A New Tool for the Evaluation and Optimization of the Scheduling of Preventive Maintenance in for Chemical Process Plants

Miguel Bagajewicz(+), Kehinde Adesoye,

Christopher Brammer, Mike Mills, and DuyQuang Nguyen

School of Chemical, Biological and Materials Engineering The University of Oklahoma

100 E. Boyd St., T335 Norman, OK 73019

Keywords: Preventive Maintenance, Corrective Maintenance, (+) Corresponding Author

Abstract A new methodology designed to optimize both the scheduling of preventive maintenance and the amount of resources needed to perform maintenance on a chemical process plant is presented. The methodology is based on the use of genetic algorithms to determine what schedule is most appropriate, while evaluating each of these using a Monte Carlo simulation. The overall goal of this method is to facilitate improvements in plant safety, reduce equipment replacement costs, and reduce economic losses due to downtime or reduced production. The simulation will accurately describe the equipment in a process plant by including several factors, such as equipment failure types, mean time between failures, maintenance cost, resources limitations, labor cost, repair downtime, failed but un-repaired equipment performance due to lack of resources, and other maintenance rules. This method is expected to alleviate the problems encountered with other methods, which include the over simplification of analytical techniques and the large computation time needed for the Markov method. Optimization of the well-known Tennessee Eastman Plant Problem is used to illustrate the method. The results of which include the optimization of both preventive maintenance intervals and resource limitations. A Fortran model was constructed that sampled a failure list using a reliability function. The model divided the time horizon given into weeks due to the maintenance schedule being created on a weekly basis. The model identified all preventative and corrective maintenance requests and categorized them based on their priority. The program then would schedule the maintenance work to be performed each week based on the priority of the repair. A workforce resource limitation was added to determine the amount of maintenance work that could be performed each week. If all maintenance could not be performed in a given week, all corrective maintenance will be scheduled for the next week and any preventative maintenance would be seven days later.

From the models results, it was shown that the preventative maintenance makes a large impact on the total cost. In the model that considered corrective maintenance only, cost soared to around $33 million for a one year horizon and $99 million for the three year horizon. This is related to the high economic loss associated with performing only corrective maintenance. Whereas, when applying the model that included preventative and corrective maintenance with no resource limitations, the best results where obtained arriving at a total cost of around $5 million for the one year and $18 million for the three year horizon. Finally applying the resource limitation of the number of laborers and adding the labor cost incurred with them the model arrives at a solution including not only protective and corrective maintenance costs and their associated economic losses but includes also the labor cost. This gives a model that accounts for almost all maintenance costs. For this model, the total cost of around $6.5 million for the one year and around $23 million for the three year model.

So, from the results the model shows that applying the right work force and performing preventative maintenance in accordance with corrective maintenance can save approximately $26.5 million over a one year horizon and around $75.6 million over a three year horizon.

1. Introduction According to Guidelines for Improving Plant Reliability through Data Collection and Analysis, maintenance is defined as “the combination of all technical and administration actions, including supervision actions, intended to retain an item in, or restore it to, a state in which it can perform a required function” (1998). It is a very important part of running any processing plant. Maintenance can also be described as the action that sustains plant production. Not counting scheduled outages, a typical refinery experiences about 10 days downtime per year due to equipment failures with an estimated economic lost of $20,000-$30,000 per hour (Tan and Kramer, 1997). Many industries all over the world have begun to realize the importance of having an effective maintenance policy, especially because the typical situation is that the activity is constrained by resource availability. Millions of dollars are now spent every year trying to preserve the different processes involved in production. The annual cost of maintenance (corrective and preventive) as a fraction of total operating budget can go up to 40-50 percent for the mining industry (Murphy et al, 2002), 20-30% for the chemical industry (Tan and Kramer, 1997). The typical size of a plant maintenance group in a manufacturing organization varied from 5 to 10% of the total operating force (Dhillon, 2002). It is estimated that over $300 billion are spent on plant maintenance and operations by U.S. industry each year, and that approximately 80% of this is spent to correct the chronic failure of machines, systems and human errors (Dhillon, 2002). The elimination of these chronic failures through effective maintenance can reduce the cost between 40 and 60% (Dhillon, 2002). There are three major reasons why maintenance is perceived as important and they include the following:

1) Safety: Most plant incidents are a result of bad maintenance practices or when maintenance is not done properly. Equipment pieces can hardly be isolated from each other in a process plant and therefore the effect of improper maintenance on one piece of equipment leading to its failure is felt in other equipment and can lead to unsafe situations. Unfortunately, some of these equipment effects do not present themselves immediately. For instance, the blocking of heat exchanger tube due to lack of cleaning can cause a heat imbalance which can result in a fire or an explosion in the plant. Various hazard evaluation techniques have been developed to analyze and evaluate safety hazard in a process plant, among which the most popular technique is Hazard and Operability Analysis (HAZOP). By careful analysis in a systematic fashion of process or operation, the HAZOP team lists potential causes and consequences of process deviations as well as existing safeguards protecting against the deviation. HAZOP technique requires detail information concerning the design of operation of process. Another popular technique is Failures Modes and Effects Analysis (FEMA), which itself is an important component in modern maintenance programs like Reliability Centered Maintenance (RCM). The FEMA tabulates failure modes (how equipment fails) and their effects on a system or plant. Other useful techniques are Fault Tree Analysis, which identifies and displays graphically various causes of a particular accident or system failure, Event Tree Analysis, which analyzes and shows graphically various outcomes of an accident initiated by an equipment failure or human error and Cause – Consequence Analysis, which is a blend of Fault Tree and Event Tree Analysis. More details can be

found in textbook “Guidelines for Hazard Evaluation Procedures”, Center for Chemical Process Safety, 2002.

2) Equipment and/or Equipment Parts replacement Costs: The costs associated with any piece of equipment can be related to the speed with which that piece of equipment deteriorates. The faster the condition worsens, the faster the equipment performance worsens. Usually, the decline of equipment conditions is slowed down by proper maintenance. As the equipment undergo maintenance, their frequency of mean time before failure (MTBF) increases. In some cases, the piece is restored to new. Most plant managers are looking to reduce the frequency of the MTBF because they are very keen on avoiding the replacement of that piece at all costs.

3) Economic Losses: Maintenance reduces downtime in a plant associated to major failures. A large cost (lost revenue) is associated to each plant shutdown on top of the cost of repairs. However, not all equipment failures lead to plant shutdown. Some failures deteriorate plant performance and most have associated lost revenue on top of the cost of repair as well.

Because of its significant impact on plant performance (both in economic and technical term), maintenance management and optimization have been extensively studied by people in the field of Operations Research and Manufacturing Engineering. The modern practices and management philosophy of maintenance can be found in various textbooks, e.g. Maintenance Engineering Handbook (Mobley et al, 2002). In short, modern maintenance philosophy suggests that: i) maintenance should focus on the whole system rather than individual equipments

/components ii) Maintenance should be performed in preventive or proactive mode (to preserve equipment

condition and keep system functioning) rather than reactive mode in response to a particular equipment failure (because the reactive mode leads to frequent downtime and high production loss), iii) maintenance should be considered as an integrated part of production process rather than a supporting part.

Plant maintenance can easily be divided into two general types. They include the following:

1) Corrective Maintenance (repair): this type of maintenance deals with fixing already

malfunctioning equipment. The key here is the ability to react quickly to any failure. For corrective maintenance alone, no steps are taken before the actual breakdown of the equipment. When this occurs, the equipment is immediately replaced as long as resources (labor and/or parts) are available. Therefore, to achieve immediate response a prohibitive large number of overtime laborers (likely sometimes idle) may be needed to repair an equipment failed at an unexpected time as well as a well stocked inventory of spare parts needs to be kept. Some equipment might even stay in the store through out the plant lifetime without being used. It is well-known that without preventive maintenance the failure frequency is higher and therefore production is affected more than when judicious preventive maintenance schedule is run in parallel. Finally, under resource limitations, prioritization schemes need to be established and the resources be devoted to those tasks for which there are spare parts available and have higher priority, leaving the rest unattended until resources are available.

2) Preventive Maintenance: this type of maintenance is geared towards taking actions that help reduce the number of failures of specific equipment. It is usually time and equipment driven. In other words, preventive maintenance has to follow a schedule that is created based on different factors depending on the piece of equipment being considered. Two major factors that help the scheduling of preventive maintenance are the difference between the cost of the maintenance program and the reduction in repair costs and secondly, the regularity of that equipments use. That is, it might not be profitable to perform preventive maintenance on some equipment pieces because they have low replacement costs or are not used regularly. In addition, Resource limitations usually subvert carefully planned maintenance schedules because at times certain equipment failure is in need of immediate repair (because of safety or high economic loss issues) that personnel assigned to preventive maintenance is required to attend these emergency repairs.

Aside form the broad classification there are many other corrective and preventive maintenance policies that differ by the methodology applied to perform them: .Indeed, modern maintenance practices (e.g. Reliability Centered Maintenance) considers the following important issues:

- If resources (personnel, materials) are limited as it is the case usually, then prioritization of equipment maintenance is necessary (even when it is corrective and not preventive), that is, important components in the system are paid more attention than others. The reason is that the objective of maintenance is to keep system functioning, minimize downtime (at a limited resource) rather than to maintain every individual equipment.

- Preventive and predictive maintenance (that render proactive mode of maintenance) is performed at scheduled times to prevent failure; intervening failures are corrected by corrective maintenance.

- Planning, scheduling and optimization (i.e. optimum resources allocation) of preventive maintenance (PM) is an important part of an effective maintenance program

Various time-driven preventive maintenance (PM) policies have also been proposed by researchers. They are summarized in a review paper by Wang (2002) as follows:

- Age-dependent PM policy: the PM times are based on the age of the unit. - Periodic PM: a unit is preventively maintained at fixed time intervals kT (k = 1,

2, . . .) independent of the failure history or age of the unit. - Failure limit policy: PM is performed only when the failure rate or other

reliability measures of a unit reach a predetermined level - Sequential PM: a unit is preventively maintained at unequal time intervals.

Usually, the time intervals become shorter and shorter as time passes. The maintenance policies mentioned above are for single unit or multi-unit systems where independence between units is assumed. For multi-unit systems with dependence between units, then group maintenance or opportunistic maintenance policies should be used (Wang, 2002). Opportunistic maintenance is defined as follows: when a piece of equipment is undergoing

maintenance, there could be an opening to perform maintenance on another piece of equipment. These techniques consist of “optimally utilize system downtime opportunities to perform preventive maintenance at a lower overall cost. Thus, during every system downtime opportunity, preventive maintenance activities need to be investigated to determine if the benefits from future reliability and production outweigh the current maintenance costs. The optimization trade-off is between maintenance costs and production. On the one hand, performing preventive maintenance during an opportunity (before it is regularly scheduled) may increase maintenance costs per unit time. On the other hand, opportunistic maintenance may improve equipment reliability, reducing future system downtime and increasing production and net income. Thus, during every system downtime opportunity, preventive maintenance activities need to be investigated to determine if the benefits from future reliability and production outweigh the current maintenance costs” (Tan and Kramer, 1997). Condition-driven PM and predictive maintenance monitor and detect in advance any failure symptom of equipment, then perform planned repair for the failure-prone equipment to avoid downtime. Since there is very limited number of decision variables involved for these kinds of maintenance policies, they are usually not subjects for maintenance optimization research (but they can be investigated together with time-driven PM in an integrated maintenance optimization framework). Maintenance optimization has been extensively studied extensively and a large amount of published maintenance models (Wang, 2002). Many models were discussed and summarized in the excellent textbook by Wang and Pham (2006) and various review papers (for example, Wang, 2006, Garg and Deshmukh, 2006). Most of the models are deterministic models that use simplified assumptions, or Markov-decision models. Mathematical programming techniques are usually used to solve the formulated deterministic models. The models differ in the assumptions and mainly in PM policy; hence different decision variables are sought. The decision variables depend on the PM policy; for example, time interval length needs to be optimized in periodic PM. The most common optimization criteria are based on maintenance cost (to be minimized): maintenance cost rate (cost per unit time), total maintenance, inventory and lost production costs; maintenance labor cost can also be taken into account. The constraints are requirements on system reliability measures: availability, average uptime or downtime. For systems like nuclear power plants or power generation systems where reliability is much more important than cost, the optimization criteria are highest reliability measures at given maintenance budget

Tse (1996) developed a method that picks out maintenance tasks and selects periodicity of maintenance by minimizing downtime and optimizing labor expenditure. It was reported to work well for equipment with high wear out failures and whose failure times are Weibully distributed. In this method an economic cost per unit time is calculated using the cost of planned replacement, the cost of failure and the number of failures during that time. In order to find the optimum maintenance time period, a plot of maintenance cost/unit time vs. time is made and the minimum obtained. Iterations are carried out over infinitely small time values to obtain this graph. This used the Weibull parameters and the preventive maintenance cost and downtime as

inputs. Overall, the approximation method uses a specific cost rather than cost approach to optimize preventive maintenance. Some of the setbacks of this methodology include the fact that it is complicated and it is not flexible for different data from different plants. It also requires more computation time to optimize large plants than running a Monte Carlo simulation directly.

More recently, (Okogbaa, 1996) proposed a method for preventive maintenance analysis under transient response. This method is based on the following assumptions: (1) When equipment fails it is replaced (corrective action) with identical but new equipment. Also after a time period, it is replaced (preventive action) by a new one. (2) Maintenance on a piece of equipment that has reached a certain age is performed if resources are available. (3) Cost of maintenance is compute using variable and fixed portions for both replacements and repairs. To obtain a functional maintenance policy a constant failure rate for each piece of equipment is applied to simplify the model while accounting for opportunistic maintenance opportunities. In this case, the failure-repair process usually contains the failure distribution of that equipment and the conditional failure probability of all the other equipment in the plant. The model ends up being formulated in terms of differential equations that are integrated. Some of the setbacks of this methodology include numerical inaccuracies and computation errors. It is also very complicated and cannot be easily modified for different plants as in the case of a simulation. There is increasing benefit to use genetic algorithm (GA) to solve complicated maintenance optimization models, which consider simultaneously many decision variables, for example, optimum PM time interval, spare parts inventory level, labor workforce size, resources allocation, replacement strategy, use of predictive maintenance. The benefit of using the GA is that with the combination of a Monte Carlo the objective function, costs, can be minimized by recognizing and reproducing good maintenance policies and converging on a population of low-cost maintenance policies (Tan and Kramer 1997). GA is also used to solve the models of opportunistic maintenance policy as well as preventative maintenance policies through the ability to recognize and reproduce good maintenance policies. Monte- Carlo simulation, on the other hand, is usually used to estimate parameters in the model, especially reliability measures of complex systems such as availability, MTBF (or MTTF). Of all the tools that can address complex models with a variety of decision variables, Monte Carlo simulations are excellent for assessment purposes. In addition, to optimize maintenance schedules, prioritize jobs, as well as manage spare parts acquisition, one can eventually add stochastic optimization techniques (simulated annealing or genetic algorithms). There are few techniques that utilize both Monte- Carlo simulation and GA (Tan and Kramer, 1997). Hundreds of recent publications have demonstrated the use of analytical techniques of Markov models for narrow maintenance optimization problems. However both of these methods have disadvantages and limitations. The analytical techniques (1) can only mark a component as either operating or failed, (2) has only cost as the objective function, (3) have no constraints for when to perform maintenance, (4) only consider corrective and preventive maintenance, (5) always consider equipment to be as good as new, (6) finds optimums based on infinite time horizon, (7) does not consider the time-value of money, (8) can result in optimization to a local minimum if the failure frequencies are not monotonically increasing with time, (9) has shortcomings when dealing with opportunistic maintenance, including solution accuracy,

versatility, and tractability. The Markov method (1) has difficulties with computation times, which grow exponentially as the number of components increase, (2) considers opportunistic maintenance occurrences to be time-independent, which has been shown to be invalid, (3) has shortcomings when dealing with opportunistic maintenance, including solution accuracy, versatility, and tractability. (Tan and Kramer) The method of using genetic algorithm with Monte Carlo simulations does not have these disadvantages and can be used for more complex models incorporating equipment wear, inventory, partial bottlenecks, and imperfect maintenance. This method can also optimize non-deterministic objective functions and can be integrated easily with general process planning and scheduling. It can also provide sensitivity analysis, with out additional calculations. (Tan and Kramer) Tan and Kramer (1997) optimized the opportunistic maintenance policy using Monte Carlo techniques to evaluate each proposed solution and GA to generate new ones. Their framework considers both situations: “as good as new” maintenance or perfect maintenance and “as good as old” maintenance (minimal repair). They optimized “opportunistic maintenance policy”, which is a more realistic PM policy for chemical processes that usually have dependency between units, although it could be cumbersome to implement. They did not, however, consider spare parts purchasing policies and resource limitations. In this work, we consider simple periodic PM policy for each piece of equipment, mostly because it is suitable for labor organization, we assume independence between units, and we address resource limitations and spare parts inventory policy. All these elements of maintenance where not considered together before. To do this, we include a set of rules about corrective maintenance prioritization and spare parts purchasing to a Monte Carlo simulation tool. This evaluation tool is later used as part of a GA algorithm, in a scheme that is similar to that utilized by Tan and Kramer (1997). The article is organized as follows. The existing methods for PM scheduling are presented first, followed by a description of our evaluation procedure. We then discuss optimization and finally present the results.

2. Equipment failure data The mean time before failure of different pieces of equipment can be obtained from literature or through data logging on a plant. It is used in the distribution equation to obtain the probability of failure of each piece of equipment. Different distributions can be used depending on maintenance preferences or data availability. The following are examples of commonly used distributions:

i) Exponential: this distribution is based on a constant rate of failure, given by the MTBF. It is usually used when there is limited information or data about the equipment.

ii) Weibull: this is one of the most commonly used distributions in industry. It measures the rate of failure through the MTBF and a parameter called the shape factor (β). This makes the distribution open to a wide range of failure

data types because it accounts for different failure rates. When the shape factor equals one the Weibull reduces to the exponential distribution.

iii) Normal: this distribution is used in cases where wear out failures and repair times are considered. It can only be used in the case of increasing failure rates.

iv) Logarithmic: this is a modification of the normal distribution and is used when model value deviations are by proportions e.g. factors, percentages and not absolute values. It is also used only in cases of increasing failure rates.

Finally, equipment dependencies are needed to be determined and the conditional probabilities need to be established. In our case, without loss of generality, we use the exponential (one parameter) distribution and we ignore the equipment dependencies. 3. Costs and Economic Losses The cost of maintenance (TC) is given by

TC = EL + EC + PMcost + CMcost (1)

where EL is the economic loss due to failure and unrepaired equipment, EC is the spare parts costs, and CMcost and PMcost are the corrective and preventive maintenance cost (fixed and labor/incidentals), respectively.

To determine economic losses (EL) a failure analysis is carried out on each piece of equipment to determine the economic effect of each failure. Since equipment spare parts (or even complete equipment replacement) are taken care of in another term (EC), this term concentrates in determining any effect from the loss of production throughput (capacity), even shutdown, the deterioration of product quality, the effect of accidents, etc. These effects are then translated into a monetary counterpart. In addition to the costs (labor, materials and incidentals) incurred in the repair itself, there is an economic loss associated to the period the equipment is serviced (increased operating costs, or loss of production, like in heat exchanger cleaning, or loss of product quality). All these need to be listed in EL. 3. Safety Safety is of course always a matter of concern. Some equipment failure lead to accidents, as noted above, which have economics consequences that can be listed in EL, but some also could lead to personnel injuries. As tempting as it might be to associate personnel injuries to economic losses, which there are of course, one should actually make sure that, regardless of the cost, safety associated to human injury prevention is handled in a different way. We believe this aspect, aside from the economic losses that have to be listed anyway, needs to be associated to a constraint limiting the likelihood of the event happening.

4. Maintenance Rules and Scheduling Our assumed rules are:

1. Each repair corresponding to each failure is classified through several priority categories: Emergency, Urgent, Pressing, and Affordable.

2. Each repair priority category is characterized by the time one can afford before there is a catastrophic failure leading to an unacceptable loss. The sustainable category is characterized by a very long time.

3. Repairs in the emergency category take precedence, that is, any planned maintenance, corrective or not are suspended and all available resources are devoted to it. If spare parts are not available the repair starts when these parts arrive.

4. Preventive maintenance (PM) is scheduled at regularly recurring intervals. 5. If equipment has undergone corrective maintenance a predetermined period of time prior

to the scheduled action, such action is suspended so that resources can be used elsewhere. 6. Each week corrective maintenance repair actions schedule is planned ahead, by allocating

resources as follows: All jobs in the Urgent category are first included, unless spare parts are not available. If there are resources left, pressing jobs and sustainable cases are included. Pressing categories are upgraded to urgent and urgent to emergency when the allotted time for catastrophic failure is about to take place in the planned week.

7. Preventive maintenance on all major equipment is performed at the same time to minimize plant downtime.

8. Opportunistic maintenance, equipment dependencies and delayed detection of failure are not considered. .

9. If there is an online backup of a piece of equipment, switch to it when corrective or preventive maintenance will require the online piece of equipment to be taken off-line in order for maintenance to occur.

Priority categories are established using a double entry matrix (Table 1). A high, medium and low probability of occurrence is loosely associated to probabilities to take place in a week, a month or between a month and for example a year. High consequences of failures include failures in which a failure occurs, the unit or even plant may have to be shutdown creating large revenue losses or where a major spill to the land creating major environmental hazards resulting in large fines. Also, significant safety risks to employees with in the plant are present. Medium consequences of failures include failures in which a failure occurs, the unit will have to be run at a reduced rate causing revenue losses in production or where a level two environmental accident occurs (level two incident is a spill to land that is significant and defined by the EPA but does not result in a major environmental event) resulting in a some monetary losses. Safety risks to employees are still present but not to the extent as are present in high consequence situations. Finally, low consequences of failures include failures that when they are occurring cause no significant deviation from normal operation and involve only minor environmental issues such as a drip leak. Nearly no safety concerns are present.

Table 1: Levels of Failures for Maintenance Concerns (following Tischuk, 2002)

Consequence of Failure Probability of subsequent catastrophic Failure High Medium Low

High 1 2 3 Medium 2 3 4

Low 3 4 5

Then, high-high and medium-high Urgent, low-high, high medium and medium pressing. Finally, the rest are in affordable. While the above scheme seems reasonable, optimizations at each week to determine the best corrective maintenance schedule seem even more appealing. While this is not addressed in this work, it is entirely possible to undertake within the framework we present. 5. Preventive Maintenance frequencies The Tennessee Eastman Plant used contained seven different types of equipment. This equipment included:

Equipment • 11 - Valves • 2 - Pumps • 1 - Compressor • 2 – Heat Exchangers • 1 – Reactor • 1 – Stripping Column • 1- Flash Drum

Each type of equipment has different failure rates. In order to assign MTBFs for each type of equipment, an average MTBF was obtained from Guidelines for Process Equipment Reliability Data with Data Tables (1982). From the average MTBF, each type of equipment went through a probability analysis that considered the occurrence of each distinct type of failure for each type of equipment. If a failure was found to have a higher probability of occurrence, it was then scaled in accordance with that probability to have a higher frequency of occurrence than that of the average MTBF. Likewise, if a distinct failure was considered to have a lower probability of occurrence it was scaled in accordance with that lower probability to give a lower frequency of occurrence than that of the average MTBF. Incorporating the probability of the failure occurring was also combined with the priority/severity of the failure. For example, if a piece of equipment encountered a failure due to corrosion, the level of the corrosion (i.e. severe, moderate, slight) was considered in determining the failures MTBF, meaning that the severe corrosion failure would have a lower frequency of occurrence resulting in a larger value for the failures MTBF.

6. Spare Parts Acquisition Policy In order to determine a spare parts acquisition policy for the opportunity cost lost by having the spare parts on hand was employed. To determine the opportunity cost lost by having the spare parts in inventory, the following equation was used to determine the opportunity cost.

PCiPCEC MTBF −+= ))1(*(

EC – Spare Parts Opportunity Cost PC – Parts Cost i – Interest Rate MTBF – Mean Time Between Failure in years

Calculating the spare parts cost as an opportunity cost allows for the spare parts cost to be displayed as the cost per part incurred by keeping the part in inventory. By presenting the inventory cost in this fashion, it can easily be optimized by considering the spare parts cost per part by the number of parts on hand versus the economic loss incurred by having to wait for the parts to be received by the plant (i.e. – how long maintenance is delayed by not having the parts on hand vs. having them available immediately). 7. Evaluation using Monte Carlo Simulation This technique is based on repeated sampling of the equipment failure and evaluation of the cost, the economic losses associated to failed states, costs or repair and costs of preventive maintenance actions for each sample. The method continues sampling and computes an average until it reaches the set sample size. Sampling procedure to simulate equipment status within a finite time horizon in accordance with a maintenance policy

- Failure events of equipments are sampled using reliability function (failure rate) of equipments

- Preventive maintenance requests for equipments are generated in accordance with predetermined preventive maintenance schedule (predetermined PM policy)

- The planning time horizon is divided into time intervals of weeks. - In each week:

i) Identify all the CM requests (when equipments failed) and all the scheduled PM requests.

ii) CM request for equipments with highest priority will be fulfilled. Continuing with CM requests of equipments with lower priority until the resource available is used up (for the time being only labor resource is considered). More specifically, when a maintenance action is performed in response to a maintenance request, the available labor hour is subtracted by the labor hour needed to perform that maintenance activity. When all labor hour is used up, no more maintenance

actions are possible. The total labor hour available at the beginning of a week is calculated as the number of employees * 40 labor hour / person / week. Of course, this is just an approximate calculation of the maintenance activities management problem. Rigorous calculation has to consider travel time of employees to locations of equipment, number of “unoccupied” employees at the current time to take care of unfulfilled maintenance requests and available spare parts / tools necessary for maintenance operations.

iii) If all CM requests are fulfilled, continue with PM requests until the resource available is used up, also start with PM actions for equipment with highest priority.

iv) If a CM request or PM request is not fulfilled, it has to be delayed to next week. Delayed CM request is scheduled to be fulfilled at the early of next week while delayed PM request is scheduled to be fulfilled exactly 7 days after the original PM schedule.

v) If a CM action on equipment was performed prior to scheduled PM request for that equipment a predetermined period (current value is 7 days), that PM request will be ignored.

vi) If CM action for an equipment has been delayed more than a predetermined period (current value is 21 days), the priority level of that equipment will be upgraded one level.

- When a maintenance action is performed on an equipment at time t, that equipment is assumed to be as good as brand new and failure events for that equipment will be resampled (updated) starting from time t.

- The next week is considered and the calculation is repeated. The procedure continues until the end of planning time horizon is reached.

Thus, given - PM schedule. - Spare part replenishment policy - Resources available to repair each type of equipment And the rules above, one can obtain the economic impact of adopting these decision variables. Optimization is the logical next step. 7. Optimization In order for optimization to occur both models are employed to see the optimum resource limitations. In the current model, the resource limitations considered is labor. In the corrective maintenance model, this simply results in running the model with a different amount of workers to obtain the lowest average cost and then including the labor cost, which is a fixed salary per worker, to arrive at the lowest total cost. While the corrective maintenance model only requires the optimization of the number of workers, the corrective and preventative maintenance model requires the optimization of not only the number of workers but also the preventative maintenance interval (PMI). The PMI is optimized by assuming infinite resource limitations (workers) with no labor costs and running

the model based on the assumptions to determine the optimal PMI. The PMI’s are set to be a ratio of each of the equipment failures MTBF. After each ratio is ran through the model, the lowest total cost is found and gives the optimal PMI. After determining the optimal PMI, the resource limitations (workers) is optimized using the optimal PMI. Through using different sample sizes the average total costs are used to find the minimal total cost giving the optimal number for resource limitations (number of workers needed). 8. Illustration

A safety/maintenance module for process plants was designed and explained as described above. It consists of a scheduler which incorporates when to perform preventive maintenance on several pieces of equipment on the plant. In addition, a system of predicting equipment failure was used to assess potential losses while the frequency of failure of parts was used to determine the economical maintenance policy in the plant. The sample plant on which this analysis is carried out on is the Tennessee Eastman plant. This analysis is carried out on a 1 and 3 year time period but could be increased to cover a longer time period if needed. This plant is a theoretical plant originally created to be used as a case study for researchers in different areas including process control, estimation and optimization. The system variables are not defined but this is not a huge problem as we are not particularly interested in the production but in the system layout. The Process Flow Diagram of the plant is given in Fig. 6.

Figure 1: Tennessee Eastman Process Flow Diagram.

Currently, each piece of equipment is being considered in the Tennessee Eastman Plant, allowing for the total findings of the maintenance cost for the plant. Equipment failure analysis In order to predict safety failures in a plant, the equipment in the plant have to be studied individually and in detail. This study mostly surrounds the failure analysis of the equipment. There are different levels of detail expected from a failure analysis. This detail varies with information obtained from different sources or plant specific issues that may arise for the equipment. For this project a summary table of the equipment failures for the flash drum is shown below due to its simplicity.

V2 V1

V3 P1

ST

HX

Equipment I.D

Equipment Type Part

Type of Failure Level MTBF TNCM

Economic Loss CM cost

hrs hrs $ $

PV-1 Flash Drum Vessel Severe Fatigue 1 87600 72 $60,000 $40,000

PV-1 Flash Drum Vessel Moderate Fatigue 3 43800 24 $20,000 $4,000

PV-1 Flash Drum Vessel Slight Fatigue 5 21900 0 $0 $0

PV-1 Flash Drum Vessel Severe Corrosion 1 94685 72 $60,000 $40,000

PV-1 Flash Drum Vessel Moderate Corrosion 3 47343 24 $20,000 $10,000

PV-1 Flash Drum Vessel Slight Corrosion 5 23671 0 $0 $0

PV-1 Flash Drum Vessel Severe Wear 1 90288 72 $60,000 $40,000

PV-1 Flash Drum Vessel Moderate Wear 3 45144 24 $20,000 $4,000

PV-1 Flash Drum Vessel Slight Wear 5 22572 0 $0 $0

Table 2: Failure Data for the Flash Drum PV-1

Equipment data for the flash drum shown in table 2 was provided to allow for the Monte Carlo simulation to randomly select failures and then calculate its results based on the average from the different samples taken. The types of failures that occur where found from determining the parts of each piece of equipment and from this list determining which type of failures the equipment was prone to. The levels were assigned based on the type of failure and the consequence that could result as presented previously. Also, for the various levels of corrosion, it was assumed that the plant had a corrosion monitoring system as much do, keeping corrosion effects for most equipment at a level (priority) of three or above for most equipment except for large pressure vessels. The MTBF for each of the failures were based on the probability of occurrence based on the average MTBF from Guidelines for Process Equipment Reliability Data with Data Tables (1982) as was explained previously. The TNCM (Time Needed for Corrective Maintenance) was based on the priority level assigned for the failure and the type of equipment itself. The economic loss was calculated based on the TNCM and the cost of shutdown and loss of production of our product. While the CM cost in our tables providing data to our Fortran model is that of just the cost of the equipment and its replacement parts. The equipment was priced using Plant Design and Economics for Chemical Engineers (Peters, Timmerhaus, and West 2003). Each different type of equipment has a different failure list. However, multiple pieces of the same type of equipment are considered to have exactly the same data. Meaning the eleven valves in the Tennessee Eastman Plant are exactly identical and all have identical failure data. This was done to meet time limitations. Monte Carlo Sample Sizes One concern when performing Monte Carlo simulation is including enough samplings in each scenario, so that variations in the running average of the expected cost are minimized. This

allows the simulations to converge and enable an accurate analysis to be performed for the specified scenario. To determine the number of samplings needed for each scenario, the simulation program was run for 60,000 samplings using CM with no resource limitations, with the running average outputted after each sampling. Only corrective maintenance was included; by excluding the preventive maintenance the amount of variations in the expected cost is maximized. This ensures that the worst case scenario is accounted for because including PMs decreases the amount of variation in the average expected cost. After running the simulation for 60,000 samplings, the variation in the average expected cost was reduced significantly. Corrective Maintenance without Resource Limitations As stated above, the corrective maintenance model without resource limitations was used to determine the sampling size. Sample sizes of 60,000 samples where used and the average cost converged to a consistent and steady value. When performing CM without resource limitations, one is insuring that all CM actions will take place. As well, in this model no labor costs are considered. Finally and most importantly, that this model represents the lowest cost that one can obtain through only performing CM. To further show this, figures 2 & 3 will show not only the ending average total cost graphically but also how the average total cost converges to its true average amount as the number of samples are increased; however, the plots can only accept 32,000 samples not allowing for the full 60,000 samplings to be shown. Figure 2 represents a one year time horizon, while figure 3 represents at three year time horizon.

Figure 2: Average Total Cost vs. Number of Samples – 1 yr. Horizon

Figure 3: Average Total Cost vs. Number of Samples – 3 yr. Horizon From both figures 2 & 3, the average total costs are seen to be around $32.6 million and $98 million respectively. This large sum of money is rather high for one unit; however it represents how ineffective it is to only perform CMs. Corrective Maintenance with Resource Limitations The corrective maintenance model takes into consideration the occurrence of only corrective maintenance and is only limited by the number of workers available as a resource limitation. The model was run at both a time horizon (period) of 1 and 3 years. The following two figures, figures 4 & 5, show the results for each of the time horizons when only corrective maintenance is done.

Figure 4: Results for CM Model – 1 yr. Horizon.

Figure 5: Results for CM Model – 3 yr. Horizon

From the two plots, it can easily see that for the CM model the optimized number of workers to perform all corrective maintenance is the four for the one year time horizon, while only three workers were needed for the three year horizon model. Once the curves begin to level out, the

CM Model Cost per # of Workers: 3 Year

$-

$100,000,000

$200,000,000

$300,000,000

$400,000,000

$500,000,000

$600,000,000

$700,000,000

0 1 2 3 4 5 6 7 8 9 10

# of workers

CM

Cos

t

Total Cost

Ave Total EL

Ave CM Cost

CM with Resource Limitations - 1 Year

$0

$5,000,000

$10,000,000

$15,000,000

$20,000,000

$25,000,000

$30,000,000

$35,000,000

$40,000,000

$45,000,000

2 3 4 5 6 7 8 9 10

# of Workers

Cos

CM

LaborCost

EL Cost

TotalCost

cost is slightly increasing due to the increase in labor cost, which is a fixed salary of $60,000 per year; however, it is so small when compared on the same scale as the economic loss currently. The optimal average total cost for the one year and three year models can be seen below along with the economic loss that occurred and the CM cost, which in this model only represents the cost of the parts involved in the corrective maintenance taken. Table 3 includes the results of both the CM with and without resource limitations.

CM Models Years Model # of Workers Total Cost

1 CM Model - No Resource Limitations Infinite $32,670,224 1 CM Model - With Resource Limitations 4 $32,892,092 3 CM Model - No Resource Limitations Infinite $98,026,767 3 CM Model - With Resource Limitations 3 $98,657,573

Table 3: Cost for CM Models for 1 & 3 Year Horizon

The table above shows the difference resource limitations currently make within our models. The resource limitations are only the number of workers and their respective $60,000 salary which has little effect on the overall outcome of our results due to the total cost being so heavily reliant on the economic loss occurred.

Corrective & Preventative Maintenance Model

The CM and PM model takes into account the occurrence of PMs. However, in order for the model to find the optimized cost solution, the preventative maintenance interval (PMI) must be optimized first. In order to accomplish this, the data provided to the model considers an infinite workforce at no cost (labor cost) allowing the only costs to be considered to be the actual maintenance cost. Also, this allows for all of the corrective and preventative maintenance that is scheduled to be completed each week. In order to determine the PMI, ratios of the average MTBF for each piece of equipment are inputted as the PMI giving different PMIs for each type of equipment. Using these methods, the following figures, figures 6 & 7, are created showing the optimal PMI from the ratio of the average MTBF.

Figure 6: PMI optimization based on MTBF Ratio – 1 yr. Horizon

Figure 7: PMI optimization based on MTBF Ratio – 3 yr. Horizon

For each of the plots, a minimum can be seen. This minimum represents the optimum PMI for each of the different time horizons. The results for each of the PMI runs are displayed in the table below.

PMI Optimization: 3 Year Basis - No Resources

$-

$10,000,000

$20,000,000

$30,000,000

$40,000,000

$50,000,000

$60,000,000

$70,000,000

$80,000,000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x MTBF

Tota

l Cos

tPMI Optimization with Infinite Labor

$0

$2,000,000

$4,000,000

$6,000,000

$8,000,000

$10,000,000

$12,000,000

$14,000,000

$16,000,000

$18,000,000

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Fraction of MTBF

Cost

PMI Optimization Horizon PMI (Ratio of MTBF) Total Cost 1 yr. 1/50 $5,114,4053 yr. 1/54 $18,021,749

Table 4: PMI Optimization & Total Cost at Infinite Resource Limitations

From the table above, the significance of PM with an optimal PMI can be seen by such a low total cost when compared to the CM models. However, at infinite resource limitations (infinite workers) the labor cost is not considered. So, to further develop the model the number of workers must be considered to truly develop a reliable CM and PM model.

PMs and CMs with resource limitations After optimizing the PMI with infinite workers, the model including both CMs and PMs is ready to have the size of its workforce optimized. Using the optimal PMI found previously because the PMI is independent of labor limitations is inserted into the model and the size of the workforce is varied over multiple model runs to find the run with the lowest cost. Initially a low number of samplings were used to find a rough estimate of the optimum number of labor needed to minimize average total cost, and then those scenarios were run at 60,000 samplings for each time horizon. For the one year time horizon with 60,000 samples the labor resources where run at 13, 14, 15, 16, and 17 workers. For the three year time horizon with 60,000 samples the labor resources where run at 19, 20, 21, 22, 23, and 24 workers. Figures 8 & 9 show the results obtained from the running of the model at these values.

Figure 8: Workforce Optimization via the CM & PM Model – 1 yr. Horizon

Figure 9: Workforce Optimization for CM & PM Model – 3 yr. Horizon

From figure 8, it can be seen that the optimum number or workers is 15, while in figure 9 the optimum number of workers is 22. These plots show visually the difference that on or two workers away from the optimum can drastically effect the overall cost is some cases, while in others it is not that great of an effect. However, no matter the effect the plots provide a visualization of how one worker can affect the overall average total cost. The resulting costs and a comparison with the CM models can be seen in table 5. All Models Years Model # of Workers Total Cost

1 CM Model - No Resource Limitations Infinite $32,670,224 1 CM Model - With Resource Limitations 4 $32,892,092 1 PM & CM Model 15 $6,421,160 3 CM Model - No Resource Limitations Infinite $98,026,767 3 CM Model - With Resource Limitations 3 $98,657,573 3 PM & CM Model 22 $23,027,813

Table 5: Results for PM & CM Model

This table shows the significance of performing CM. The cost differential of performing PM compared to not performing PM is quit large. For the one year time horizon, the difference is approximately $26.5 million, while for the three year time horizon it is approximately $75.6 million. Both results represent a large disparity between the CM and the PM & CM models for a single unit. With the large disparity, the importance for PMs to take place is increased.

After optimizing the number of workers, it is now time to compare the results with those found when optimizing the PMI. When optimizing the PMI, the best possible result is produced due to the workforce being an infinite amount of workers, working at no cost. As well, this comparison will also allow for verification that the PMI does not change with the optimum number of workers. This analysis can be seen in figures 10 & 11.

Figure 10: PMI Optimization Effect of Including Labor – 1 yr. Horizon

Figure 11: PMI Optimization Effect of Including Labor – 3 yr. Horizon

After visual inspection of the plots, one can see that the PMI remains the same. As for the difference in cost, they can be seen in table 6.

PM & CM Models Comparison

Years Model # of Workers Total Cost Years Model

# of Workers Total Cost

1 PM & CM Model 15 $6,421,160 3

PM & CM Model 22 $23,027,813

1 PM & CM Model Infinite $5,114,405 3

PM & CM Model Infinite $18,021,749

Difference $1,306,755 Difference $5,006,064

Table 6: Comparison of PM & CM Models

From table 6, it is shown that the workforce accounts for about a million dollar difference while in the three year model it comes to a five million dollar difference. This increase when including labor is associated to the labor costs, equipment repairs that are delayed that are incurring an economic loss due to their respective failure, and not as many PMs are completed.

9. Conclusion From the results, it can easily be seen that the PM makes a large impact on the total cost. In the CM only model, cost soared to around $33 million for the one year and $99 million for the three year. This is related to the high economic loss associated with performing only CM. Whereas, when applying the CM & PM model with no resource limitations, the best results where obtained arriving at a total cost of around $5 million for the one year and $18 million for the three year horizon. Finally applying the resource limitation of the number of labors and adding the labor cost incurred with them the model arrives at a solution including not only PM and CM cost and their associated economic losses but include the labor cost. This gives a model that accounts for most maintenance costs. For this model, the total cost of around $6.5 million for the one year and around $23 million for the three year model.

So, from the results the model shows that applying the right work force and performing PM in accordance with CM can save approximately $26.5 million over a one year horizon and around $75.6 million over a three year horizon.

References

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