{"id":100264,"date":"2026-02-15T20:30:28","date_gmt":"2026-02-15T20:30:28","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100264"},"modified":"2026-07-15T21:25:55","modified_gmt":"2026-07-15T21:25:55","slug":"tolerance-independence-iso8015","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/ro\/calculators\/tolerance-independence-iso8015\/","title":{"rendered":"Controlled Linear-Size Interval Worksheet"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Controlled Linear-Size Interval Worksheet\",\"description\":\"A provenance-controlled arithmetic worksheet for transcribing a declared linear-size interval and comparing a recorded observation range. It does not issue an ISO conformity verdict.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/tolerance-independence-iso8015\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any web browser\",\"isAccessibleForFree\":true,\"publisher\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"}}\n<\/script>\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Linear-size interval 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print{#li-tool{max-width:none}.li-actions{display:none}.li-card{box-shadow:none}.li-result[data-visible=\"false\"]{display:none}}\n<\/style>\n\n<main id=\"li-tool\">\n  <header class=\"li-hero\">\n    <p class=\"li-kicker\">Controlled arithmetic \u00b7 not a conformity decision<\/p>\n    <h1>Linear-Size Interval Worksheet<\/h1>\n    <p class=\"li-lead\">Transcribe one declared numeric size interval and compare it with a recorded observation range. The worksheet performs arithmetic only; it does not infer the applicable GPS operator, evaluate form or envelope requirements, include measurement uncertainty, or declare ISO conformity.<\/p>\n    <div class=\"li-badges\"><span class=\"li-badge\">No presets<\/span><span class=\"li-badge\">No PASS\/FAIL<\/span><span class=\"li-badge\">Source record required<\/span><\/div>\n  <\/header>\n\n  <div class=\"li-warning\"><strong>Do not use this result as an acceptance or rejection record.<\/strong>A conformity decision requires the controlled specification, the correct characteristic and specification operator, a released measurement procedure and the applicable decision rule including measurement uncertainty. Those inputs cannot be recovered from nominal size and two observed numbers.<\/div>\n\n  <section class=\"li-card\" aria-labelledby=\"li-input-title\">\n    <div class=\"li-card-head\"><h2 id=\"li-input-title\">Entered interval and observations<\/h2><p>Use one unit throughout. Signed deviations are added to the nominal value exactly as entered.<\/p><\/div>\n    <form class=\"li-form\" id=\"li-form\" autocomplete=\"off\" novalidate>\n      <div class=\"li-grid\">\n        <div class=\"li-field\"><label for=\"li-unit\">Unit<\/label><select class=\"li-select\" id=\"li-unit\" required><option value=\"\" selected>Select unit<\/option><option value=\"mm\">millimetres (mm)<\/option><option value=\"in\">inches (in)<\/option><\/select><\/div>\n        <div class=\"li-field\"><label for=\"li-nominal\">Nominal value <span class=\"li-hint\">positive plain decimal<\/span><\/label><input class=\"li-input\" id=\"li-nominal\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 50\" required><\/div>\n        <div class=\"li-field\"><label for=\"li-lower-dev\">Lower deviation <span class=\"li-hint\">signed<\/span><\/label><input class=\"li-input\" id=\"li-lower-dev\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. -0.025\" required><\/div>\n        <div class=\"li-field\"><label for=\"li-upper-dev\">Upper deviation <span class=\"li-hint\">signed<\/span><\/label><input class=\"li-input\" id=\"li-upper-dev\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 0\" required><\/div>\n        <div class=\"li-field\"><label for=\"li-observed-min\">Recorded observation minimum<\/label><input class=\"li-input\" id=\"li-observed-min\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 49.980\" required><\/div>\n        <div class=\"li-field\"><label for=\"li-observed-max\">Recorded observation maximum<\/label><input class=\"li-input\" id=\"li-observed-max\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 49.995\" required><\/div>\n        <div class=\"li-field li-field-full\"><label for=\"li-source\">Specification and measurement record <span class=\"li-hint\">3\u2013500 characters<\/span><\/label><textarea class=\"li-textarea\" id=\"li-source\" maxlength=\"500\" placeholder=\"Drawing, revision, characteristic\/operator and released measurement report or data-set identifier\" required><\/textarea><\/div>\n        <label class=\"li-confirm li-field-full\" for=\"li-confirm-record\"><input id=\"li-confirm-record\" type=\"checkbox\" required><span>I transcribed one controlled size characteristic and operator, and the minimum and maximum are comparable results from the same released measurement procedure and record.<\/span><\/label>\n        <label class=\"li-confirm li-field-full\" for=\"li-confirm-boundary\"><input id=\"li-confirm-boundary\" type=\"checkbox\" required><span>I understand that numeric containment is not a conformity verdict. This worksheet does not evaluate measurement uncertainty, form, envelope, maximum-material boundaries or the complete GPS specification.<\/span><\/label>\n      <\/div>\n      <div class=\"li-actions\"><button class=\"li-button li-primary\" type=\"submit\">Calculate numeric containment<\/button><button class=\"li-button li-secondary\" type=\"reset\">Clear<\/button><\/div>\n      <div class=\"li-message\" id=\"li-message\" role=\"alert\" aria-live=\"polite\"><\/div>\n    <\/form>\n    <div class=\"li-result\" id=\"li-result\" data-visible=\"false\" aria-live=\"polite\">\n      <div class=\"li-status\" id=\"li-status\"><\/div>\n      <div class=\"li-result-grid\">\n        <div class=\"li-result-card\"><div class=\"li-result-label\">Entered lower limit<\/div><div class=\"li-result-value\" id=\"li-r-lower\">\u2014<\/div><\/div>\n        <div class=\"li-result-card\"><div class=\"li-result-label\">Entered upper limit<\/div><div class=\"li-result-value\" id=\"li-r-upper\">\u2014<\/div><\/div>\n        <div class=\"li-result-card\"><div class=\"li-result-label\">Interval width<\/div><div class=\"li-result-value\" id=\"li-r-width\">\u2014<\/div><\/div>\n        <div class=\"li-result-card\"><div class=\"li-result-label\">Observation span<\/div><div class=\"li-result-value\" id=\"li-r-span\">\u2014<\/div><\/div>\n        <div class=\"li-result-card\"><div class=\"li-result-label\">Lower arithmetic margin<\/div><div class=\"li-result-value\" id=\"li-r-lower-margin\">\u2014<\/div><\/div>\n        <div class=\"li-result-card\"><div class=\"li-result-label\">Upper arithmetic margin<\/div><div class=\"li-result-value\" id=\"li-r-upper-margin\">\u2014<\/div><\/div>\n        <div class=\"li-result-card li-record\"><div class=\"li-result-label\">Source record<\/div><div class=\"li-result-value\" id=\"li-r-record\">\u2014<\/div><\/div>\n      <\/div>\n      <p class=\"li-result-note\" id=\"li-r-note\"><\/p>\n    <\/div>\n  <\/section>\n\n  <section class=\"li-card\">\n    <div class=\"li-section\">\n      <h2>Arithmetic implemented<\/h2>\n      <div class=\"li-formula\">LL = N + d<sub>L<\/sub><br>UL = N + d<sub>U<\/sub><br>T = UL \u2212 LL<br>S = x<sub>max<\/sub> \u2212 x<sub>min<\/sub><br>m<sub>L<\/sub> = x<sub>min<\/sub> \u2212 LL<br>m<sub>U<\/sub> = UL \u2212 x<sub>max<\/sub><\/div>\n      <p><code>N<\/code> is the entered nominal value; <code>dL<\/code> and <code>dU<\/code> are the signed entered deviations; <code>LL<\/code> and <code>UL<\/code> are the resulting numeric limits; <code>xmin<\/code> and <code>xmax<\/code> are the recorded extrema. \u201cInside\u201d means only <code>xmin \u2265 LL<\/code> and <code>xmax \u2264 UL<\/code> for the entered numbers.<\/p>\n      <p>All quantities retain the selected unit. Decimal point and decimal comma are accepted. Scientific notation, units inside numeric fields, partial numeric strings, non-finite values and inconsistent intervals are rejected.<\/p>\n    <\/div>\n    <div class=\"li-section\">\n      <h2>What this worksheet deliberately does not calculate<\/h2>\n      <ul>\n        <li><strong>Form error:<\/strong> the spread between maximum and minimum observed sizes is not automatically roundness, cylindricity, straightness or any other form deviation.<\/li>\n        <li><strong>Envelope or maximum-material boundary:<\/strong> two extrema do not establish whether an actual surface violates a perfect-form boundary.<\/li>\n        <li><strong>Specification operator:<\/strong> the applicable size characteristic and operator must already be defined in the controlled specification.<\/li>\n        <li><strong>Conformity or nonconformity:<\/strong> no uncertainty budget, guard band or ISO 14253-1 decision rule is implemented.<\/li>\n        <li><strong>Fit, function or interchangeability:<\/strong> numeric containment alone does not establish assembly function.<\/li>\n      <\/ul>\n      <div class=\"li-scope\"><strong>Required escalation:<\/strong> use the licensed controlled standards, the complete drawing\/specification, calibrated measurement results with uncertainty, and an authorized metrology decision process for acceptance or rejection.<\/div>\n    <\/div>\n    <div class=\"li-section\">\n      <h2>Standards status and scope<\/h2>\n      <div class=\"li-table-wrap\"><table class=\"li-table\"><thead><tr><th>Document<\/th><th>Verified public status<\/th><th>Relevance and boundary<\/th><\/tr><\/thead><tbody>\n        <tr><td>ISO 8015:2011, edition 2<\/td><td>Published; ISO records confirmation in 2021.<\/td><td>Fundamental GPS concepts, principles and rules for specification and verification. The public ISO card does not provide enough normative detail to turn this worksheet into an ISO compliance test.<\/td><\/tr>\n        <tr><td>ISO 14405-1:2025, edition 3<\/td><td>Published 2025-08; replaces withdrawn ISO 14405-1:2016.<\/td><td>Requirements for indicating linear sizes and default\/special specification operators for applicable features of size. This worksheet does not infer or select an operator.<\/td><\/tr>\n        <tr><td>ISO 14253-1:2017, edition 3<\/td><td>Published; confirmed in 2023.<\/td><td>Decision rules for verifying conformity or nonconformity, including cases close to limits and measurement uncertainty. Those rules are not implemented here.<\/td><\/tr>\n      <\/tbody><\/table><\/div>\n      <p>The arithmetic formulas above are general interval arithmetic, not formulas claimed to be prescribed by ISO. Exact principles, operators, modifiers and decision-rule implementation require licensed controlled copies of the relevant standards.<\/p>\n    <\/div>\n    <div class=\"li-section li-source\">\n      <h2>Official source records<\/h2>\n      <ul>\n        <li><a href=\"https:\/\/www.iso.org\/standard\/55979.html\" rel=\"noopener\" target=\"_blank\">ISO 8015:2011 official record<\/a> \u2014 edition, status, lifecycle and public abstract; accessed 2026-07-15.<\/li>\n        <li><a href=\"https:\/\/www.iso.org\/standard\/14405-1\" rel=\"noopener\" target=\"_blank\">ISO 14405-1:2025 official record<\/a> \u2014 current edition, scope and replacement lifecycle; accessed 2026-07-15.<\/li>\n        <li><a href=\"https:\/\/www.iso.org\/standard\/70137.html\" rel=\"noopener\" target=\"_blank\">ISO 14253-1:2017 official record<\/a> \u2014 current edition, scope, confirmation and uncertainty boundary; accessed 2026-07-15.<\/li>\n        <li><a href=\"https:\/\/www.iso.org\/standard\/65202.html\" rel=\"noopener\" target=\"_blank\">ISO 14405-1:2016 official withdrawn record<\/a> \u2014 replacement evidence; accessed 2026-07-15.<\/li>\n      <\/ul>\n    <\/div>\n  <\/section>\n\n  <p class=\"li-footer\">Engineering arithmetic aid only. Preserve the displayed source record with any exported or transcribed result.<\/p>\n<\/main>\n\n<script>\n(function(){\n  'use strict';\n  var form=document.getElementById('li-form'),message=document.getElementById('li-message'),result=document.getElementById('li-result'),status=document.getElementById('li-status');\n  var fields={unit:document.getElementById('li-unit'),nominal:document.getElementById('li-nominal'),lowerDev:document.getElementById('li-lower-dev'),upperDev:document.getElementById('li-upper-dev'),observedMin:document.getElementById('li-observed-min'),observedMax:document.getElementById('li-observed-max'),source:document.getElementById('li-source'),confirmRecord:document.getElementById('li-confirm-record'),confirmBoundary:document.getElementById('li-confirm-boundary')};\n  var outputs={lower:document.getElementById('li-r-lower'),upper:document.getElementById('li-r-upper'),width:document.getElementById('li-r-width'),span:document.getElementById('li-r-span'),lowerMargin:document.getElementById('li-r-lower-margin'),upperMargin:document.getElementById('li-r-upper-margin'),record:document.getElementById('li-r-record'),note:document.getElementById('li-r-note')};\n  function hide(){result.dataset.visible='false';status.textContent='';status.removeAttribute('data-kind');Object.keys(outputs).forEach(function(k){outputs[k].textContent=k==='note'?'':'\u2014';});}\n  function fail(text){hide();message.dataset.kind='error';message.textContent=text;}\n  function parsePlain(value,label){var s=String(value).trim();if(s.length===0||s.length>40||!\/^[-+]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s))throw new Error(label+' must be one complete plain decimal number. Scientific notation and unit suffixes are not accepted.');s=s.replace(',','.');var n=Number(s);if(!Number.isFinite(n)||Math.abs(n)>1e9)throw new Error(label+' is outside the supported finite range (absolute value at most 1,000,000,000).');var negative=s.charAt(0)==='-',unsigned=\/^[+-]\/.test(s)?s.slice(1):s,parts=unsigned.split('.'),fraction=parts[1]||'',digits=((parts[0]||'0')+fraction).replace(\/^0+(?=\\d)\/,'');return{coefficient:(negative?-1n:1n)*BigInt(digits||'0'),scale:fraction.length};}\n  function pow10(n){return 10n**BigInt(n);}\n  function fmt(q,scale){var negative=q<0n;if(negative)q=-q;var s=q.toString().padStart(scale+1,'0');if(scale){s=s.slice(0,-scale)+'.'+s.slice(-scale);s=s.replace(\/\\.?0+$\/,'');}if(s==='')s='0';return(negative&&s!=='0'?'-':'')+s;}\n  form.addEventListener('submit',function(event){event.preventDefault();message.textContent='';message.removeAttribute('data-kind');hide();try{\n    if(fields.unit.value!=='mm'&&fields.unit.value!=='in')throw new Error('Select millimetres or inches.');\n    var nominal=parsePlain(fields.nominal.value,'Nominal value'),lowerDev=parsePlain(fields.lowerDev.value,'Lower deviation'),upperDev=parsePlain(fields.upperDev.value,'Upper deviation'),observedMin=parsePlain(fields.observedMin.value,'Observation minimum'),observedMax=parsePlain(fields.observedMax.value,'Observation maximum'),scale=Math.max(nominal.scale,lowerDev.scale,upperDev.scale,observedMin.scale,observedMax.scale),at=function(v){return v.coefficient*pow10(scale-v.scale);},nominalQ=at(nominal),lowerDevQ=at(lowerDev),upperDevQ=at(upperDev),observedMinQ=at(observedMin),observedMaxQ=at(observedMax);\n    if(nominalQ<=0n)throw new Error('Nominal value must be greater than zero.');\n    if(lowerDevQ>upperDevQ)throw new Error('Lower deviation cannot exceed upper deviation.');\n    var lower=nominalQ+lowerDevQ,upper=nominalQ+upperDevQ;\n    if(lower<=0n||upper<=0n)throw new Error('The entered deviations must produce positive finite lower and upper limits.');\n    if(observedMinQ<=0n||observedMaxQ<=0n)throw new Error('Recorded observations must be greater than zero.');\n    if(observedMinQ>observedMaxQ)throw new Error('Observation minimum cannot exceed observation maximum.');\n    var source=fields.source.value.trim();if(source.length<3||source.length>500)throw new Error('Enter a specification and measurement source record of 3 to 500 characters.');\n    if(!fields.confirmRecord.checked)throw new Error('Confirm the controlled characteristic, operator and comparable measurement record.');\n    if(!fields.confirmBoundary.checked)throw new Error('Confirm the arithmetic-only boundary before calculating.');\n    var width=upper-lower,span=observedMaxQ-observedMinQ,lowerMargin=observedMinQ-lower,upperMargin=upper-observedMaxQ,inside=lowerMargin>=0n&&upperMargin>=0n,u=fields.unit.value;\n    status.dataset.kind=inside?'inside':'outside';status.textContent=inside?'The entered observation range lies inside the entered numeric interval.':'The entered observation range extends outside the entered numeric interval.';\n    outputs.lower.textContent=fmt(lower,scale)+' '+u;outputs.upper.textContent=fmt(upper,scale)+' '+u;outputs.width.textContent=fmt(width,scale)+' '+u;outputs.span.textContent=fmt(span,scale)+' '+u;outputs.lowerMargin.textContent=fmt(lowerMargin,scale)+' '+u;outputs.upperMargin.textContent=fmt(upperMargin,scale)+' '+u;outputs.record.textContent=source;outputs.note.textContent='Arithmetic relation only \u2014 not an ISO conformity or nonconformity verdict. Form, envelope, specification-operator interpretation, measurement uncertainty and the applicable decision rule remain outside this calculation.';result.dataset.visible='true';\n  }catch(error){fail(error.message);}});\n  form.addEventListener('reset',function(){setTimeout(function(){message.textContent='';message.removeAttribute('data-kind');hide();},0);});\n  hide();\n}());\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Compare a documented observation range with a transcribed numeric size interval using exact decimal arithmetic. This worksheet does not issue an ISO conformity verdict.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100264","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/calculator\/100264","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":3,"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/calculator\/100264\/revisions"}],"predecessor-version":[{"id":102607,"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/calculator\/100264\/revisions\/102607"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/media?parent=100264"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/categories?post=100264"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/tags?post=100264"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}