Monte Carlo Simulation offers an excellent tool to help engineers to make decisions regarding maintenance strategy. The quality of the recommendations is dependent upon the quality of the input data, and Enterprise Resource Planning (ERP) Systems such as SAP can be a useful source of data for analyses, providing details about system architecture, current maintenance strategies and failure history.

SAP PM is a module of the SAP ERP system that provides a framework for storing plant maintenance information, including, but not limited to, locations and assets, maintenance plans, resources and maintenance orders. Data mined from SAP PM may be used as input for maintenance optimisation as part of a wider Reliability Centered Maintenance (RCM) scheme. Optimised maintenance plans may then be uploaded back to the SAP system for implementation.

Monte Carlo simulation

Monte Carlo simulation uses random numbers to sample a distribution and thus predict a parameter of interest. Examples of parameters that are relevant to RAMS applications include Time to Failure (TTF) and Time to Repair (TTR). The results of a Monte Carlo analysis are averaged across many simulations, and are thus subject to statistical errors. The greater the number of simulations performed, the better the statistics and thus the more accurate the results. Figure 1 shows the Monte Carlo simulation process for the failure and repair of a single equipment over its lifetime.

Figure 1: The Monte Carlo Simulation process

These principles can be extended to more complex models, where a number of different distributions are sampled in order to model the interaction of equipment that makes up a system, and thus predict the failure and maintenance behaviour of the system as a whole.

Maintenance optimisation

A key benefit of Monte Carlo simulation is that is a provides a means to model and optimise preventative and predictive maintenance. Take for example, a single piece of equipment with a mean lifetime of 2 years; in the event of failure the equipment is replaced with a spare costing $500 (1 stored on site, 24 hours lead time to acquire a new spare). The task is performed by a maintenance engineer. Engineer call out cost is $100 for corrective maintenance and $70 for preventative maintenance. Replacement takes 6 hours at a cost of $10,000. Scheduled replacement of the equipment takes place at regular intervals, and the task is identical to the corrective task. However, failure results in a cost of $5000 per hour due to loss of production.

Optimisation is achieved by running a complete set of lifetime simulations with each of a range of possible maintenance intervals. A recommendation is then made for the optimum scheduled maintenance interval based on a parameter of interest, typically cost or availability. Figure 2 shows the cost optimisation plot for the preventative task. Fifty intervals were tested at increments of 730 hours (1 month). The interval predicted to give the lowest lifetime cost is 7 months.

Figure 2: Optimisation plot for a PM task

Each point on the plot represents 10,000 simulations of the equipment lifetime with the corresponding maintenance interval.

In this case, the estimated cost benefit ratio (the ratio between the lifetime cost associated with the recommended interval and the cost of running to failure) for the recommended interval of 5110 is 0.4675, indicating a saving of approximately 53% of the cost of running to failure.

SAP PM data mining

The input data for maintenance optimisation analysis (as described above) may be drawn from an SAP PM system. The following sub sections outline the SAP PM data that may prove useful for such an analysis.

1. Functional hierarchy

Used to provide a framework for a maintenance optimisation analysis, the hierarchy comprises functional locations, equipment, and equipment failure causes.
In SAP PM, functional location objects represent locations, systems and sub systems within a plant. Equipment objects represent the plant equipment upon which maintenance is performed.

The properties of an equipment are stored in the associated catalogue profile, which lists all of the code groups relevant to the equipment. In SAP PM, different types of equipment properties are represented by catalogues.

For example, to analyse a pump – listed in SAP PM as PUMP01, located in the pumping house, listed in SAP PM as functional location PMP-HSE-01– the catalogue profile attached to PUMP01 lists the various code groups associated with the equipment, which together completely describe its properties. For the purposes of maintenance optimisation analysis, it is necessary to extract the failure causes. These are listed in the code group PUMPS, which in this example SAP system is stored in catalogue 5 (causes). The data extracted from SAP PM may be presented as shown in Figure 3.

Figure 3: Functional hierarchy mined from SAP PM

2. Failure Characteristics

Accurate simulation of failure behaviour requires details of failure characteristics. This is best obtained by performing a Weibull analysis of historical failure and maintenance data for the equipment – available in the form of corrective and schedule maintenance orders in SAP PM.

Maintenance orders may be extracted from SAP PM and plotted on a cumulative probability plot. A trend line may then be fitted the data points, and the resulting fit parameters used as failure data for the simulation. Corrective work orders must be grouped by cause, as each failure cause is likely to have a distinct failure characteristic.

3. Effects & resources

Optimisation of maintenance with respect to cost requires some knowledge of the costs of both failure and maintenance. One source of cost is the effects of failure, such as production loss and regulatory penalties. These costs may be applied to an optimisation model in the form of effects.

Effects may be extracted from SAP and allocated to the failure causes in the optimisation model. However, effects in SAP PM do not contain any numerical cost data, so costs will need to be entered after the effects have been added to the model.

Returning to the optimisation model for PUMP01, a breakdown of the pump motor requires an unscheduled replacement of the pump. This task is performed by a maintenance engineer and takes 6 hours to complete. The standard price of a new pump listed in SAP PM is $1000, and the cost of calling out an engineer is $200. SAP lists the effect of a pump motor breakdown as ‘Loss of production’. A loss of production is estimated to cost $10,000 per hour.

Maintenance plans

In SAP PM, the maintenance tasks associated with equipment and the frequency with which the tasks take place are described by a maintenance plan. Each maintenance plan has an associated task list, which outlines the individual tasks, or operations, that take place as part of the plan.

A maintenance plan may be either a single-cycle plan or a strategy plan.  A single-cycle plan consists of tasks that take place at a single, common interval, whereas the tasks in a strategy plan may take place with different frequencies. It is possible to optimise either type of plan using Monte Carlo simulation.

PUMP01 is subject to a strategy maintenance plan. The task list for the plan includes the scheduled lubrication of the pump motor. Lubrication by an engineer and takes 1 hour to perform. The system must be shut down in order for the task to take place, meaning that production loss is incurred for the duration of the task.

Figure 4 shows the maintenance optimisation plot for the lubrication of the PUMP01 motor. The recommendation is to lubricate the motor every 8 months. The optimised maintenance task is expected to give a cost benefit ratio of 0.63.

Figure 4: Optimisation plot for scheduled replacement of PUMP01

This process of optimisation could be performed for all other tasks in the strategy plan and the improved plan then uploaded to SAP PM ready for implementation.

David Wiseman works in customer training & support at Isograph

https://www.isograph.com/