{"id":100299,"date":"2026-02-15T20:32:33","date_gmt":"2026-02-15T20:32:33","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100299"},"modified":"2026-07-17T09:52:38","modified_gmt":"2026-07-17T09:52:38","slug":"vibration-trend-remaining-life","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/id\/calculators\/vibration-trend-remaining-life\/","title":{"rendered":"Two-Point Vibration Threshold Extrapolation Worksheet"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Two-Point Vibration Threshold Extrapolation Worksheet\",\"description\":\"Compare linear and log-linear two-point vibration extrapolation scenarios against user-supplied source-controlled reference levels. This is not remaining useful life, failure prediction, ISO compliance or an operating decision.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/vibration-trend-remaining-life\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any\",\"isAccessibleForFree\":true,\"inLanguage\":\"en\"}\n<\/script><br \/>\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\":\"Two-Point Vibration Threshold Extrapolation Worksheet\",\"item\":\"https:\/\/vibromera.eu\/calculators\/vibration-trend-remaining-life\/\"}]}\n<\/script><\/p>\n<style>\n#vbm-vx{--vx-ink:#172033;--vx-muted:#536078;--vx-line:#cbd5e1;--vx-soft:#f4f7fb;--vx-blue:#155eef;--vx-blue-soft:#eef4ff;--vx-amber:#92400e;--vx-amber-soft:#fff8e6;--vx-red:#a61b1b;--vx-red-soft:#fff0f0;--vx-green:#176b3a;--vx-green-soft:#edf9f1;max-width:1100px;margin:0 auto;padding:18px 14px 42px;color:var(--vx-ink);font-family:Arial,Helvetica,sans-serif;line-height:1.55;box-sizing:border-box}\n#vbm-vx *{box-sizing:border-box}\n#vbm-vx h1,#vbm-vx h2,#vbm-vx h3{line-height:1.2;color:var(--vx-ink)}\n#vbm-vx h1{font-size:clamp(29px,5vw,45px);margin:0 0 12px}\n#vbm-vx h2{font-size:24px;margin:0 0 14px}\n#vbm-vx h3{font-size:18px;margin:20px 0 8px}\n.vx-hero,.vx-card{border:1px solid var(--vx-line);border-radius:16px;background:#fff;padding:clamp(18px,4vw,30px);margin:0 0 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14px;border:1px solid #b7c7e6;border-radius:10px;background:#f5f8ff}\n.vx-formula{overflow-x:auto;white-space:nowrap;border:1px solid var(--vx-line);background:var(--vx-soft);border-radius:9px;padding:12px 14px;font-family:Consolas,monospace;margin:9px 0}\n.vx-table-wrap{width:100%;max-width:100%;min-width:0;overflow-x:auto}\n.vx-table{width:100%;border-collapse:collapse;min-width:760px;font-size:14px}\n.vx-table th,.vx-table td{border:1px solid var(--vx-line);text-align:left;vertical-align:top;padding:9px}.vx-table th{background:var(--vx-soft)}\n.vx-note{border:1px solid var(--vx-line);border-radius:10px;padding:11px 13px;margin:10px 0;background:#fff}\n.vx-note summary{font-weight:700;cursor:pointer}\n.vx-source-boundary{background:var(--vx-amber-soft);border:1px solid #e7c986;border-radius:10px;padding:12px 14px;margin:14px 0}\n.vx-ok{color:var(--vx-green)}.vx-warn{color:var(--vx-red)}\n@media(max-width:720px){.vx-grid,.vx-checks,.vx-result-grid{grid-template-columns:minmax(0,1fr)}.vx-full,.vx-wide{grid-column:auto}.vx-card,.vx-hero{padding:17px}.vx-result span{font-size:18px}}\n<\/style>\n<p><main id=\"vbm-vx\"><\/p>\n<section class=\"vx-hero\" aria-labelledby=\"vx-title\">\n<h1 id=\"vx-title\">Two-Point Vibration Threshold Extrapolation Worksheet<\/h1>\n<p class=\"vx-lead\">Compare two deliberately assumed mathematical continuations of two comparable vibration observations. The worksheet reports arithmetic crossings of your own controlled reference levels; it does not estimate remaining useful life or failure time.<\/p>\n<div class=\"vx-badges\"><span class=\"vx-badge\">Not RUL<\/span><span class=\"vx-badge\">No embedded ISO values<\/span><span class=\"vx-badge\">Two scenarios shown together<\/span><span class=\"vx-badge\">No operating action<\/span><\/div>\n<div class=\"vx-boundary\"><strong>Boundary:<\/strong> two observations cannot establish model adequacy, residual scatter, outliers, confidence or prediction intervals. A mathematical crossing is not an alarm, danger state, maintenance interval, failure prediction, ISO compliance or permission to continue operating.<\/div>\n<\/section>\n<form id=\"vx-form\" class=\"vx-card\" novalidate>\n<h2>Controlled observation and reference record<\/h2>\n<div class=\"vx-grid\">\n<div class=\"vx-field\"><label for=\"vx-case\">Case \/ calculation ID<\/label><input id=\"vx-case\" type=\"text\" autocomplete=\"off\" required><span class=\"vx-hint\">Unique traceable identifier; no default case is assumed.<\/span><\/div>\n<div class=\"vx-field\"><label for=\"vx-asset\">Asset \/ machine set<\/label><input id=\"vx-asset\" type=\"text\" autocomplete=\"off\" required><\/div>\n<div class=\"vx-field\"><label for=\"vx-point\">Measurement point, axis and sensor chain<\/label><textarea id=\"vx-point\" required><\/textarea><span class=\"vx-hint\">Include mounting, positive direction and any channel processing relevant to comparability.<\/span><\/div>\n<div class=\"vx-field\"><label for=\"vx-quantity\">Quantity, unit, band and amplitude convention<\/label><textarea id=\"vx-quantity\" required><\/textarea><span class=\"vx-hint\">Example format only: velocity, mm\/s RMS, stated band. Do not copy an example as evidence.<\/span><\/div>\n<div class=\"vx-field\"><label for=\"vx-baseline-id\">Baseline observation ID \/ timestamp<\/label><input id=\"vx-baseline-id\" type=\"text\" autocomplete=\"off\" required><\/div>\n<div class=\"vx-field\"><label for=\"vx-current-id\">Current observation ID \/ timestamp<\/label><input id=\"vx-current-id\" type=\"text\" autocomplete=\"off\" required><\/div>\n<div class=\"vx-field\"><label for=\"vx-condition0\">Baseline operating and measurement condition<\/label><textarea id=\"vx-condition0\" required><\/textarea><\/div>\n<div class=\"vx-field\"><label for=\"vx-condition1\">Current operating and measurement condition<\/label><textarea id=\"vx-condition1\" required><\/textarea><\/div>\n<div class=\"vx-field\"><label for=\"vx-v0\">Baseline value V0<\/label><input id=\"vx-v0\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" required><span class=\"vx-hint\">Positive value in the exact declared quantity\/unit\/convention.<\/span><\/div>\n<div class=\"vx-field\"><label for=\"vx-v1\">Current value V1<\/label><input id=\"vx-v1\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" required><\/div>\n<div class=\"vx-field\"><label for=\"vx-elapsed\">Elapsed time \u0394t<\/label><input id=\"vx-elapsed\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" required><\/div>\n<div class=\"vx-field\"><label for=\"vx-time-unit\">Time unit for \u0394t and horizon<\/label><select id=\"vx-time-unit\" required><option value=\"\">Select one<\/option><option value=\"hours\">Hours<\/option><option value=\"days\">Days<\/option><\/select><\/div>\n<div class=\"vx-field\"><label for=\"vx-ref-a\">Reference level A<\/label><input id=\"vx-ref-a\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" required><span class=\"vx-hint\">Positive user-supplied level from the exact controlled source below.<\/span><\/div>\n<div class=\"vx-field\"><label for=\"vx-ref-a-basis\">Reference A basis<\/label><textarea id=\"vx-ref-a-basis\" required><\/textarea><span class=\"vx-hint\">Document\/procedure, edition\/revision, clause\/table\/page, applicability and accountable owner.<\/span><\/div>\n<div class=\"vx-field\"><label for=\"vx-ref-b\">Reference level B (optional)<\/label><input id=\"vx-ref-b\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"vx-hint\">If supplied, its basis is mandatory. No alarm\/danger meaning is inferred.<\/span><\/div>\n<div class=\"vx-field\"><label for=\"vx-ref-b-basis\">Reference B basis (required only when B is supplied)<\/label><textarea id=\"vx-ref-b-basis\"><\/textarea><\/div>\n<div class=\"vx-field\"><label for=\"vx-horizon\">Future comparison horizon h<\/label><input id=\"vx-horizon\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" required><span class=\"vx-hint\">Uses the same selected time unit as \u0394t.<\/span><\/div>\n<div class=\"vx-field\"><label for=\"vx-reviewer\">Reviewer and review date<\/label><input id=\"vx-reviewer\" type=\"text\" autocomplete=\"off\" required><\/div>\n<\/p><\/div>\n<h3>Eight applicability and decision gates<\/h3>\n<div class=\"vx-checks\">\n      <label class=\"vx-check\" for=\"vx-ev-chain\"><input id=\"vx-ev-chain\" type=\"checkbox\">Same point, axis, sensor, mounting and acquisition\/processing chain are confirmed.<\/label><br \/>\n      <label class=\"vx-check\" for=\"vx-ev-quantity\"><input id=\"vx-ev-quantity\" type=\"checkbox\">Same physical quantity, unit, frequency band and RMS\/peak convention are confirmed.<\/label><br \/>\n      <label class=\"vx-check\" for=\"vx-ev-condition\"><input id=\"vx-ev-condition\" type=\"checkbox\">Speed, load, temperature and process conditions are comparable or normalized by a controlled method.<\/label><br \/>\n      <label class=\"vx-check\" for=\"vx-ev-trace\"><input id=\"vx-ev-trace\" type=\"checkbox\">Both observations and the measurement system have traceable IDs and quality review.<\/label><br \/>\n      <label class=\"vx-check\" for=\"vx-ev-event\"><input id=\"vx-ev-event\" type=\"checkbox\">Interventions, step changes and known external events between observations were reviewed.<\/label><br \/>\n      <label class=\"vx-check\" for=\"vx-ev-model\"><input id=\"vx-ev-model\" type=\"checkbox\">The user accepts that both curves are unvalidated scenarios, not fitted\/selected prognosis models.<\/label><br \/>\n      <label class=\"vx-check\" for=\"vx-ev-reference\"><input id=\"vx-ev-reference\" type=\"checkbox\">Each entered reference level is applicable and traceable to a controlled source.<\/label><br \/>\n      <label class=\"vx-check\" for=\"vx-ev-decision\"><input id=\"vx-ev-decision\" type=\"checkbox\">An accountable owner will make any action separately; this worksheet never recommends operation or shutdown.<\/label>\n    <\/div>\n<div class=\"vx-actions\"><button class=\"vx-button\" type=\"submit\">Calculate both scenarios<\/button><button class=\"vx-button vx-secondary\" id=\"vx-clear\" type=\"button\">Clear<\/button><\/div>\n<div id=\"vx-errors\" class=\"vx-errors\" role=\"alert\" aria-live=\"assertive\">\n<p>Cannot calculate:<\/p>\n<ul id=\"vx-error-list\"><\/ul>\n<\/div><\/form>\n<section class=\"vx-card\" aria-labelledby=\"vx-result-title\">\n<div class=\"vx-result-head\">\n<div id=\"vx-result-title\" class=\"vx-result-title\">No result<\/div>\n<div id=\"vx-out-evidence\" class=\"vx-evidence\">0 of 8<\/div>\n<\/div>\n<p id=\"vx-result-summary\" class=\"vx-summary\">Enter a traceable record and submit explicitly.<\/p>\n<div class=\"vx-result-grid\">\n<div class=\"vx-result\"><strong>Relative change from V0 to V1<\/strong><span id=\"vx-out-change\">\u2014<\/span><\/div>\n<div class=\"vx-result\"><strong>Current state versus reference A<\/strong><span id=\"vx-out-state-a\">\u2014<\/span><\/div>\n<div class=\"vx-result\"><strong>Linear rate m<\/strong><span id=\"vx-out-m\">\u2014<\/span><\/div>\n<div class=\"vx-result\"><strong>Log-linear rate k<\/strong><span id=\"vx-out-k\">\u2014<\/span><\/div>\n<div class=\"vx-result\"><strong>Linear remaining time to A<\/strong><span id=\"vx-out-la\">\u2014<\/span><\/div>\n<div class=\"vx-result\"><strong>Log-linear remaining time to A<\/strong><span id=\"vx-out-ea\">\u2014<\/span><\/div>\n<div class=\"vx-result\"><strong>Linear remaining time to B<\/strong><span id=\"vx-out-lb\">\u2014<\/span><\/div>\n<div class=\"vx-result\"><strong>Log-linear remaining time to B<\/strong><span id=\"vx-out-eb\">\u2014<\/span><\/div>\n<div class=\"vx-result\"><strong>Linear value after horizon h<\/strong><span id=\"vx-out-lh\">\u2014<\/span><\/div>\n<div class=\"vx-result\"><strong>Log-linear value after horizon h<\/strong><span id=\"vx-out-eh\">\u2014<\/span><\/div>\n<div class=\"vx-result vx-wide\"><strong>Scenario difference at horizon |VE \u2212 VL|<\/strong><span id=\"vx-out-spread\">\u2014<\/span><\/div>\n<\/p><\/div>\n<div id=\"vx-model-note\" class=\"vx-model-note\">No preferred model is selected. The difference between scenarios is not a confidence interval and does not cover measurement or model uncertainty.<\/div>\n<\/section>\n<section class=\"vx-card\">\n<h2>Equations, dimensions and decision boundary<\/h2>\n<p>Place the baseline at t=0 and the current observation at t=\u0394t. Both scenarios pass exactly through the same two points, so neither has a residual-based goodness-of-fit advantage.<\/p>\n<div class=\"vx-formula\">Linear: m = (V1 \u2212 V0) \/ \u0394t; VL(t) = V0 + m t<\/div>\n<div class=\"vx-formula\">Log-linear: k = ln(V1 \/ V0) \/ \u0394t; VE(t) = V0 exp(k t)<\/div>\n<div class=\"vx-formula\">Future horizon: VL(\u0394t+h) = V1 + m h; VE(\u0394t+h) = V1 exp(k h)<\/div>\n<div class=\"vx-formula\">If R &gt; V1 and the rate is positive: \u03c4L = (R \u2212 V1)\/m; \u03c4E = ln(R\/V1)\/k<\/div>\n<p>V0, V1 and each reference R must have the same declared vibration dimension and amplitude convention. m has vibration-unit\/time and k has 1\/time. Crossing time has the selected time unit. If the current value is at or above a reference, the worksheet reports that state instead of a fictitious positive remaining time. A non-increasing scenario has no future upward crossing.<\/p>\n<div class=\"vx-source-boundary\"><strong>Normative boundary:<\/strong> these equations are elementary scenario arithmetic, not formulas issued by ISO 13381, ISO 17359 or ISO 20816. No ISO numerical boundary is embedded. Exact prognosis-process, condition-monitoring and machine-vibration requirements require the applicable licensed controlled documents.<\/div>\n<\/section>\n<section class=\"vx-card\">\n<h2>Source register and use boundary<\/h2>\n<div class=\"vx-table-wrap\">\n<table class=\"vx-table\">\n<thead>\n<tr>\n<th>ID<\/th>\n<th>Source and lifecycle<\/th>\n<th>Used for<\/th>\n<th>Not used for<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr id=\"source-S1\">\n<td>S1<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/88029.html\" target=\"_blank\" rel=\"noopener\">ISO 13381-1:2025, Edition 3<\/a> \u2014 Published<\/td>\n<td>Current prognosis-process public scope and lifecycle.<\/td>\n<td>No two-point RUL formula, limit, confidence or action inferred. Protected requirements: NEEDS_LICENSED_SOURCE.<\/td>\n<\/tr>\n<tr id=\"source-S2\">\n<td>S2<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/51436.html\" target=\"_blank\" rel=\"noopener\">ISO 13381-1:2015, Edition 2<\/a> \u2014 Withdrawn; replaced by 2025 edition<\/td>\n<td>Historical lifecycle only.<\/td>\n<td>Not current authority.<\/td>\n<\/tr>\n<tr id=\"source-S3\">\n<td>S3<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/71194.html\" target=\"_blank\" rel=\"noopener\">ISO 17359:2018, Edition 3<\/a> \u2014 Published; confirmed 2023<\/td>\n<td>Public scope for a controlled condition-monitoring programme.<\/td>\n<td>No universal threshold, interval or action inferred. Protected procedures: NEEDS_LICENSED_SOURCE.<\/td>\n<\/tr>\n<tr id=\"source-S4\">\n<td>S4<\/td>\n<td><a href=\"https:\/\/www.itl.nist.gov\/div898\/handbook\/pmd\/section1\/pmd141.htm\" target=\"_blank\" rel=\"noopener\">NIST\/SEMATECH 4.1.4.1<\/a> \u2014 Linear least squares<\/td>\n<td>Model fitting, residual concept and warnings about extrapolation\/outliers.<\/td>\n<td>Does not validate two-point RUL or vibration limits.<\/td>\n<\/tr>\n<tr id=\"source-S5\">\n<td>S5<\/td>\n<td><a href=\"https:\/\/www.itl.nist.gov\/div898\/handbook\/pmd\/section1\/pmd142.htm\" target=\"_blank\" rel=\"noopener\">NIST\/SEMATECH 4.1.4.2<\/a> \u2014 Nonlinear least squares<\/td>\n<td>Parameter-estimation and model-validation context.<\/td>\n<td>Does not support a hidden fixed p=2 power model.<\/td>\n<\/tr>\n<tr id=\"source-S6\">\n<td>S6<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/63180.html\" target=\"_blank\" rel=\"noopener\">ISO 20816-1:2016, Edition 1<\/a> \u2014 Published; to be revised<\/td>\n<td>Public measurement\/evaluation and operational-limit scope.<\/td>\n<td>No RUL equation or generic 4.5\/7.1\/8.5\/11.2 values inferred. NEEDS_LICENSED_SOURCE.<\/td>\n<\/tr>\n<tr id=\"source-S7\">\n<td>S7<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/89921.html\" target=\"_blank\" rel=\"noopener\">ISO\/FDIS 20816-1, Edition 2<\/a> \u2014 Under development, stage 50.00<\/td>\n<td>Pending lifecycle only.<\/td>\n<td>Not a published replacement.<\/td>\n<\/tr>\n<tr id=\"source-S8\">\n<td>S8<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/78311.html\" target=\"_blank\" rel=\"noopener\">ISO 20816-3:2022, Edition 1<\/a> \u2014 Published; to be revised<\/td>\n<td>Public industrial-machine scope and machine-specific caution.<\/td>\n<td>No preset or automatic action inferred. NEEDS_LICENSED_SOURCE.<\/td>\n<\/tr>\n<tr id=\"source-S9\">\n<td>S9<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/18866.html\" target=\"_blank\" rel=\"noopener\">ISO 10816-1:1995 + Amd 1:2009<\/a> \u2014 Withdrawn<\/td>\n<td>Obsolete lifecycle.<\/td>\n<td>Not used for current limits or actions.<\/td>\n<\/tr>\n<tr id=\"source-S10\">\n<td>S10<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/14883.html\" target=\"_blank\" rel=\"noopener\">ISO 7919-1:1996, Edition 2<\/a> \u2014 Withdrawn<\/td>\n<td>Obsolete shaft-vibration lifecycle.<\/td>\n<td>Not mixed with casing-velocity reference levels or RUL.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><small>Source access and technical review: 17 July 2026. Recheck lifecycle before later normative use.<\/small><\/p>\n<\/section>\n<section class=\"vx-card\">\n<h2>Corrections made to the former page<\/h2>\n<details class=\"vx-note\">\n<summary>\u201cRemaining useful life\u201d was removed<\/summary>\n<p>A crossing of a user-entered reference under an assumed curve is not component life, failure time or RUL. The replacement reports threshold-extrapolation arithmetic only.<\/p>\n<\/details>\n<details class=\"vx-note\">\n<summary>The hidden p=2 power law was removed<\/summary>\n<p>Two observations cannot estimate both a free power exponent and scale while also validate the model. The old code fixed p=2 while claiming adaptation.<\/p>\n<\/details>\n<details class=\"vx-note\">\n<summary>Universal presets and ISO values were removed<\/summary>\n<p>No pump, motor or turbine level is assumed. Every reference must have an exact controlled source and applicability record.<\/p>\n<\/details>\n<details class=\"vx-note\">\n<summary>Alarm, danger and shutdown outputs were removed<\/summary>\n<p>The worksheet compares numbers but never names a condition zone or recommends continued operation, maintenance or shutdown.<\/p>\n<\/details>\n<details class=\"vx-note\">\n<summary>Both assumptions are shown together<\/summary>\n<p>The page no longer lets a selector hide model-form uncertainty. Linear and log-linear results are displayed side by side.<\/p>\n<\/details>\n<details class=\"vx-note\">\n<summary>Two-point limitations are explicit<\/summary>\n<p>There is no residual scatter, fit statistic, outlier assessment or confidence\/prediction interval from two exact points.<\/p>\n<\/details>\n<details class=\"vx-note\">\n<summary>Unsafe parsing and persistence were removed<\/summary>\n<p>No parseFloat, preset, auto-calculate, URL state, browser storage, clipboard or dynamic result HTML remains.<\/p>\n<\/details>\n<details class=\"vx-note\">\n<summary>Current standard lifecycle was added<\/summary>\n<p>ISO 13381-1:2025 is current. ISO 10816-1 and ISO 7919-1 are withdrawn; ISO 20816 limits remain machine- and measurement-specific licensed-source topics.<\/p>\n<\/details>\n<\/section>\n<p><\/main><br \/>\n<script>\n(function(){\n  'use strict';\n  var form=document.getElementById('vx-form'),clearButton=document.getElementById('vx-clear');\n  var required=['vx-case','vx-asset','vx-point','vx-quantity','vx-baseline-id','vx-current-id','vx-condition0','vx-condition1','vx-v0','vx-v1','vx-elapsed','vx-time-unit','vx-ref-a','vx-ref-a-basis','vx-horizon','vx-reviewer'];\n  var requiredNames={'vx-case':'Case \/ calculation ID','vx-asset':'Asset \/ machine set','vx-point':'Measurement point, axis and sensor chain','vx-quantity':'Quantity, unit, band and amplitude convention','vx-baseline-id':'Baseline observation ID \/ timestamp','vx-current-id':'Current observation ID \/ timestamp','vx-condition0':'Baseline operating and measurement condition','vx-condition1':'Current operating and measurement condition','vx-v0':'Baseline value V0','vx-v1':'Current value V1','vx-elapsed':'Elapsed time \u0394t','vx-time-unit':'Time unit','vx-ref-a':'Reference level A','vx-ref-a-basis':'Reference A basis','vx-horizon':'Future comparison horizon h','vx-reviewer':'Reviewer and review date'};\n  var gates=['vx-ev-chain','vx-ev-quantity','vx-ev-condition','vx-ev-trace','vx-ev-event','vx-ev-model','vx-ev-reference','vx-ev-decision'];\n  var outputIds=['vx-out-change','vx-out-state-a','vx-out-m','vx-out-k','vx-out-la','vx-out-ea','vx-out-lb','vx-out-eb','vx-out-lh','vx-out-eh','vx-out-spread'];\n  var hasResult=false;\n  function byId(id){return document.getElementById(id)}\n  function parseStrict(value){var s=String(value).trim();if(!\/^[+]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s)||(\/[.]\/.test(s)&&\/,\/.test(s)))return null;var n=Number(s.replace(',','.'));return Number.isFinite(n)?n:null}\n  function fmt(n,d){if(!Number.isFinite(n))return '\u2014';if(n===0)return '0';var s=n.toFixed(d);return s.replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\n  function clearErrors(){var list=byId('vx-error-list');while(list.firstChild)list.removeChild(list.firstChild);byId('vx-errors').classList.remove('vx-show')}\n  function showErrors(errors){clearErrors();var list=byId('vx-error-list');errors.forEach(function(message){var li=document.createElement('li');li.textContent=message;list.appendChild(li)});byId('vx-errors').classList.add('vx-show')}\n  function clearOutputs(){outputIds.forEach(function(id){byId(id).textContent='\u2014'});byId('vx-out-evidence').textContent='0 of 8';byId('vx-model-note').textContent='No preferred model is selected. The difference between scenarios is not a confidence interval and does not cover measurement or model uncertainty.'}\n  function setNoResult(title,summary){clearOutputs();byId('vx-result-title').textContent=title;byId('vx-result-summary').textContent=summary;hasResult=false}\n  function unitLabel(unit){return unit==='hours'?'hours':'days'}\n  function state(value,reference){if(value>reference)return 'above A';if(value===reference)return 'equal to A';return 'below A'}\n  function crossing(reference,current,rate,isLog,unit){if(reference===null)return 'not supplied';if(current>=reference)return 'at\/above at current observation';if(rate<=0)return 'no future upward crossing in scenario';var time=isLog?Math.log(reference\/current)\/rate:(reference-current)\/rate;if(!Number.isFinite(time)||time<0)return 'no finite future crossing';return fmt(time,6)+' '+unit}\n  function evidenceCount(){return gates.reduce(function(sum,id){return sum+(byId(id).checked?1:0)},0)}\n  function markStale(){if(!hasResult)return;byId('vx-result-title').textContent='Result is stale';byId('vx-result-summary').textContent='An observation, condition, reference, evidence gate or review field changed. Submit again before using the arithmetic.'}\n  form.addEventListener('submit',function(event){\n    event.preventDefault();clearErrors();var errors=[];\n    required.forEach(function(id){if(!String(byId(id).value).trim())errors.push(requiredNames[id]+' is required.')});\n    var v0=parseStrict(byId('vx-v0').value),v1=parseStrict(byId('vx-v1').value),elapsed=parseStrict(byId('vx-elapsed').value),refA=parseStrict(byId('vx-ref-a').value),horizon=parseStrict(byId('vx-horizon').value);\n    var refBText=String(byId('vx-ref-b').value).trim(),refBBasis=String(byId('vx-ref-b-basis').value).trim(),refB=refBText?parseStrict(refBText):null;\n    [['Baseline value V0','vx-v0',v0],['Current value V1','vx-v1',v1],['Elapsed time \u0394t','vx-elapsed',elapsed],['Reference level A','vx-ref-a',refA],['Future horizon h','vx-horizon',horizon]].forEach(function(pair){if(String(byId(pair[1]).value).trim()&&(pair[2]===null||pair[2]<=0||pair[2]>1e12))errors.push(pair[0]+' must be finite, greater than 0 and no greater than 1e12.')});\n    if(refBText&&(refB===null||refB<=0||refB>1e12))errors.push('Reference level B must be finite, greater than 0 and no greater than 1e12.');\n    if(refBText&&!refBBasis)errors.push('Reference B basis is required when reference B is supplied.');\n    if(!refBText&&refBBasis)errors.push('Reference level B is required when a reference B basis is supplied.');\n    var unit=byId('vx-time-unit').value;if(unit&&unit!=='hours'&&unit!=='days')errors.push('Time unit must be Hours or Days.');\n    if(errors.length){showErrors(errors);setNoResult('Cannot calculate','Correct the listed fields. All previous numerical outputs were cleared.');return}\n    var m=(v1-v0)\/elapsed,k=Math.log(v1\/v0)\/elapsed,linearH=v1+m*horizon,expH=v1*Math.exp(k*horizon),change=(v1\/v0-1)*100,spread=Math.abs(expH-linearH);\n    if(![m,k,linearH,expH,change,spread].every(Number.isFinite)){showErrors(['The scenario calculation did not remain finite for the entered values.']);setNoResult('Cannot calculate','All previous numerical outputs were cleared.');return}\n    var u=unitLabel(unit),count=evidenceCount();\n    byId('vx-out-change').textContent=(change>0?'+':'')+fmt(change,6)+'%';\n    byId('vx-out-state-a').textContent=state(v1,refA);\n    byId('vx-out-m').textContent=(m>0?'+':'')+fmt(m,10)+' value\/'+u.slice(0,-1);\n    byId('vx-out-k').textContent=(k>0?'+':'')+fmt(k,10)+' \/'+u.slice(0,-1);\n    byId('vx-out-la').textContent=crossing(refA,v1,m,false,u);\n    byId('vx-out-ea').textContent=crossing(refA,v1,k,true,u);\n    byId('vx-out-lb').textContent=crossing(refB,v1,m,false,u);\n    byId('vx-out-eb').textContent=crossing(refB,v1,k,true,u);\n    byId('vx-out-lh').textContent=fmt(linearH,10)+' declared value unit';\n    byId('vx-out-eh').textContent=fmt(expH,10)+' declared value unit';\n    byId('vx-out-spread').textContent=fmt(spread,10)+' declared value unit';\n    byId('vx-out-evidence').textContent=count+' of 8';\n    byId('vx-model-note').textContent='Both scenarios pass through the same two observations. Neither is selected or validated; the displayed spread is only their arithmetic difference at h.';\n    if(count===8){byId('vx-result-title').textContent='Scenario arithmetic \u2014 evidence record complete';byId('vx-result-summary').textContent='All eight gates are recorded. The numbers remain conditional threshold-extrapolation scenarios, not RUL, failure prediction, ISO compliance or an operating decision.'}\n    else{byId('vx-result-title').textContent='Scenario arithmetic \u2014 evidence incomplete';byId('vx-result-summary').textContent='The arithmetic is shown, but only '+count+' of 8 applicability\/decision gates are recorded. Do not use it as a prognosis or action.'}\n    hasResult=true\n  });\n  form.addEventListener('input',markStale);form.addEventListener('change',markStale);\n  clearButton.addEventListener('click',function(){form.reset();clearErrors();setNoResult('No result','Enter a traceable record and submit explicitly.');byId('vx-case').focus()});\n})();\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Compare linear and log-linear two-point vibration scenarios against source-controlled reference levels. Not RUL, failure prediction, ISO compliance or an operating decision.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100299","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/calculator\/100299","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/calculator\/100299\/revisions"}],"predecessor-version":[{"id":102648,"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/calculator\/100299\/revisions\/102648"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/media?parent=100299"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/categories?post=100299"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/tags?post=100299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}