Principles of modeling and optimization

In general, maintenance optimization models cover four aspects: (1) the description of a technical system, how it functions and what the importance of it is; (2) how the

system deteriorates over time and what the consequences of this deterioration are to other system components; (3) a description of the available information regarding the system and open possibilities of actions for management; and (4) an objective func-tions of the operators in the model and an optimization technique which helps in find-ing the best balance. (Dekker 1996, p. 231-232)

Every maintenance model incorporates prediction or extrapolation of future perfor-mance of a system, whether it is deterministic or probabilistic. Uncertainty of the fu-ture performance is always present in the real life situations, at least to some degree, which means probabilistic approach to modeling is necessary. (Frangopol et al. 2004, p. 197-198) Mathematical and probability-based maintenance models are complex, but they usually provide the most accurate results in forecasting and optimizing maintenance strategies. (IEEE / PES Taskforce 2001, p. 643-644)

In the figure 6 it is shown a conceptual view of maintenance activities over time. The figure illustrates how a system may operate over time and how maintenance acts on or responds to functional condition of the system. Worth noticing is that degradation time of a system is dependent on the technical aspects of the system, and also on the age of the system. Usually, degradation time decreases (i.e. degradation is faster) as the age of a system increases. That is due to imperfect maintenance: usually, a system cannot be restored to initial condition but the system is younger after each mainte-nance task. This is mainly due to repairing a wrong part, only partial repair, unintend-ed damaging of a system during maintenance, incorrect assessment of maintenance requirements, wrong timing of maintenance, hidden faults, human errors and / or re-placements with faulty parts. (Pham et al. 1996, p. 425) There are actually many op-timization models, which study optimal maintenance strategies on infinite time span.

This is the case basically because it is theoretically easier to study optimal strategies on infinite rather than finite time span. In reality, however, infinite operating time is impossible and thus, optimization models should take into account the age of equip-ment. (Nakagawa et al. 2009, p. 89-90)

Functional level

Time Initial malfunction

Functional degradation

Failure

Change of the required functional

level Upgrade

PM CM Improvement

Required functional

level

Delays in maintenance

service Degradation time 1 Degradation time 2

Figure 6. A conceptual view of maintenance activities over time. (Adapted from Ta-kata et al. 2004)

In the table 7, the most relevant maintenance optimization variables are summarized and related aspects are outlined. Not all of these variables are being optimized in AB model made for this study, and actually in most maintenance optimization models only one variable is being optimized. In this study, the optimal maintenance strategy is defined to be the one that maximizes profitability. In addition, there are quality and risk related variables in the model that affect the profitability optimization.

Table 7. Maintenance optimization variables and related aspects.

Maintenance influences the productivity and profitability of the manufacturing equipment. For example Alsyouf (2007, p. 73-77) showed that maintenance is actually a profit generating function, not a mere cost center. In addition to the view that maintenance can increase profitability of equipment owners, it is also interesting to analyze which decisions increase profitability of the maintainers of the equipment, if these are separate organizational units. Already at this point before introducing the AB model made for this study, it is argued that profitability should be the focus number one in optimizing maintenance tasks. Yet, this seems not to be the case, as optimization of other variables has been conducted way more than the optimization of profitability.

Total costs

Part of the maintenance strategy is, of course, to either minimize or optimize maintenance costs.

Maintenance includes costs of direct labor, materials, fuel power, equipment and purchased ser-vices. If maintenance costs are broken down to pieces, we can identify three typical types of costs:

costs of regular planned, unplanned and irregular (for refurbishments) maintenance. Typically, costs of regular planned maintenance (PM) are way lower than unplanned (CM) costs. However, the downtime cost of equipment due to maintenance tasks should also be taken into account. Thus, if the total costs of maintenance are the optimization target in maintenance strategy, then the goal is to find the optimal level of maintenance service, which minimizes total costs of maintenance tasks and equipment downtime. (Woodward 1997, p. 338-339)

Reliability of equip-ment

In maintenance management context, reliability means predictable and manageable performance of the system. In RCM the goal is to maximize the system reliability. In other words, the goal is to balance the costs and benefits of maintenance. In theory, balancing is possible when the assump-tion that the reliability of equipment is a funcassump-tion of the design and the build quality holds true.

(Rausand 1998, p. 122)

Risks of machine failures

Taking the probable risks of machine failures into account when optimizing maintenance strategy means: first, the possible risks have to be identified, their probabilities have to be estimated, and the hazard level of the consequences has to be reviewed. Then, the maintenance activities have to be planned so that the risks are optimized (risk levels are acceptable) in relation to maintenance costs. Either the maintenance activities have to be done more frequently or the probability of ma-chine failures has to be reduced. (Arunraj et al. 2007, p. 655-659)

Quality in production

Ben-Daya et al. (1995, p. 22-23) insist on taking product quality into account also, when optimiz-ing maintenance services and costs. In general, equipment that is not maintained properly experi-ences speed losses and / or lack of precision, which results in defects in products and runs manu-facturing processes out of control. This leads to increased production costs and lower profitability.

The role of maintenance is therefore to control production quality as well.

Spare part inventory levels

There are a few unique aspects to managing maintenance inventories compared to traditional ones.

These are: (1) maintenance policies dictate the need for inventories; (2) reliability information is generally not available to the degree needed for the prediction of failure times; (3) part failures are often dependent on each other; (4) demand for parts is sometimes met through cannibalization of other parts or units; (5) costs of being out of spare parts generally include quality reduction and lost production, and maybe risks to personnel; (6) machine obsolescence reduces the need for spare parts and increases the need for machine replacements; and (7) components of equipment are more likely to be stocked than complete units, if the major unit of equipment is expensive, and repair may be preferred to part replacements. (Kennedy et al. 2002, p. 202)

Scheduling of mainte-nance activ-ities

There are often coordination problems between production and maintenance job processing. A machine may be idle, yet production jobs are waiting, or machine may not be broken, but it is still waiting for maintenance personnel to come conduct PM. This leads to increased downtime of equipment and wasted resources. An optimized job schedule could increase uptime of equipment by determining when to perform maintenance activities and when to process each job. (Lee et al.

2000)