Thesis Msc Technology and Operations Management
If down, do.
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Abstract
The aim of this research is to come up with a fast method to estimate the time to repair (TTR) when a failure occurs. When the TTR is estimated, this can be used to schedule preventive maintenance tasks, which can be performed during the reparation of the breakdown. This will be called the ‘if down, do’ principle. Using this special case of opportunistic maintenance, the total downtime of the factory will be decreased, which will lead to more throughput and more profit in the end. The TTR estimation is done for a production process with multiple units in series configuration with perishable goods, because eliminating downtime in such a production process will gain the most.
First, the TTR is explained and the composition of this TTR is provided. Afterwards the ‘if down, do’ principle will be explained more detailed and certain methods of TTR estimation are given. The selected method of estimating the TTR is examined within a case study at FrieslandCampina. The data of this company is analyzed and based on this analysis a method is chosen, which will be a reliable method for this environment.
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Preface
Since February I have done a research at FrieslandCampina Bedum for my final thesis of the master degree Technology and Operations Management at the University of Groningen. Now it is finalised and I am satisfied and proud of the final version of my Master thesis. While I was writing this thesis, I learned a lot about the subject, but also about myself and the company involved. It was an interesting experience which helped me to apply my knowledge, gained over the last years studying, at an actual problem within a company. The company involved, Royal FrieslandCampina Bedum, was very benevolent and assistant. All data and information needed was provided by the company. Unfortunately the data needed was not available at FrieslandCampina. Therefore the approach of my research needed to change.
I would like to thank everyone who had helped me during the last months. First of all I would like to thank dr. N.D. van Foreest for being a great supervisor during the project. For every little thing he was there to provide advice and feedback and to think along. Even when there was a problem during my thesis about the data I needed, he helped me to continue completing my thesis by giving new insights on how the problem can be looked at.
I would also like to thank my supervisor of FrieslandCampina Bedum Edwin Kreder for always giving a warm welcome. For every question he took time to help and he was always available for providing data needed for my thesis.
After all I would like to thank my fellow students who also did their thesis at FrieslandCampina. Due to the meetings we had, new insights were born. And because of the reviews given on my thesis I was able to deliver this thesis.
June, 2014
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Table of contents
1. Introduction ... 7 1.1 Motivation ... 7 1.2 Earlier work ... 8 1.3 This research ... 9 1.4 Research questions ... 10 2. Theoretical background ... 11 2.1 Opportunistic maintenance ... 11 2.2 Time to repair (TTR) ... 12 2.3 Conceptual model ... 16 3. Findings ... 17 3.1 Data collection... 17 3.2 Data Analysis ... 19 4. Results ... 21 4.1 Entropy maximization ... 214.2 Practical use at FrieslandCampina ... 24
4.2.1 One employee ... 24
4.2.2 Multiple employees with nearly the same opinion ... 24
4.2.3 Multiple employees with a completely different opinion ... 26
4.3 Model ... 27
5 Conclusion ... 29
6 Discussion ... 30
References ... 31
Appendix ... 33
Appendix A: OEE FrieslandCampina... 33
Appendix B: Lognormal Distribution ... 35
Appendix C: Data ... 36
Appendix D: Model ... 37
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Appendix D.2 Output ... 38
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1. Introduction
Every company in the production industry will have downtime, which can have a significant negative impact on profit (Waeyenbergh & Pintelon 2004). This is mainly because a long downtime will cause a loss of throughput when the production stops (Enginarlar et al. 2002). Furthermore the downtime will cause high levels of system variation relative to processing time variation or setup time variation, which will cause a lower throughput (Patti & Watson 2010). At the end, a production company wants to achieve the highest throughput possible, because this is their revenue.
With a good maintenance strategy, the downtime can be lowered and this can improve efficiency, productivity, quality and decreasing prices. This will lead to a higher level of customer satisfaction and eventually to an increased market share. Furthermore, profitability and prosperity are achieved (Waeyenbergh & Pintelon 2004). A good maintenance strategy can be opportunistic maintenance, which might decrease the downtime. Opportunistic maintenance refers to the situation in which preventive maintenance is carried out at opportunities, either by choice or by restriction, and might decrease the total downtime (Dekker et al. 1997). However, there is no framework available in literature which shows how to act structurally during an opportunity. Therefore a principle will be created, which will be named the ‘if down, do’ principle. The ‘if down, do’ principle will be used to provide a framework for a possible planning for doing preventive maintenance tasks during the unplanned downtime. This framework will be used to come up with a planning of preventive maintenance tasks as soon as possible when a failure occurs. The first step after a failure is estimating the time available for the preventive maintenance tasks, so the schedule can be fitted in this time span. Because of the fact the time to repair (TTR) needs to be determined immediately after a failure, there is also a time constraint: all time spent on determining the TTR will reduce the time left for preventive maintenance. The aim of this research is to come up with a fast method to estimate the time to repair (TTR) when a failure occurs.
The first chapter is divided into four sections. The first section will explain why this research is necessary and why it is interesting. Section 1.2 will provide earlier work on this subject. This research will be clarified in section 1.3 and in the last section the research question are provided. At the end of this research these research questions will be answered.
1.1 Motivation
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Using the ‘if down, do’ principle the total downtime can be reduced. The preventive maintenance will be applied during the unplanned downtime. Therefore, there will be two maintenance lines parallel to each other. This will mean that the total preventive maintenance duration can be reduced by the total duration of the unplanned downtime.
However, the downtime will not only decrease by combining the preventive maintenance with the breakdowns. Using preventive maintenance, the lifetime of a machine will increase and the number of breakdowns will be reduced (Samet et al. 2012).
Most published research on preventive maintenance only deals with single-unit systems, while almost every company holds a multi-unit systems (Zhou et al. 2009). Downtime for a multi-unit system with multiple units in series configuration is even more undesirable. This is mainly because of the fact that when one machine will be down, starving and blocking will occur in the other machines, which implies, every machine will be down. In a production company with perishable goods, downtime can cause perishing of the product. In these companies it is even more important to act immediately, as every minute of wasting time could mean the product can be wasted. This research will focus on opportunistic preventive maintenance for a company with multiple units in series configuration with perishable goods.
1.2 Earlier work
The ‘if down, do’ framework will start with the question how long the unplanned downtime will be before providing a schedule of tasks possible in this time. The unplanned downtime is characterized by the mean time between failures and the mean time to repair (MTTR) (Patti & Watson 2010). To estimate the duration of a failure during the breakdown not the MTTR but the TTR needs to be estimated. The TTR defines how long it takes to restore the functionality of the equipment of its failure (Gupta et al. 2013).
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1.3 This research
This research provides a case study analysis within Royal FrieslandCampina in Bedum. FrieslandCampina Bedum is a company that produces cheese and has whey as a by-product. Whey is used for producing infant food. There is a very high demand at infant food, which implies it is important to produce as much whey as possible. This will be realized when the throughput of the cheese factory is as high as possible and the downtimes are low. Furthermore, due to the milk quota abolition, FrieslandCampina Bedum expects to have a higher throughput, which means the availability of the machines needs to increase.
The products in the production process of FrieslandCampina are perishable. The shelf life of the product when the process is down is normally fifteen minutes. However, when the process will be down for sixteen minutes, the product can be used. The quality of the product might be decreased and therefore a sample is needed to test whether or not the quality of the product is high enough and the product can be sold. The longer the product is in the process while it is down, the harder it will be to get it out. Because the whey will be more crushed out of the curd, as the curd will be dryer and thicker. It will be the safest to keep in mind that the downtime needs to be below fifteen minutes.
FrieslandCampina produces continuously, with multiple machines in series configuration. This means that when one machine shows a failure, the whole production process will be down. The production line is not down that often, but every downtime is waste. To maximize their profit, they want to minimize their downtime as much as possible. Right now, when a failure occurs all the employees of the technical services are focused on the failure, while it might be more efficient if only one employee will repair the failure. The other employees can do preventive maintenance, instead of just panicking about repairing the failure as soon as possible.
Looking at the downtime data of Friesland Campina (Appendix A) for a certain part of the factory in the period of 2012 until now, the unplanned downtime was 923.3 hours, while the planned downtime was 178 hours. The total downtime can be reduced by applying the preventive maintenance parallel to the unplanned downtime, which implies the downtime can be reduced by 178 hours in the best case scenario. This is a reduction of sixteen percent. Due to the fact that preventive maintenance will cause fewer breakdowns, it is possible this reduction of downtime will be even higher.
Every hour of downtime will cost FrieslandCampina about €1.250 for the discussed part of the factory. However, when the production line is down, there will be no throughput. This lost needs also be taken into account. With this information, the total costs for an hour downtime will be about €5.000. Using the ‘if down, do’ principle and based on the best case scenario this will save FrieslandCampina about €890.000 yearly. Therefore, this research will be relevant for FrieslandCampina.
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TTR can be determined in a quick and efficient way, so a decision can be made which preventive maintenance tasks can be carried out.
In chapter 2 the theory needed to answer these research questions is provided in the theoretical background. Chapter 3 will provide the findings during the research at FrieslandCampina. These findings will be analyzed and will turn into the results, explained in chapter 4. When the results are known, a conclusion drawn in chapter 5. In chapter 6 there will be a discussion about this research.
1.4 Research questions
The goal of this research is to give an answer on the main research question:
How can the time to repair be estimated in a quick and sufficient way?
To give an answer, first information is needed about the TTR. Therefore the research question is divided in several sub-questions. Hereby the research will be structured and all the parts of the research question will be exposed. To answer the research question the following sub-questions need to be solved:
What is definition of TTR?
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2. Theoretical background
The aim of this research is to come up with a method to estimate the TTR at the moment when a failure occurs. In the theoretical background the theory necessary to give an answer to the sub questions is provided. In section 2.1 there will be an introduction about opportunistic preventive maintenance and how this research fit in this principle. Section 2.2 will discuss the expression ‘time to repair’. The conceptual model is provided in section 2.3.
2.1 Opportunistic maintenance
Maintenance can be divided into planned and unplanned maintenance (Veldman et al. 2011). Unplanned maintenance occurs when a machine fails (Veldman et al. 2011). When this happens a member of the maintenance staff needs to stop with everything he or she was doing to repair the failure. It will cost extra man hours and it will stop production for the time being (Bolton 2010). Planned maintenance is also called preventive maintenance (Veldman et al. 2011). Opportunistic maintenance combines these two types of maintenance.
Flynn (1989) describes opportunistic maintenance as the use of preventive maintenance when a failure occurs. At that moment, the machine needs to be shut down and will cause starving downstream and blocking upstream. Therefore, the total production process will be down. After the repair, the machine can be restarted and will feed the machines behind gradually. It will take some time before the products are reaching the end of the line, so preventive maintenance can be done behind the machine where the failure occurred (Flynn 1989). In fact the preventive maintenance will be done by walking in front of the first product coming from the repaired machine.
Zhou et al. (2009) describe an opportunistic maintenance strategy in which they combine the preventive maintenance tasks of multiple units in series. Using the opportunistic maintenance strategy it is assumed that at the time a preventive maintenance action is performed on a unit, the whole system has to stop because of the serial form, and so there is an opportunity for maintaining the other units. However, using this model, the production line still needs to be shut down for preventive maintenance tasks, which will cause downtime.
In contrast to Flynn (1989) and Zhou et al. (2009) in this research it is assumed that preventive maintenance tasks are applied at the same time as the repair of the unplanned downtime caused by failures: ‘if down, do’. Using this principle, the production line does not need to shut down for preventive maintenance, because it is already down. The ‘if down, do’ principle states that by doing preventive maintenance tasks during the corrective maintenance the total downtime will reduce. Therefore the following three steps need to be fulfilled:
1.
The first step of the ‘if down, do’ principle is to determine the TTR. In order to do your12
this step is done well, otherwise an adequate schedule for preventive maintenance tasks cannot be created. When the TTR is estimated too long and the realized repair time is shorter, the preventive maintenance tasks are already done. Therefore time will be lost because there is no parallel line for preventive maintenance tasks. When the TTR is estimated too short, the line will be down because the preventive maintenance tasks are not done yet.
2.
The second step is to find out which preventive maintenance tasks are available at the moment a failure occurs or in the near future.3.
Finally, the two results need to be combined and a schedule can be made about which preventive maintenance tasks can be done during the TTR.In this research the first step will be examined. The second step is research by De Wolf
(2014) and the third step is explained in the research of Schuurman (2014).
2.2 Time to repair (TTR)
The time to repair is the estimated time needed to repair the breakdown or failure on a machine. For this research, this TTR will be derived from a certain probability distribution and will be defined as: The time that is less than or equal to the realized repair time for a certain service level (S) or:
( ) ( ) Equation 2.2_ 1
To determine the TTR the distribution of the probabilities needs to be known. The TTR is assumed to be a lognormal distributed variable (Guo et al. 2008; Wang et al. 2005). This is based on extensive analysis of field data which have shown that the lognormal distribution provides a good fit to the data. However, when a lognormal assumption does not hold, a distribution free method should be employed (Anon 1973). X has a lognormal distribution if Y = ln(X) has a normal distribution (Mitzenmacher 2004). Mitzenmacher (2004) provide a distribution function for a lognormal distribution: ( ) √ ( ( ) ) Equation 2.2_ 2 In which:
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Figure 2.2_ 1 Lognormal distribution
A characteristic of the lognormal distribution is the shape, a high peak with a long tail. When x has a lognormal distribution, then in a log-log plot the graph will be nearly a straight line for a large part of the distribution. When the variance is large, the distribution may appear linear on a log-log plot (Appendix B). The shape of the graph depends on the mean and the standard deviation. This mean and standard deviation can be determined by the following functions:
∑ Equation 2.2_ 3 √ ∑( ) Equation 2.2_ 4
Using these equations a probability distribution can be made. Using data of previous failures will give the mean and standard deviation, which can be used to solve the distribution function for the lognormal distribution.
The TTR consists of multiple actions, as time for preparation, fault verification, spares procurement, actual repair, testing and administrative work. The TTR is determined by adding all the times of these small activities which all have a variance (Gupta et al. 2013). Because every step of the TTR can contain a variance, the summation of these steps, which will be the TTR, can have a large variation. In figure 2.2_2 the composition of the TTR can be seen. To determine the TTR all the parts of this variable needs to be taken into account, or there needs to be a good declaration why it does not need to be in the determination. Therefore, every task will be explained and discussed whether or not it will be taken into account for the determination of the TTR.
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Time for preparation
Time for fault verification
Time to spares procurement Actual repair time
Duration of testing
Time for administrative
work
Figure 2.2_ 2 Composition TTR
Time for preparation consists of collecting the right tools. Walking to the warehouse for
collecting the right tools is considered a constant for each breakdown. This will not be taken into account though, because the TTR, resulted from the model, will be used to schedule preventive maintenance tasks. For these tasks, tools are also necessary and it will take the same amount of time to collect these.
Fault verification consists of discovering why the failure occurred and what needs to be done
to repair it. This will not be included, because this needs to be done before estimating the TTR. Just after the fault verification the TTR will be determined.
Spares procurement will be combined with the time for preparation. After all, both the spares
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For every failure it will be possible to take the right spares and tools in only one walk. Spares procurement will not be taken into account for determining the TTR
Actual repair is the time needed to repair the failure. This is basically what the TTR is about,
therefore the actual repair time is taken into account.
Testing is the time after the repair but before the production process will continue. Testing will
also been done during the repair and there is no possibility to separate these two steps. Therefore also the testing time will be taken into account.
Administrative work is for example maintaining the OEE file. With other words,
administrative work is the work to keep the data of FrieslandCampina up to date. This will be done after the restart of the production line. Therefore it will not be used for determining the TTR.
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2.3 Conceptual model
Based on the theoretical background the conceptual model will be presented. The conceptual model is shown in figure 2.3_1 With a reliable and plausible TTR, a suitable preventive maintenance schedule can be built. The better and reliable the TTR, the better and more appropriate the schedule will be. With a more appropriate schedule for the preventive maintenance tasks, the total downtime will be less. At the same time the total preventive maintenance duration can increase, because there is more time to do preventive maintenance, as the line does not have to shut down to provide preventive maintenance. Therefore it will not take an extra amount of time to apply preventive maintenance. More preventive maintenance will cause less breakdowns and failures and so the downtime will decrease even further. Less downtime will cause more availability and so a higher throughput what will cause more profit.
Reliability TTR
Fitting preventive maintenance
schedule
Total downtime Throughput Profit
+ - - + Amount of Preventive Maintenance Number of failures Lifetime of the machines + + -- +
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3. Findings
This chapter will provide the findings at FrieslandCampina. In the first section there will be explained how the data is collected. Afterwards this data is analyzed in section 3.2
3.1 Data collection
In the introduction and theoretical background the problem is introduced and is proved this research will fill up a gap in literature. However, it is not tested for FrieslandCampina. To be sure the problem is present at FrieslandCampina, the employees of the technical services will be asked if the problem is really relevant for FrieslandCampina. The employees of the technical service are related to the scope of the problem and will understand whether or not the problem is relevant for FrieslandCampina Bedum.
The research question: ‘How can the expected time to repair be estimated in a quick and
sufficient way?’ will lead to a case study, supported by the fact that the downtime is a contemporary
event and there is no control of behavioral events required. Furthermore a non-existing problem is explored.
The goal of the research is to come up with a model, which will tell FrieslandCampina Bedum how much time there will be during a breakdown, so a planning of preventive maintenance tasks can be made. This way, there is a support, and there is no need to make decisions in a crisis situation. However, it is only a recommendation, the real decision will be made by FrieslandCampina Bedum, and so this research will be a case study, combined with a decision support system.
To analyze the problem the right data needs to be exposed. The right data for this research will be the durations of the downtime for a certain department of the factory, so the scope will not be too big. To keep the data up to date, only data of the past two years will be used, from 2012 until now. These data will be used to compose a probability distribution so the TTR can be determined.
To prevent a too wide scope, FrieslandCampina has chosen a machine which will be appropriate for this research. The Conomatics are the part of the production process where the curd will be pumped into barrels before they go into an immersion. This part of the process produces 24 hours a day and therefore it is very important that the downtime of the Conomatics needs to be minimized. Furthermore, the Conomatics have a certain amount of failures, so that is why there will be data available about the breakdowns and their durations.
To understand the problem, first of all it is necessary to understand the production process at FrieslandCampina. Therefore the working principle of the Conomatics needs to be analyzed. An employee of FrieslandCampina described and explained the production process with in particular the Conomatics. By understanding the production process, the data is better to understand.
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in which they divide the downtime into planned and unplanned downtime. For this thesis the focus will be at the unexpected downtime, the breakdowns and failures. From their OEE file the data for the unexpected downtimes can be obtained. In this file a selection can be made about the part of the production process for which the data is needed. In this research, only the data about the Conomatics will be used.
By talking to an employee of the technical service, more information is gathered about how the breakdowns are divided and furthermore about how the duration of the breakdown is realized. It might be that some of the data is not reliable for any reason.
To be sure the data is reliable, interviews are arranged with multiple employees with different functions within FrieslandCampina. By talking with these employees, a clear view is created about how the problem is existing within the company. Furthermore they can tell whether or not they believe if the ‘if down, do’ principle will work for FrieslandCampina. They can also tell what will happen when a failure occurs.
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3.2 Data Analysis
Using the data gathered from the OEE file and the interviews with the employees of FrieslandCampina, all details of the unplanned downtime can be requested. All the data of the unplanned downtime can be plotted in a graph and is shown in figure 4.2_1
Figure 3.2_ 1 Breakdown distribution
From figure 3.2_1 can be derived that the TTR at FrieslandCampina comes close to the shape of the lognormal distribution with a high peak in the beginning and a tail towards infinity. When this graph is changed into the probability distribution and the data of the graph is used to create the lognormal distribution the two graphs can be plotted in one figure 3.2_2
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The shape of the two graphs are quite similar except for the variations in the real data. Therefore there can be assumed that the lognormal distribution is a suitable distribution for the TTR within FrieslandCampina.
With this knowledge an estimation of the TTR can be made. However, it will not be very specific. Therefore the data needs to be specified in multiple categories as: employee, part of the machine; description of the failure, etc. With this, the variation might be lowered.
In the OEE file, for every failure the following categories are specified: name of the factory; name of the machine; start time; description of the failures; duration (Appendix C). However, there is no specification about which employee repaired the failure and also the descriptions of the failures are not that specific. Therefore it is impossible to make multiple categories for the different types of failures. Furthermore, the file cannot be used to determine the TTR, because FrieslandCampina works with sheets which the employee needs to fill in by itself. It will probably be that the data is not precise, because they can also fill it in days after the breakdown. A solution would be to collect the data by observing the breakdowns, however this will take a lot of time because there are a lot of different breakdowns possible and they do not occur that often. So gathering enough reliable data with the right specifications will take too long.
Furthermore, FrieslandCampina tries to avoid repeated failures. Whenever a certain failure occurs multiple times, they will start a research to find a solution for this problem. Therefore, the data and the breakdown durations available at FrieslandCampina is not reliable enough to come up with a trustworthy model for determining the TTR.
The employees of the technical services are professionals and they know the production process of FrieslandCampina by heart. To make a distribution of the TTR, the best data can be obtained by asking the available employees to estimate the duration of the repair.
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4. Results
As can be concluded from the findings from chapter 3, the original idea of providing a probability distribution to the data of FrieslandCampina is not usable for this company, because of the fact there is no data available which can be used to fill in the equation of the lognormal distribution. This will probably be the same case for many other companies, because of the precise data needed, the absence of repeatable failures and employees knowing the process better than anyone and anything else. Therefore a new research question came up:
How can the TTR be estimated in a quick and sufficient way when the current data cannot be used to provide a probability distribution?
In this chapter there will be provided an answer to the new research question. In section 4.1 the principle will be introduced what is needed to estimate the TTR. Section 4.2 will explain how this principle can be used at FrieslandCampina. This knowledge is used to build a model provided in section 4.3
4.1 Entropy maximization
The answer to the new research question needs to give a method to determine the TTR for which ( ) ( ). Therefore a probability measure is needed. To find this probability measure, data is needed. The data available is the estimations about the TTR from the employees. A distribution needs to be made with only one estimation as input data. This estimation can be seen as the expected value of a distribution. The expected value can be determined by the following equation (Hamming 1991):
( ) ∑ Equation 4.1_ 1
However, with only an expected value, there is not a distribution of the TTR. Hamming et al. (1991) states that when there is not enough information to determine the whole probability distribution, the maximum entropy principle can be used to determine a probability distribution.
Entropy is basically the measure of uncertainty and can be calculated by the formula (Rényi 1987; Hamming 1991):
( ) ∑ Equation 4.1_ 2
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To maximize the entropy function, multiple constraints are necessary. First the sum of the probabilities needs to be one. However every chance needs to be positive to create a reliable distribution. And finally the expected value fitting to the distribution is a constraint, in this case 4.5. These three constraints will lead to the following linear programming problem:
( ) ∑ Equation 4.1_ 3 Subject to: ∑ Equation 4.1_ 4 ( ) ∑ Equation 4.1_5 * + Equation 4.1_ 6
This mathematical problem can be solved with the solver of Microsoft Excel and will give the cumulative probability distribution given in figure 2.4_2
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This principle can also be used for the probability distribution of the TTR. However the solver in Microsoft Excel will take a long time before calculating the right distribution, while one restriction of this research is that when a failure occurs there needs to be an answer quickly.
When the expected value is known in the maximum entropy distribution and this is the only constraint, the probability distribution is given by (Kapur & Kesavan 1992):
( ) Equation 4.1_ 7
Where ‘c’ and ‘k’ are constants which can be solved by the following equations (Kapur & Kesavan 1992):
∫ Equation 4.1_ 8
∫ ( ) Equation 4.1_ 9
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4.2 Practical use at FrieslandCampina
The equations provided in section 4.1 will be used to provide a probability distribution to come up with a TTR. This TTR will be based on the expectations of the technical service and the service level they want to achieve.
When a failure occurs at FrieslandCampina there are in general three situations possible:
– One employee. When there is only one employee available, there will also be just one expected value.
– Multiple employees with nearly the same opinion. With multiple employees, also multiple expected values are available. These expected values can be close to each other. This means that the input data has low variation
– Multiple employees with a complete different opinion. In this situation the expected values of the employees lie far apart. Therefore the expected values have high variation.
These three situations will be explained in the next sections
4.2.1 One employee
When one employee is available at the moment a failure occurs there is no variation present so we can use the function given for only the constraint of the expected value (Kapur & Kesavan 1992):
( ) Equation 4.2.1_ 1
This equation will be reliable for the range [0;∞]. The equation needs to be rewritten in the right form so it can be used to determine the probability distribution. This will give the following equation:
( ( )) ( ) Equation 4.2.1_ 2
4.2.2 Multiple employees with nearly the same opinion
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√ ( )
Equation 4.2.2_ 1
However, the TTR has not got a range of [-∞;∞] though, it will always be positive. To be sure there will be no data lost, a certain percentage of the distribution needs to be above zero. Using the normal distribution, two times the standard deviation plus and minus the mean will contain 95% of the probability distribution (figure 4.2.2_1 & equation 4.2.2_2)
Figure 4.2.2_ 1 Normal distribution
Equation 4.2.2_ 2
When we take 95% as reliable, this area needs to be in the positive section of the graph:
Equation 4.2.2_ 3
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4.2.3 Multiple employees with a completely different opinion
When the employees available have a completely different opinion, equation 4.2.2_3 will not be true. When the normal distribution will be used anyway, the probability distribution will be as in figure 4.2.3_1.
Figure 4.2.3_ 1 Normal Distribution high variance
As can be seen, the distribution goes negative. These probabilities will be lost when it is about the TTR, because this cannot have a negative value. In this case, the cumulative distribution is already 12% when it will become positive. So this distribution cannot be used, because it is not a reliable approximation.
To solve the problem occurred for multiple employees with high variance, there needs to be a numerical solution where the variance will be included in the probability distribution. For now it is only possible to determine the mean of the given expected values and treat it just as one expected value. However, this is not a reliable solution, because of the lack of variability between the different expected values. Therefore, for now it is assumed there is no reliable solution for this problem.
The only way this problem can be handled for now, is assuming that when the expected values are completely different, they are not likely to be true. Therefore, when the variation is too high, the employees need to realize why the expected values are that far apart. By communication the employees need to come up with expected values closer to each other.
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4.3 Model
Using the equations out of chapter 4.1, the probability distribution can be determined for two out of the three situations. Using Microsoft Excel, a model is created. The input of the model is the expectations of the employees and the service level they want to achieve, as can be seen in appendix D.1. When this data is filled in, they can hit the button ‘start’. The model will search whether there are one or multiple expected values filled in. When there are multiple values it will determine whether the values have high or low variation.
When there will be a high variation between the different opinions of the employees, the model will give an error, because for now there is no good solution for this problem. The only solution for now will be to use the mean of the expected values. However this will not be reliable enough. The employees will need to discuss why there is such a different in the different expected values of the employees and need to come up with a consensus.
The output of the model can be seen in Appendix D.2. It will give two graphs, one of the cumulative probability distribution and one of the probability distribution. Furthermore it will give a TTR belonging to the given service level and the service level belonging to a TTR of fifteen minutes, the point where the quality of the product might be decreasing. These results will only help the employee to make a decision: a decision support system. At the moment the employee knows which TTR they want to use for providing preventive maintenance tasks, this TTR can be used as input for a schedule of preventive maintenance tasks.
The use of the model is very primitive. The only input the model needs is the expected values and the desired service level. By simply clicking on the ‘start’ button, the results of the model will be provided. By hitting the ‘back’ button, the home screen will be shown again. With this principle the model is easy to use and it will take only a moment to determine the TTR. These were two constraints the model needs to fulfill. This way all the employees can use the model.
To test whether or not the model is usable for FrieslandCampina, the model is presented to FrieslandCampina, so they can use it for a while. An explanation about how the model works (Appendix E) and a short introduction about how the result is realized will be given. The model will be used at FrieslandCampina for a certain time so they can explore the model and use it in the testing period.
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5 Conclusion
When data is available, the lognormal distribution can be used to provide a probability distribution. With this distribution, a TTR can be determined, given a certain service level. However when data is not available or not reliable enough, the maximum entropy principle can be used.
FrieslandCampina maintains their data quite well, however their data is not reliable enough to determine the TTR based on the data of the past. Furthermore they try to avoid repeatable failures. Therefore it is hard to determine the TTR based on the data of failures of the past. Knowing that the employees of the technical service are specialists on their production line, it seems better to use the knowledge of the employees to determine the TTR.
When there is not enough data to create a possibility distribution function, the maximum entropy principle can be used (Hamming 1991). With the maximum entropy principle a distribution of the probabilities can be determined. There can be three situations for estimating the TTR: One employee will give an expected value, multiple employees will give their opinion about the TTR and basically agree, so the variance is low, or they absolutely do not agree and the variance is high. For the first two situations a distribution can be composed. The last situation is not solvable for now. They need to come up with a consensus and commit that their own estimation will probably not be reliable.
The probability distribution is the output of a model, while the input will only be the expected values of the employees and the service level they want to achieve. The model shows how long the TTR will be for a certain service level. This TTR will be used to provide an adequate schedule of the preventive maintenance tasks necessary at that moment.
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6 Discussion
During the research became clear that FrieslandCampina eliminates recurrent failures and their data is not usable for determining the TTR. The research needed another solution to determine the TTR. For other companies it may be that there are repeated failures and reliable data of these failures. Then, the entropy maximization is not necessary. A distribution can be made based on the data available and from this distribution a TTR can be given a certain service level.
The service level tells how certain it will be that the realized repair time is smaller or equal to the TTR. When the actual repair time is smaller than the TTR, the production process will still be down when the preventive maintenance tasks are not ready yet, whereas the intention of the ‘if down, do’ principle is to eliminate downtime. However, all the time where the preventive maintenance is done during the repair of a failure is gained, because the production line does not have to shut down, only for the preventive maintenance tasks. On the other hand, the actual repair time can be longer than the TTR, this will be less of a problem: the preventive maintenance tasks will be done while the repair of the failure takes longer. In this situation the same applies: all the time where the preventive maintenance and corrective maintenance are done at the same time is gained.
The model can only be tested reliably, when it will be used for a longer time. This makes it clear whether or not the service levels are correct. The couple of weeks testing at FrieslandCampina cannot give certainty about whether or not the outcome of the model is trustworthy. Because it might be that at an expected value of fifteen, the realized repair time will be one hour. According to the model there is only a chance of 0.1%, but it is possible. By testing the model a longer time and documenting the realized repair time of the failures, the possibility distribution can be justified.
When it is justified the distribution is reliable, the model can be used for the principle it is created for. The whole principle of ‘if down, do’ needs to be tested. By testing the principle, it can be said whether or not the total downtime will be actually less than before.
For now there is no solution when there are multiple employees with a completely different opinion about the TTR. There needs to be a numerical trick to take the variation between the expected values into account. It is recommended to do further research on this topic.
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Appendix
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The TTR (time to repair) is the amount of time necessary to repair an unexpected breakdown of a machine. This TTR only consists of the actual repair time and the testing phase, so from the moment the employee starts working on the repair until the moment the production process restarts. This TTR will be determined using a probability distribution based on the expected values of the technical service. This technical service has a lot of experience in this production process and knows their system really good.
Normally there are three situations for estimating the TTR: – One employee available one expected value
– Multiple employees with nearly the same opinion Multiple expected values with low variation
– Multiple employees with a complete different opinion Expected values with high variation
The model can be used for all three situations. Every employee available and involved in the breakdown area needs to fill in the expected value at the E(X) position. The rest of the input needs to be empty (-). For the service level can be filled in every value desired. This service level tells what the possibility is that the TTR is lower or equal to the realized repair time. After filling in the input click on the button ‘start’.
The output of the model consists of two graphs. A cumulative distribution and a distribution of the probabilities. For FrieslandCampina the table in the upper right corner is the most important part of the output. This table will tell the TTR given for the service level provided by the input. Furthermore the service level will be given for a TTR of fifteen minutes. Fifteen minutes is the point where the quality of the product will decrease. Based on the output of the model, the TTR can be chosen and with this TTR a schedule can be created for the preventive maintenance tasks.
When the expected values of the employees differ drastically, the output will give an error. The expected values are not a reliable base to create a trustworthy estimation of the probability distribution. To create a probability distribution anyway, the employees need to deliberate and come up with expected values closer to each other. This situation will be very rare, because when the expected values differ that much, they will probably not very plausible.
