: The EXAKT Cost Model

Transcription

1 1 of 13 11/03/ :48 PM The EXAKT Cost Model By:Murray Wiseman on:sun 21 of Jan., :24 MST (346 Reads) The EXAKT Cost Model Return to WikiHome Slide 1 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 devinely 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'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: "killed" by the competition. We gather information for optimized decision making, as a precursor to action. A policy is a procedure (model) for making decisions in the face of facts. Achieving value from our decision policy depends on: 1. having the right data, and 2. transforming that data into the correct (best) action Slide 2

2 2 of 13 11/03/ :48 PM In the management of a physical asset, we acquire and analyze two main types of data: age or "event" data, namely: 1. the beginning a life-cycle 2. the ending of a life-cycle 1. by failure, either 1. potential 2. functional, or 2. by suspension 3. the partial rejuvination of a life-cycle, and 4. events that influence condition monitoring data, and condition monitoring data 1. measurements and inspection observations, and/or 2. process data 1. external variables 2. internal variables From this data we build our optimal decision models. We invoke one or more models each time we make a maintenance decision. EXAKT decision models comprise: A cost and availability model, derived from 1. a hazard model 2. a transition probability model, and 3. cost and downtime for failure and preventive repair in the current operating context a remaining useful life model EXAKT models provide decision support. They improve continuously with the benefit of engineering judgement. Slide 3

3 3 of 13 11/03/ :48 PM Top graph Hazard (also called hazard rate or failure rate) is the probability of an item failing at any given instance. Hazard may change in time as result of many factors. We ask the questions, in forming our decision policy, "At what hazard level should we intervene? Should we ignore hazard altogether, or should we act at some specific value of the hazard rate?". Bottom graph The profit and loss statement of a company recognizes good performance as low, per unit, production cost. Therefore, we would wish to choose a hazard level intervention point that results in low cost. Intuitively, we surmise that a policy resulting in very low hazard will be expensive (as illustrated on the left extremity of the cost plot). On the other hand, chosing to operate at a very high hazard rate will approach the cost of ignoring hazard and running to failure. We conclude that there must be a best policy somewhere between the two extremes. Hence the optimal cost curve will likely be troughshaped (as illustrated) when plotted against increasing hazard. Our challenge is to find that optimal hazard level, corresponding to minimal cost. In practice, to complete the CBM decision process, we will need to find an additional relationship. We will need to establish the relationship between hazard and significant operational (age and condition monitoring) data. The EXAKT decision model, therefore, includes the hazard relationship (with working age and significant condition monitoring variables). Slide 4

4 4 of 13 11/03/ :48 PM Up to version 4.1, EXAKT based its cost model on the user supplied average cost of a functional failure and the average cost of a preventive action. The analyst was required to weigh in the composite costs (e.g. materials, labor, lost production), "C", of planned maintenance and the added economic impact (e.g. materials, labor, lost production, secondary damage to equipment or the environment), K, as a result of the unplanned nature of the functional interruption. EXAKT, issued its optimal recommendation by minimizing the expression shown here. Slide 5 Any cost value on the curve consists of a red portion, attrubutable to unplanned failures, and a green portion, representing the average costs associated with preventive maintenance. The table 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 "run-to-failure" 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. The table'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%). Slide 6

5 5 of 13 11/03/ :48 PM EXAKT delivers a maximum availability model as one of three options for the selection of an optimal predictive maintenance strategy. The analyst must supply the parameters of this strategy. They are fixed values for the downtimes incurred by: preventive renewal (maintenance), and renewal as a result of failure. 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 (defined as 100%*uptime/(uptime+downtime)). Slide 7 This example illustrates the trade-off made in optimizing for availability. In the cost model we "bought" lower overall cost by "paying" for it with more frequent intervention. We assumed that the time-torepair was negligeable, or was proportional to the cost, and therefore could be ignored. The difference between failure and preventive repair costs dictated the exact nature of the compromise in order that overall impact on the per unit production cost be minimum. In a symmetrical way, the maximium availability model focuses completely on downtime. In this example, we have "bought" 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 times (rather than costs) dictated the exact nature of the compromise to achieve high equipment availabilty. Slide 8

6 6 of 13 11/03/ :48 PM The parameters of this (complex) economic strategy formulation are: 1. fixed costs of preventive and failure replacement (maintenance), 2. fixed downtimes due to preventive and failure replacements, and 3. costs per unit time of downtimes (which may be different for preventive and failure replacements). Slide 9 The combined cost and availabiltiy optimization option is used to minimize expected cost per unit time taking into account costs and duration of preventive and failure downtimes, and cost of downtime. This cost model allows for flexibility in setting up realistic parameters upon which to build the optimal decision model. For example, the fixed cost of failure replacement may be high (say due to the cost of a new part), but the downtime required may be short (just to replace the part) Or, by comparison, the situation may be that: 1. the cost of preventive work can be small, but 2. the time to complete the work (downtime) can be long. This option (which is the main development of EXAKTversion 4.2) resolves the extremely difficult problem of deciding upon maintenance policies in the light of actual maintenance costs. The new feature will encourage maintenance managers to elicit good cost information because they can

7 7 of 13 11/03/ :48 PM now use it effectively in their decision process. Slide 10 The generalized cost and availability optimization model is described by a slightly more complex graph and table shown in the slide. 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: 1. Cost: 93 $/d (73% better than running to failure) 2. Availabilty 99% (35% better than running to failure) 3. Average running time between interventions: 866 days (280 days worse than the RTF policy) 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 best (lowest ultimate bottom line cost) is attained by the decision modeling and deployment process. Slide 11

8 8 of 13 11/03/ :48 PM Sensitivity analysis tells us how accurate we need our cost data to be in order to assure ourselves of the benefits of applying the optimal model. In the ''Hazard Sensitivity" function we are given the option of determining the sensitivity of the optimal hazard rate to: 1. ratio of costs between preventive and reactive renewal 2. ratio of downtimes between preventive and reactive renewal 3. ratio of costs of downtime Slide 12 Having selected "Fixed Cost Ratio" we receive a graph of the optimal hazard level as a function of the cost ratio. We can read precisely from the table, the effect of changes in C f/c p. For example, in this case, the hazard is insensitive to changes from 20% to changes of 140% of the cost ratio. Slide 13

9 9 of 13 11/03/ :48 PM The optimal policy is less sensitive to the higher cost ratios, above two. That is, a moderately inaccurate estimate of a high cost ratio would not affect the optimal policy very much. A more precise estimate is required for the lower cost ratios. Slide 14 There are two lines on the Cost Sensitivity graph. The red line is of primary interest. It tells us whether, in using our model, our optimal cost will change, if, for some reason (without our becoming aware of it) the actual cost ratio changes. The blue line tells us, if we were to recalculate the model based on a different cost ratio, how would the new optimal cost compare to the orignal one. Slide 15

10 10 of 13 11/03/ :48 PM A similar sensitivity analysis may be performed, as easily on the Downtime Ratio or the Downtime Cost Ratio. Slide 16 The Cost Comparison Report is a method provided by EXAKT to assess the future impact of a proposed CBM policy. The report compares the expected performance of the current policy with that of a range of variations (not shown) of the proposed optimal policy. The range of results span the extremities regarding the possible outcomes of undecided histories in the sample. The methodology has been designed, so that the statistically minded analyst gains confidence in the applicability (and effectiveness) of the proposed decision model. Slide 17

11 11 of 13 11/03/ :48 PM This example illustrates the simplest case of a Weibull analysis with no condition monitoring data and a random failure behavior. The replacement strategy selected is "Cost & Availability". Hence, the set of parameters includes the relative (proactive and reactive) repair costs, downtimes, and unit downtime costs. Since the ultimate purpose of the model is to minimize global cost, the "Optimize Availability" radio button is deactivated. These parameters produce an interesting result. Slide 18 The black curve is the Availability as a function of replacement interval policy. The red and green indicate, as before, the failure and preventive maintence costs as they vary with replacement interval policy. The Table shows the cost and downtime parameters that have been set by the analyst for model building. Slide 19

12 12 of 13 11/03/ :48 PM This interesting example illustrates that the best policy found by EXAKT is to carry out no preventive renewals of this asset. In the current policy 14 preventive replacements have been made. Nevertheless, as the comparison table shows, these preventive replacements resulted in no economic advantage over running to failure. Slide 20 The six parameters of this model, entered as shown on the slide, are such that an unusual recommendation results from the model. In this case the model is a simple Weibull. No additional observational (condition monitoring) data is available Slide 21

13 13 of 13 11/03/ :48 PM Strangely, the recommendation is "Do Not Operate" at all. (I.E. the optimal replacement time is zero). The condition leading to this recommendation is that the mean life is so short and the cost of failure (relative to the cost of preventing failure) is so high, that no useful work will be achieved by the asset. For those who are interested, the mathematical condition leading to this result (of having minimized the cost and availability expression of Slide 9) is: When this condition holds, the optimal policy is "Run To Failure", otherwise, the optimal policy is "Do Not Operate". More information on the derivation can be found here.