{"id":1127,"date":"2011-04-21T17:17:00","date_gmt":"2011-04-21T22:17:00","guid":{"rendered":"http:\/\/www.livingreliability.com\/en\/?p=1127"},"modified":"2025-11-06T05:58:19","modified_gmt":"2025-11-06T10:58:19","slug":"cbm-optimization","status":"publish","type":"post","link":"https:\/\/www.livingreliability.com\/en\/posts\/cbm-optimization\/","title":{"rendered":"CBM Optimization"},"content":{"rendered":"<p><em>Nature, and therefore humankind, must optimize to survive and prosper. Each species in the animal kingdom strives for the best long term results of its actions. Whether divinely designed or as a result of natural selection, activity is calculated (optimized) to balance low energy expenditure with maximum caloric intake. No less true is a business&#8217;s need to optimize, if it is to compete in the global jungle for its very survival. Companies that offer better goods and services at lower cost survive better in the marketplace and tend to accumulate an ever-growing market share. Poorly-adapting companies will be forced out by better-adapting ones: &#8220;killed&#8221; by the competition.<\/em><\/p>\n<p>We gather information in maintenance as a precursor to decision making and action. A policy or &#8220;model&#8221; is a procedure\u00a0 for making decisions in the face of facts. Achieving value from a decision policy depends on:<\/p>\n<ol>\n<li>Having the right data, and<\/li>\n<li>Transforming that data into the correct (best) action.<\/li>\n<\/ol>\n<h2>1. The right data<\/h2>\n<p>This slide presentation divides data into two major categories, and a number of sub-categories. By understanding the nature of maintenance related data, Reliability Engineers will collect and analyze the &#8220;right&#8221; data.<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/docs.google.com\/presentation\/d\/1C-BGFdqcs4HNw6Bm76fALwvtKrpO-kTwVidkMQivmUM\/embed?start=false&amp;loop=false&amp;delayms=5000\" width=\"640\" height=\"500\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>LRCM is a process that ensures the right data is used for designing maintenance decision policies. Those policies will be applied day-to-day to make the <em>optimal <\/em>decisions that will achieve the enterprise&#8217;s long run objectives.<\/p>\n<h2>2. Optimal CBM Decisions<\/h2>\n<h3>The principle of EXAKT<\/h3>\n<figure id=\"attachment_1161\" aria-describedby=\"caption-attachment-1161\" style=\"width: 293px\" class=\"wp-caption alignright\"><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/twoDecisionPaths.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1161\" title=\"twoDecisionPaths\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/twoDecisionPaths.jpg\" alt=\"\" width=\"293\" height=\"228\" \/><\/a><figcaption id=\"caption-attachment-1161\" class=\"wp-caption-text\">Figure 1 Two decision paths in EXAKT<\/figcaption><\/figure>\n<p>The flow diagram of Figure 1 illustrates two ways of deciding whether an item, component, or failure mode is in a Potential Failure (P) state.\u00a0 The two decision processes can be categorized as:<\/p>\n<ol>\n<li>An optimal decision based on the combination of failure probability <em>and<\/em> the quantifiable consequences of the failure (Path 1), and<\/li>\n<li>A decision based solely on failure probability (Path 2).<\/li>\n<\/ol>\n<p>The first CBM decision making strategy will support decisions related to operational and non-operational consequences of failure whose economic impact can be quantified, for example, the failure of a component in a production line. The second method will apply to decisions that must be based strictly on probability. These include situations beyond the expected, whose failure costs are unknown or incalculable, such as where catastrophic environmental, health, and safety consequences are concerned. Managers use both types of decision methods regularly within the compass of their responsibilities. This article will describe the optimal decision process based on business factors combined with failure probability.<\/p>\n<h2>Cost minimization review<\/h2>\n<p>The top graph of Figure 2 plots the hazard rate (also called failure rate). It is the probability of an item failing at any \u00a0instant given that it has survived to that point in time.<\/p>\n<figure id=\"attachment_3364\" aria-describedby=\"caption-attachment-3364\" style=\"width: 355px\" class=\"wp-caption alignright\"><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/hazardAndCostPlots1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3364\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/hazardAndCostPlots1.jpg\" alt=\"Figure 2 Hazard and Cost Plots\" width=\"355\" height=\"246\" srcset=\"https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/hazardAndCostPlots1.jpg 355w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/hazardAndCostPlots1-300x207.jpg 300w\" sizes=\"auto, (max-width: 355px) 100vw, 355px\" \/><\/a><figcaption id=\"caption-attachment-3364\" class=\"wp-caption-text\">Figure 2 Hazard and Cost Graphs<\/figcaption><\/figure>\n<p>Hazard may change in time as a result of many factors. We ask these questions, in forming our decision policy, &#8220;At what hazard level should we intervene?&#8221; &#8220;Should we ignore hazard altogether, or should we act when the hazard reaches\u00a0 some specific value?&#8221;<\/p>\n<p>The bottom graph of Figure 2 recognizes that an enterprise&#8217;s profit and loss statement considers good performance as being low cost per unit of production (working age). Therefore, we would wish to choose a hazard level intervention point that results in lowest cost. Intuitively, we surmise that a policy of operating at very low hazard will be expensive (as illustrated on the left extremity of the cost plot). On the other hand, choosing to operate at a very high hazard rate will ignore hazard and incur the costs of running to failure. We conclude that there will be a <em>best<\/em> policy somewhere between the two extremes. Hence the cost curve will be trough-shaped (as illustrated) when plotted against the operating hazard rate. Our objective is to find the <em>optimal<\/em> hazard level that corresponds to the low point on the curve, resulting in minimal overall cost.<\/p>\n<p>To apply the optimal CBM decision modeling procedure the Reliability Engineer (RE) will need to discover how hazard varies with observed operational and condition monitoring data. He finds such a relationship by estimating the parameters of the Proportional Hazard Model (PHM).<sup>[<a href=\"#cbm-optimization-n-1\" class=\"footnoted\" id=\"to-cbm-optimization-n-1\">1<\/a>]<\/sup><\/p>\n<h2>EXAKT&#8217;s basic cost model<\/h2>\n<p>The Reliability Engineer, upon establishing the relationship among hazard rate, age and relevant condition indicators, enters the required business information into the form shown in Figure 3.<\/p>\n<figure id=\"attachment_1143\" aria-describedby=\"caption-attachment-1143\" style=\"width: 323px\" class=\"wp-caption alignright\"><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/decisionModelParametersCost.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1143\" title=\"decisionModelParametersCost\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/decisionModelParametersCost.jpg\" alt=\"Figure 3 Decision model parameters for cost minimization\" width=\"323\" height=\"375\" srcset=\"https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/decisionModelParametersCost.jpg 323w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/decisionModelParametersCost-258x300.jpg 258w\" sizes=\"auto, (max-width: 323px) 100vw, 323px\" \/><\/a><figcaption id=\"caption-attachment-1143\" class=\"wp-caption-text\">Figure 3 Decision model parameters for cost minimization<\/figcaption><\/figure>\n<p>The software finds the CBM and age control limits that, if acted upon consistently by the maintenance department, will result in lowest overall maintenance costs. The optimal decision model is found by minimizing the cost function:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.livingreliability.com\/en\/wp-content\/ql-cache\/quicklatex.com-dd79f5823a3e71132e81cd6ce745ef51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#95;&#123;&#69;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#67;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#45;&#81;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#67;&#43;&#75;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#81;&#125;&#123;&#87;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"167\" style=\"vertical-align: -6px;\"\/><\/p>\n<p>Where:<br \/>\nC<sub>E<\/sub> is the total expected cost per unit of working age of maintaining the asset (Item, Failure Mode)<br \/>\nQ is the failure probability<br \/>\nW is the working age at renewal<br \/>\nC is the cost of the preventive maintenance action.<br \/>\nK is the penalty cost of failure.<\/p>\n<p>EXAKT bases its cost model on the user supplied average cost of a functional failure and the average cost of a preventive action.<sup>[<a href=\"#cbm-optimization-n-2\" class=\"footnoted\" id=\"to-cbm-optimization-n-2\">2<\/a>]<\/sup> In this simplest of the EXAKT optimization procedures, the analyst provides the costs (e.g. materials, labor, lost production), <strong>&#8220;C&#8221;<\/strong>, of <em>planned<\/em> maintenance and the <em>added<\/em> economic impact (e.g. materials, labor, lost production, secondary damage to equipment or the environment), <strong>K<\/strong>, as a result of the <em>unplanned<\/em> nature of the functional interruption.<\/p>\n<figure id=\"attachment_1149\" aria-describedby=\"caption-attachment-1149\" style=\"width: 291px\" class=\"wp-caption alignright\"><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/costFunctionGraph.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1149\" title=\"costFunctionGraph\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/costFunctionGraph.jpg\" alt=\"\" width=\"291\" height=\"238\" \/><\/a><figcaption id=\"caption-attachment-1149\" class=\"wp-caption-text\">Figure 4 Cost Function Graph<\/figcaption><\/figure>\n<p>The results of the optimization are shown, as an example, in the graph<sup>[<a href=\"#cbm-optimization-n-3\" class=\"footnoted\" id=\"to-cbm-optimization-n-3\">3<\/a>]<\/sup> of Figure 4 and in Table 1.<\/p>\n<p>Any cost value on the curve consists of a red portion, attributable to unplanned failures, and a green portion, representing the average costs associated with preventive maintenance.<br \/>\nTable 1 summarizes the information in the graph. It compares the optimal cost ($94) and optimal mean time between asset renewals (863 d)) of the optimal policy with those ($168 and 1138 d) of the &#8220;run-to-failure&#8221; policy. It quantifies the expected preventive and failure costs ($57 and $37 respectively) and the percentage of incidences (83.5% will be preventive actions and 16.5% will be instigated by a failure) achieved when adhering to the optimal policy.<\/p>\n<table>\n<tbody>\n<tr>\n<th>Table 1<\/th>\n<\/tr>\n<tr>\n<td><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfCostAnalysis.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1153\" title=\"summaryOfCostAnalysis\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfCostAnalysis.jpg\" alt=\"\" width=\"595\" height=\"150\" srcset=\"https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfCostAnalysis.jpg 525w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfCostAnalysis-300x75.jpg 300w\" sizes=\"auto, (max-width: 595px) 100vw, 595px\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The table&#8217;s content illustrates that the optimal policy will cause us to intervene more often on the average (863 versus 1138 days), in order to achieve a net per unit saving ( of $74 or 44%).<\/p>\n<p>The foregoing described CBM optimization for the objective cost minimization. <a title=\"CBM Optimization page 2\" href=\"http:\/\/www.livingreliability.com\/en\/posts\/cbm-optimization\/2\/\" target=\"_blank\">Subsequent pages<\/a> and sections discuss the theory and procedures for the optimization of CBM programs with the objectives of achieving maximum availability or maximum profitability (accounting for both cost and downtime).<br \/>\n<!--nextpage--><\/p>\n<h2>Availability as the optimization criterion<\/h2>\n<p>The Reliability Engineer can use EXAKT to develop a maximum availability model. In order to do so, the analyst must supply the parameters for this strategy. These are fixed values for the downtimes incurred by:<\/p>\n<ol>\n<li>Preventive renewal (maintenance), and<\/li>\n<li>Renewal as a result of failure.<\/li>\n<\/ol>\n<p>The costs of materials and labor are not considered significant in this option, or they are believed to be proportional to downtimes and, thus, can be ignored. The optimal strategy maximizes expected availability per unit time. Availablity is defined as<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.livingreliability.com\/en\/wp-content\/ql-cache\/quicklatex.com-0ac34538cfcccd74123d4b36600645ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#49;&#48;&#48;&#32;&#92;&#37;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#85;&#112;&#116;&#105;&#109;&#101;&#125;&#123;&#85;&#112;&#116;&#105;&#109;&#101;&#43;&#68;&#111;&#119;&#110;&#116;&#105;&#109;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"224\" style=\"vertical-align: -9px;\"\/><\/p>\n<p>The software finds the CBM and age control limits that, if acted upon consistently by the maintenance department, will result in highest availaiblity. The optimal decision model is found by maximizing the availability function:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.livingreliability.com\/en\/wp-content\/ql-cache\/quicklatex.com-5b320dd36e8f6470b22ef373d4a28a09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#95;&#123;&#69;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#87;&#125;&#123;&#87;&#43;&#84;&#95;&#123;&#112;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#45;&#81;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#84;&#95;&#123;&#102;&#125;&#81;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"168\" style=\"vertical-align: -11px;\"\/><\/p>\n<figure id=\"attachment_1179\" aria-describedby=\"caption-attachment-1179\" style=\"width: 307px\" class=\"wp-caption alignright\"><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/availabilityOptimizationInput.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1179\" title=\"availabilityOptimizationInput\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/availabilityOptimizationInput.jpg\" alt=\"\" width=\"307\" height=\"150\" srcset=\"https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/availabilityOptimizationInput.jpg 307w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/availabilityOptimizationInput-300x146.jpg 300w\" sizes=\"auto, (max-width: 307px) 100vw, 307px\" \/><\/a><figcaption id=\"caption-attachment-1179\" class=\"wp-caption-text\">Figure 5 Availability optimization input form<\/figcaption><\/figure>\n<p>Where:<br \/>\nA<sub>E<\/sub> is the total expected Availaiblity per unit of working age or production of the asset (Item, Failure Mode)<br \/>\nQ is the failure probability<br \/>\nW is the expected working age at failure<br \/>\nT<sub>p<\/sub> is the downtime required by preventive maintenance.<br \/>\nT<sub>f<\/sub> is the downtime resulting from a failure.<\/p>\n<figure id=\"attachment_1181\" aria-describedby=\"caption-attachment-1181\" style=\"width: 322px\" class=\"wp-caption alignright\"><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/availabilityFunctionGraph.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1181\" title=\"availabilityFunctionGraph\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/availabilityFunctionGraph.jpg\" alt=\"\" width=\"322\" height=\"256\" srcset=\"https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/availabilityFunctionGraph.jpg 322w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/availabilityFunctionGraph-300x238.jpg 300w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/a><figcaption id=\"caption-attachment-1181\" class=\"wp-caption-text\">Figure 6 Availability function graph<\/figcaption><\/figure>\n<p>The example illustrates the trade-off made in optimizing for availability. In the preceding cost model we &#8220;bought&#8221; lower overall cost by &#8220;paying&#8221; for it with more frequent intervention.<br \/>\nWe assumed that the time-to-repair was negligeable, or was proportional to the cost, and therefore could be ignored. The difference between failure and preventive repair costs dictated the <em>exact nature<\/em> of the compromise in order that <em>overall<\/em> impact on the per unit production cost be minimum.<\/p>\n<table>\n<tbody>\n<tr>\n<th>Table 2<\/th>\n<\/tr>\n<tr>\n<td><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfAvailabilityAnalysis.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1183\" title=\"summaryOfAvailabilityAnalysis\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfAvailabilityAnalysis.jpg\" alt=\"\" width=\"609\" height=\"153\" srcset=\"https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfAvailabilityAnalysis.jpg 609w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfAvailabilityAnalysis-600x151.jpg 600w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfAvailabilityAnalysis-300x75.jpg 300w\" sizes=\"auto, (max-width: 609px) 100vw, 609px\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In a symmetrical way, the maximium availability model focuses <em>completely<\/em> on downtime. In this example, we have &#8220;bought&#8221; high availability by paying for it with more frequent intervention. We assumed that the cost of repair was negligeable, or was proportional to the repair time and therefore could be ignored. The difference between failure and preventive repair <em>times<\/em> (rather than costs) dictated the exact nature of the compromise to achieve high equipment availability.<br \/>\n<!--nextpage--><\/p>\n<h2>Cost and availability combined<\/h2>\n<p>The parameters of this economic strategy formulation are:<\/p>\n<ol>\n<li>The fixed costs of preventive and failure replacement (maintenance),<\/li>\n<li>The fixed downtimes due to preventive and failure replacements, and<\/li>\n<li>The costs per unit time of downtimes (which may be different for preventive and failure replacements).<\/li>\n<\/ol>\n<p>A reasonable way to formulate the total costs of reactive and preventive maintenance would be:<\/p>\n<p><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/totalCostPreventiveReactive.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1186\" title=\"totalCostPreventiveReactive\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/totalCostPreventiveReactive.jpg\" alt=\"\" width=\"604\" height=\"185\" srcset=\"https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/totalCostPreventiveReactive.jpg 604w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/totalCostPreventiveReactive-600x184.jpg 600w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/totalCostPreventiveReactive-300x91.jpg 300w\" sizes=\"auto, (max-width: 604px) 100vw, 604px\" \/><\/a><\/p>\n<p>The <em>combined cost and availabiltiy<\/em> optimization option is used to minimize expected cost per unit time taking into account costs <em>and<\/em> duration of preventive and failure downtimes, <em>and<\/em> cost of downtime.<\/p>\n<p>The software finds the CBM and age control limits that, if acted upon consistently by the maintenance department, will result in highest profitability accounting for the costs of lost production and maintenance cost penalties due failure. The optimal decision model is found by minimizing the combined cost function:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.livingreliability.com\/en\/wp-content\/ql-cache\/quicklatex.com-95b369f60359138ad714e012255d2d20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#95;&#123;&#67;&#69;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#67;&#95;&#123;&#112;&#125;&#43;&#97;&#95;&#123;&#112;&#125;&#116;&#95;&#123;&#112;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#67;&#95;&#123;&#102;&#125;&#43;&#97;&#95;&#123;&#102;&#125;&#116;&#95;&#123;&#102;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#81;&#125;&#123;&#87;&#43;&#116;&#95;&#123;&#112;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#45;&#81;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#116;&#95;&#123;&#102;&#125;&#81;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"218\" style=\"vertical-align: -11px;\"\/><\/p>\n<figure id=\"attachment_1190\" aria-describedby=\"caption-attachment-1190\" style=\"width: 334px\" class=\"wp-caption alignright\"><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/inputCombinedCostAvailability.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1190\" title=\"inputCombinedCostAvailability\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/inputCombinedCostAvailability.jpg\" alt=\"\" width=\"334\" height=\"295\" srcset=\"https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/inputCombinedCostAvailability.jpg 334w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/inputCombinedCostAvailability-300x264.jpg 300w\" sizes=\"auto, (max-width: 334px) 100vw, 334px\" \/><\/a><figcaption id=\"caption-attachment-1190\" class=\"wp-caption-text\">Figure 7 Input form for combined cost and availability model<\/figcaption><\/figure>\n<p>Where:<br \/>\nC<sub>p<\/sub>, C<sub>f<\/sub> are the fixed costs of failure and preventive actions,<br \/>\nt<sub>p<\/sub>, t<sub>f<\/sub> are the down times of failure and preventive actions,<br \/>\na<sub>p<\/sub>, a<sub>f<\/sub> are the hourly maintenance and lost production costs associated with failure and prevention.<\/p>\n<p>This cost model allows for flexibility in setting up realistic parameters upon which to build the optimal decision model. For example,<\/p>\n<ol>\n<li>the fixed cost of failure replacement may be high (say due to the cost of a new part), but<\/li>\n<li>the downtime required may be short (just to replace the part)<\/li>\n<\/ol>\n<p>Or, by comparison, the situation may be that:<\/p>\n<ol>\n<li>the cost of preventive work can be small, but<\/li>\n<li>the time to complete the work (downtime) can be long.<\/li>\n<\/ol>\n<figure id=\"attachment_1192\" aria-describedby=\"caption-attachment-1192\" style=\"width: 378px\" class=\"wp-caption alignright\"><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/costAvailabilityFunctionGraph.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1192\" title=\"costAvailabilityFunctionGraph\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/costAvailabilityFunctionGraph.jpg\" alt=\"\" width=\"378\" height=\"300\" srcset=\"https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/costAvailabilityFunctionGraph.jpg 378w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/costAvailabilityFunctionGraph-300x238.jpg 300w\" sizes=\"auto, (max-width: 378px) 100vw, 378px\" \/><\/a><figcaption id=\"caption-attachment-1192\" class=\"wp-caption-text\">Figure 8 Combined cost and availability function graph<\/figcaption><\/figure>\n<p>This option resolves the difficult problem of deciding upon maintenance policies in the light of actual maintenance costs.<\/p>\n<p>The generalized cost and availability optimization model is described by a slightly more complex graph and table shown in the slide.<\/p>\n<table>\n<tbody>\n<tr>\n<th>Table 3<\/th>\n<\/tr>\n<tr>\n<td><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfProfitabibilityAnalysis.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1194\" title=\"summaryOfProfitabibilityAnalysis\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfProfitabibilityAnalysis.jpg\" alt=\"\" width=\"648\" height=\"164\" srcset=\"https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfProfitabibilityAnalysis.jpg 648w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfProfitabibilityAnalysis-600x152.jpg 600w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/summaryOfProfitabibilityAnalysis-300x75.jpg 300w\" sizes=\"auto, (max-width: 648px) 100vw, 648px\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Some of the column headings now refer to both cost and availability, so that we can see, precisely, the results of applying the optimal CBM policy. In this example, the optimal expected results are:<\/p>\n<ol>\n<li>Cost: 93 $\/d (73% better than running to failure)<\/li>\n<li>Availabilty 99% (35% better than running to failure)<\/li>\n<li>Average running time between interventions: 866 days (280 days <em>worse<\/em> than the RTF policy)<\/li>\n<\/ol>\n<p>In the final analysis optimization addresses cost. The cost and availability model, permit us to consider the factors affecting cost and availability, separately. The optimization normalizes both sets of factors to ultimate cost. The <em>best<\/em> (lowest ultimate bottom line cost) is attained by the decision modeling and deployment process. The feature encourages maintenance engineers and managers to elicit and consider cost information about failure and normal operational costs because they can now use it effectively in their decision process.<\/p>\n\n<ol class=\"footnotes\">\n\t<li class=\"footnote\" id=\"cbm-optimization-n-1\"><strong><sup>[1]<\/sup><\/strong>The\u00a0 step-by-step PHM procedure can be found from the Sidebar under Categories | CBM | Exercises | Exercise 1. The PHM description can be found under Categories | CBM | PF Interval | The Elusive PF Interval<a class=\"note-return\" href=\"#to-cbm-optimization-n-1\">&#x21A9;<\/a><\/li>\n\t<li class=\"footnote\" id=\"cbm-optimization-n-2\"><strong><sup>[2]<\/sup><\/strong>Often managers or engineers do not know in precise terms what the average penalty losses due to failure are. But they usually have a good idea. Fortunately in most cases highly precise differential cost data is unnecessary. Usually ballpark informed estimates will do. In those cases where the estimate error\u00a0will affect the optimal CBM decision solution the software provides a &#8220;sensitivity&#8221; analysis to alert the user to the need to acquire a more accurate penalty to cost ratio. <a class=\"note-return\" href=\"#to-cbm-optimization-n-2\">&#x21A9;<\/a><\/li>\n\t<li class=\"footnote\" id=\"cbm-optimization-n-3\"><strong><sup>[3]<\/sup><\/strong>The vertical axis is the cost of preventive plus reactive maintenance per unit of operation, for example tons of ore hauled. The horizontal axis is the risk defined as the hazard rate (aka failure rate) \u00d7 the penalty K for failure.<a class=\"note-return\" href=\"#to-cbm-optimization-n-3\">&#x21A9;<\/a><\/li><\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Nature, and therefore humankind, must optimize to survive and prosper. Each species in the animal kingdom strives for the best long term results of its actions. Whether divinely designed or as a result of natural selection, activity is calculated (optimized) to balance low energy expenditure with maximum caloric intake. No less true is a business&#8217;s [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[115],"tags":[113,36,92],"class_list":["post-1127","post","type-post","status-publish","format-standard","hentry","category-exercises","tag-cbm","tag-exakt","tag-optimization"],"_links":{"self":[{"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/posts\/1127","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/comments?post=1127"}],"version-history":[{"count":6,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/posts\/1127\/revisions"}],"predecessor-version":[{"id":5801,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/posts\/1127\/revisions\/5801"}],"wp:attachment":[{"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/media?parent=1127"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/categories?post=1127"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/tags?post=1127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}