br \/> 17 Standard multivariate s-method procedures for independent quality characteristics <br \/> 17.1 General methodology  <\/td>\n<\/tr>\n<tr>\n<td><b>37<b><\/td>\n<td>17.2 Example  <\/td>\n<\/tr>\n<tr>\n<td><b>39<b><\/td>\n<td>18 Standard univariate \u03c3-method procedures <br \/> 18.1 Obtaining a plan, sampling, and preliminary calculations <br \/> 18.2 Acceptability criterion for a single specification limit or for double specification limits with separate control  <\/td>\n<\/tr>\n<tr>\n<td><b>40<b><\/td>\n<td>18.3 Acceptability criterion for double specification limits with combined or complex control  <\/td>\n<\/tr>\n<tr>\n<td><b>42<b><\/td>\n<td>19 Standard multivariate \u03c3-method procedures for independent quality characteristics <br \/> 19.1 General methodology  <\/td>\n<\/tr>\n<tr>\n<td><b>43<b><\/td>\n<td>19.2 Example  <\/td>\n<\/tr>\n<tr>\n<td><b>44<b><\/td>\n<td>20 Standard multivariate combined s-method and \u03c3-method procedures for independent quality characteristics <br \/> 20.1 General methodology  <\/td>\n<\/tr>\n<tr>\n<td><b>45<b><\/td>\n<td>20.2 Example  <\/td>\n<\/tr>\n<tr>\n<td><b>47<b><\/td>\n<td>21 Procedure during continuing inspection <br \/> 22 Normality and outliers <br \/> 22.1 Normality <br \/> 22.2 Outliers <br \/> 23 Records <br \/> 23.1 Control charts <br \/> 23.2 Lots that are not accepted  <\/td>\n<\/tr>\n<tr>\n<td><b>48<b><\/td>\n<td>24 Operation of switching rules <br \/> 25 Discontinuation and resumption of inspection  <\/td>\n<\/tr>\n<tr>\n<td><b>49<b><\/td>\n<td>26 Switching between the s-method and \u03c3-method <br \/> 26.1 Estimating the process standard deviation <br \/> 26.2 State of statistical control <br \/> 26.3 Switching from the s-method to the \u03c3-method <br \/> 26.4 Switching from the \u03c3-method to the s-method  <\/td>\n<\/tr>\n<tr>\n<td><b>50<b><\/td>\n<td>Annex A (normative)  Table for determining the sample size code letter  <\/td>\n<\/tr>\n<tr>\n<td><b>51<b><\/td>\n<td>Annex B (normative)  Form k single sampling plans: s-method  <\/td>\n<\/tr>\n<tr>\n<td><b>54<b><\/td>\n<td>Annex C (normative)  Form k single sampling plans: \u03c3-method  <\/td>\n<\/tr>\n<tr>\n<td><b>57<b><\/td>\n<td>Annex D (normative)  Form p* single sampling plans: s-method  <\/td>\n<\/tr>\n<tr>\n<td><b>60<b><\/td>\n<td>Annex E (normative)  Form p* single sampling plans: \u03c3-method  <\/td>\n<\/tr>\n<tr>\n<td><b>63<b><\/td>\n<td>Annex F (normative)  Values of fs for maximum sample standard deviation (MSSD)  <\/td>\n<\/tr>\n<tr>\n<td><b>66<b><\/td>\n<td>Annex G (normative)  Values of f\u03c3 for maximum process standard deviation (MPSD)  <\/td>\n<\/tr>\n<tr>\n<td><b>69<b><\/td>\n<td>Annex H (normative)  Estimating the process fraction nonconforming for sample size 3: s-method  <\/td>\n<\/tr>\n<tr>\n<td><b>72<b><\/td>\n<td>Annex I (normative)  Values of cU for upper control limit on the sample standard deviation  <\/td>\n<\/tr>\n<tr>\n<td><b>73<b><\/td>\n<td>Annex J (normative)  Supplementary acceptability constants for qualifying towards reduced inspection  <\/td>\n<\/tr>\n<tr>\n<td><b>74<b><\/td>\n<td>Annex K (normative)  Procedures for obtaining s and \u03c3  <\/td>\n<\/tr>\n<tr>\n<td><b>76<b><\/td>\n<td>Annex L (normative)  Estimating the process fraction nonconforming  <\/td>\n<\/tr>\n<tr>\n<td><b>82<b><\/td>\n<td>Annex M (informative)  Consumer\u2019s risk qualities  <\/td>\n<\/tr>\n<tr>\n<td><b>86<b><\/td>\n<td>Annex N (informative)  Producer\u2019s risks  <\/td>\n<\/tr>\n<tr>\n<td><b>90<b><\/td>\n<td>Annex O (informative)  Operating characteristics for the \u03c3-method  <\/td>\n<\/tr>\n<tr>\n<td><b>91<b><\/td>\n<td>Annex P (informative)  Accommodating measurement variability  <\/td>\n<\/tr>\n<tr>\n<td><b>97<b><\/td>\n<td>Bibliography  <\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p><b>Sampling procedures for inspection by variables &#8211; General specification for single sampling plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection of independent quality characteristics<\/b><\/p>\n<table class=\"shortdes-table\" style=\"width: 100%\" border=\"0\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td>Published By<\/td>\n<td>Publication Date<\/td>\n<td>Number of Pages<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/pdfstandards.shop\/product-category\/publishers\/bsi\/\"><b>BSI<\/b><\/a><\/td>\n<td>2018<\/td>\n<td>100<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":356927,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[97,2641],"product_tag":[],"class_list":{"0":"post-356921","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-03-120-30","7":"product_cat-bsi","9":"first","10":"instock","11":"sold-individually","12":"shipping-taxable","13":"purchasable","14":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product\/356921","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media\/356927"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=356921"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=356921"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=356921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}