Downtime Model

In an operational context, there is a need to adjust and optimize existing maintenance programs. In order to facilitate this, one has to be specific on failure causes and mechanisms. A Failure Mode Effect and Criticality Assessment (FMECA) module has thus been included in the RAM tool. With the FMECA module in place, the ageing and downtime modelling are further improved compared to the basic RAM model in Section 5.1. Critical failures are split into different failure modes with the related Mean Time to Failures (MTTFs) and failure causes. A description of maintenance measures is linked to each of the failure modes. Information regarding the different cost elements of maintenance and operation are registered in the maintenance-planning module, or the Reliability Centred Maintenance (RCM) module. Interval optimisation for each of the preventive maintenance tasks is derived as the interval that produces the minimum total cost. 

In case of the standard multipurpose batch plant the downtime of the reactors for the product transfer into temporary storage vessels, the transportation of the vessels to the storage and the cleaning of the reactors before product changeover have to be included. This was modelled by an adjustment of the CIP times of the three stations to 60 min. 

Energy requirements were based on a fully utilized model gin that processes machine-picked cotton at rates of 12 to 14 bales/ hr and do not include energy consumed during idling or other periods of downtime. 

As an example, I have an older unit that has been superseded by a newer model. The newer model has very nearly the same readouts and functions as the older model. However, there are a few differences, for instance, the gas supply pressure requirements. If I were to use the newer manual to operate the older model, I would apply far too much gas pressure to the unit. This could blow out a few MEAs, which would destroy part of the unit, leading to costly repairs, and downtime. 

The photographs in Fig. 8.81 show, as examples, two different executions of J.C. Steele s (see Section 14.1) Model 90AD extruder. Fig. 8.81a includes a horizontal mix-er/pug sealer and dual hinged dies while Fig. 8.81b shows a hydraulic die changer in which the die plates are not installed in the holders. Die changers are used to allow the exchange of plates with worn orifices with a minimum of downtime or to switch over from one cross section to another. Tab. 8.9 presents technical information on some... 

Failure to manage differences in reference data Mismatch of data models Potential for downtime during the migration Adverse performance impact during data extraction... 

One difficulty with this type of model is that it is difficult to provide a probability value for an absolute repair time. For example, the Mean Downtime (MDT) for P-lOlB is 3 hours this is the time it takes to repair it when it fails. It may be that this time is an absolute minimum (say due to the time it takes to isolate the pump, drain it down, repair the failure, and bring the pump back into service). Hence a simple probability value cannot truly represent this downtime. 

It is obvious that the difference between the two models is considerable in this case. Equation (9.111) leads to the same result as the foregoing consideration if is replaced there by the sum + Td. This is also true if additional waiting times are to be taken into account, for example caused by the unavailability of a person for carrying out the repair. Hence we can replace in Eq. (9.111) by the sum of all times leading to component unavailability for whatever reason, which is simply called downtime . ... 

Quantification of data for availability, downtime and mean duration versus monthly CO2 Emissions/Production (Ind lOO) and CO2 Emissions/Production on days with stoppage (Ind <100) is shown in Table 1 and in Fig. 5. Table 1 shows the model with the greatest adjustment, after calibration of twelve regression models for each variable. 

Modeling. In order to carry out the analysis of the nature of the operational phenomena in facilities and equipment, it is very useful to use statistics as a support for the quantification of the parameters. The phenomena s historical behavior is characterized based on operation and failure periods that have occurred since the commissioning time. The conditions that characterize the equipment operational time data are so numerous that it is not possible to say when exactly the next failure will occur. However, it is possible to express which will be the probability that the equipment is in operation or out of service at any given time. These times are associated with a cumulative distribution function of the random variable, which is defined as the addition of the probabilities of possible values of the variable that are lower or equal to a preset value. The mentioned random variable is constituted by the operating times and downtime of equipment or system in a given period. For its parameterization Weibull distribution is very appropriate as it is very effective and relatively simple to use in the reliability evaluation of a system by quantifying the probability of failure in the performance of the system s duties from the failure probabilities of its components based on the operation times. There are three different parameters ... 

To model the uptimes and downtimes, different assumptions are made depending on how the components are believed to be deteriorating. For some components it is reasonable to assume no deterioration, while others are likely to show strong aging effects. Two basic categories of models are used for this purpose ... 

When the underlying distrihutions in the mixture that models the heterogeneous population of components are well separated, then maintenance cost savings are obtainable. Variation in the mixture distribution parameters tends to have a greater effect on the values of optimum inspection intervals than inspection and replacement costs and downtimes. 

The RCM study enables the use of downtime costs that are based on a thorough analysis by people that are actually working with the equipment.We however find that while in inventory models often shortage costs consisting of a single number are assumed, in practice all equipment in which the spare part is used is a potential source of downtime costs, and the downtime costs of different pieces of equipment need not be equal. Another complication that came forward is redundancy. When there are two pieces of equipment, of which only one is needed to keep the plant running, a breakdown of one does not necessarily have severe economic consequences. In summary, it is not clear in what maimer the downtime costs translate to shortage costs for the spare parts. 

The rest of this paper is organized as follows. In the next section we give a literature review. In section 3 we give motivation for the use of RCM data for inventory control. We discuss the requirements of the model in terms of functionality and applicability. In section 4 the model is described. In section 5 a method is proposed to approximate the downtime costs using the model. In section 6 we describe a simulation that... 

The balance between reahsm and applicability evidently depends on the specific apphcation. For specific, very costly equipment with huge downtimecosts (> S10 /day), a detailed simulation may be a cost-effective approach to determine appropriate stock quantities for very expensive spares (> 10 ). We aim at parts with somewhat lower, but still considerable, costs, and high downtime-costs. The example given in section 7 gives a good picture of the type of applications we have in mind. For these cases, the amount of time spent on each decision must be limited. When developing the model we must therefore limit the number of details included. At the same time, we must make sure that the most important characteristics are included. 

The model that resulted from the development is described in the next sections. The model assumes that failures can occur in multiple pieces of equipment in the plant, which need not have the same downtime costs. The model can also cope with redundancy. This structure enables the use of the model in combination with the data coming from the RCM study. At the same time, we have made a number of simplifications. Because we feel that aspects excluded from the model are also important, we will discuss the exclusions as well in the next section. 

In this section we determine approximative estimates of the downtime costs. We first estimate the waiting time for spare parts. Based on the estimated waiting time, we estimate the fraction of time that each functional group has a certain mnnber of defective equipment. This approximate analysis of the system is based on the analysis of multi echelon inventory control for recoverable items in the METRIC model (Sherbrooke 1968). Based on these average long term time fractions, we can calculate the long term average downtime costs in the system. 

We base the determination of the long term expected downtime costs on the assumption that different waiting times are mutually independent. This assumption is only approximative, because the waiting time for a spare part for one repair gives an indication of the on hand inventory, and thus of the waiting time for the next repair. The approximation is similar to the one used in the analysis of the METRIC model (Sherbrooke 1968). 

To avoid confusion, let us first stress that in the simulation we aim to find downtime costs for the model described in section 4. All assiunptions discussed in this section thus remain in place. Our aim is to estimate the effect of the two approximative assumptions given by equations 1 and 4 in section 5. The former approximately determines the total demand rate for the spare. The latter assumes that the waiting time for spares for subsequent repairs are independent. 

Very effective ways to minimise downtimes of crucial system components, for example hall screws, ball bearings and drives, are condition diagnostics and condition monitoring. Furthermore grouping of maintenance activities can either rednce downtimes or maintenance costs. Since many analytical models of technical systems have significant limitations and sim-phfications, simulation techniques are applied very often, see Bertsche (2008). 

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