University of Groningen. Maintenance Optimization based on Mathematical Modeling de Jonge, Bram

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1 University of Groningen Maintenance Optimization based on Mathematical Modeling de Jonge, Bram IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2017 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): de Jonge, B. (2017). Maintenance Optimization based on Mathematical Modeling [Groningen]: University of Groningen, SOM research school Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 Chapter 1 Introduction Due to ongoing automation of production processes and increasing reliance on expensive production equipment, the importance of effectively planned and performed activities is growing. A few decades ago, was seen as a necessary evil: something that has to be done if equipment breaks down, but also something that is difficult to manage. Nowadays, is more and more seen as a profit contributor. Organizations realize that efficiency and reliability can be improved and costs can be reduced if actions are planned more effectively. As a result of the growing importance of, both the portion of employees working in and the costs are increasing (Zio and Compare, 2013). Over a quarter of the total workforce in the process industry, and up to 30% in the chemical industry, deal with operations (Waeyenberg and Pintelon, 2002). In refineries, the and operations departments are usually the largest (Dekker, 1996). Furthermore, costs typically account for 15-70% of the total production costs (Bevilacqua and Braglia, 2000; Mobley, 2002), and the amount of money spent on of engineering structures and infrastructures is increasing continuously (Van Noortwijk, 2009). Medical equipment nowadays demands large sums from hospital budgets (Cruz et al., 2014), and companies in process and chemical industries can significantly increase profits by avoiding unplanned stoppages and bad quality production (Alsyouf, 2007). Maintenance can be defined as all activities necessary to restore equipment to, or

3 2 Chapter 1 keep it in, a state in which it can perform its designated functions. This definition immediately makes clear that two types of actions can be distinguished. Maintenance can be performed after a failure or breakdown, and is then called corrective or reactive. The other type of is called preventive and is performed when equipment is still functional. It aims to prevent or postpone failures. Because potential consequences of failures include safety issues, machine damage, quality issues, unexpected machine unavailability, long repair times, and unplanned actions, it is often preferred to perform activities preventively. However, because performing preventive too often is also undesirable and costly, a balance between the preventive frequency and the risk of failures has to be found. Maintenance Corrective Preventive Time-based Condition-based (CBM) Opportunistic Age-based Block-based Continuous monitoring Inspections Figure 1.1: Schematic overview policies. A schematic overview of commonly used policies is shown in Figure 1.1. This figure indicates that a further subdivision of preventive policies can be made. Preventive actions can be based on the time that equipment is in service (i.e., time-based ; TBM), but if there are specific features that are related to the degradation process that ultimately leads to failure, and if it is technically possible to monitor these features, condition-based (CBM) allows for activities that are performed based on degradation information. For multi-unit systems it is often suboptimal to schedule actions on

4 Introduction 3 the unit level. This is caused by dependencies that generally exist between units. Dependencies that are often mentioned in the literature are economic, structural and stochastic dependence (e.g. Laggoune et al., 2010; Thomas, 1986). Economic dependence exists if cost savings can be obtained or downtime can be reduced by clustering actions. Structural dependence exists when the functioning of a system in some way depends on the functioning of various components or sub-systems. Stochastic (or probabilistic) dependence exists when lifetimes or degradation processes of various units are stochastically dependent. When dependencies between units exist, the use of opportunistic policies is often appropriate. Such a policy uses a preventive or corrective action for a certain unit as an opportunity to maintain other units as well. Age or condition information of the other units are often used to determine whether they are maintained as well. Two time-based preventive policies can be distinguished: age-based and block-based. Under the age-based policy, preventive is performed when the unit reaches the prescribed age T, or corrective is performed when the unit fails, whichever occurs first; see Figure 1.2 (a). Under the block-based policy, preventive is performed after fixed intervals with length T. Corrective is again performed when the unit fails, but failures do not affect the preventive schedule when this policy is applied; see Figure 1.2 (b). The disadvantage of block-based is that preventive is sometimes performed shortly after a failure. The main advantages, on the other hand, are the easier planning as it is known in advance when preventive will be performed, and the clustered actions when the same block-based policy is applied to multiple units. Time-based is easy to implement as only the time that a unit is in service has to be recorded. However, substantial remaining useful life is wasted if the machine is still in reasonable condition when preventive is performed, and a breakdown might occur if it happens to deteriorate faster than expected. Condition-based, on the other hand, generally results in more effectively scheduled preventive, and, in the ideal case, preventive that is performed just before failure. However, applying CBM is only possible if there are conditions that are related to the moment of failure, and if it is technically

5 4 Chapter 1 T T T T Failure (a) Age-based. Failure T T T T T Failure Failure (b) Block-based. Figure 1.2: Scheme of time-based policies. possible to monitor these conditions. Furthermore, CBM should only be applied if its benefits outweigh the efforts and costs required to apply it. These requisites include condition monitoring equipment and software to store and analyze data, and initiate actions. Whereas only a lifetime distribution needs to be specified to study time-based models, the analysis of a CBM model requires the modeling of the deterioration of a unit. Commonly used approaches in the literature range from the delay-time model that only adds one deterioration state in between the operating state and the failed state (Wang, 2012) and models with a finite number of deterioration states, to continuous-state and continuous-time models as the gamma process and the Wiener process. Figure 1.1 distinguishes two types of condition-based policies based on the frequency at which deterioration information becomes available. The condition of equipment can either be monitored continuously, or inspections might need to be performed to obtain actual deterioration levels. The main drawbacks of continuous monitoring are that it is often expensive because special devices are required, and that the continuous flow of data creates increased noise (Jardine et al., 2006). Inspection-based CBM, on the other hand, has the disadvantage that it has the possibility of missing substantial deterioration increments in between inspections. When inspections are required to obtain condition information, either a periodic or an aperiodic inspection schedule can be adopted. Periodic inspections have the advantages that they are easier to implement in an industrial context (Deloux et al.,

6 Introduction ; Zequeira and Bérenguer, 2006), that they allow the necessary manpower and budget to be anticipated and scheduled well beforehand (Van Noortwijk and Klatter, 1999), and that they are much easier to optimize as the entire inspection schedule is dictated by the specification of a single inspection interval. However, it is often much more effective to use an aperiodic inspection schedule that dynamically schedules the next inspection based on actual condition information (e.g. Dieulle et al., 2003; Grall et al., 2002; Maillart, 2006). 1.1 Outline and approach This thesis contributes to the current research on planning and optimization. We study the effect of uncertainty in the lifetime distribution on the optimal age-based strategy, and analyze whether it can be beneficial to make suboptimal decisions during the first phase of the lifespan of equipment in order to reduce this uncertainty faster. Thereafter, we broaden our scope and study how the benefits of condition-based over time-based depend on various characteristics. Finally, we consider the benefits that can be obtained by clustering actions for multiple units based on condition information. The methodology that we use is that of developing and analyzing mathematical models. Algebraic analysis, numerical calculations and simulations will be used to compare and to optimize policies. Research on time-based optimization generally assumes that the lifetime distribution of a unit is known with certainty. In practice, however, this is often not a realistic assumption. There is often a substantial amount of uncertainty in the lifetime distribution because there is usually only a limited amount of data available, the exact interpretation of stored data is often unclear, and times until failure are often not observed due to preventive activities in the past (i.e., data is right-censored). In Chapter 2 of this thesis, we consider the effect of uncertainty in the lifetime distribution on the optimal age-based policy. We also report on the cost consequences of ignoring this uncertainty and point out in what cases it is particularly important to take the uncertainty into account when determining a policy. We start with the case of a uniformly distributed lifetime that can be analyzed algebraically. Thereafter, we continue with the more realistic Weibull lifetime distribution and show that the insights are similar to those

7 6 Chapter 1 for a uniform lifetime distribution. The policies considered in Chapter 2 are static, i.e., a fixed age is chosen that minimizes the long-run expected cost rate under the information that is currently available. However, when a policy is applied, more data becomes available due to failures and preventive actions. In Chapter 3, we do update the uncertainty in the lifetime distribution when more data becomes available. Furthermore, we acknowledge that the uncertainty in the lifetime distribution can be reduced much faster if preventive actions are initially postponed. Although this will increase the expected costs during this first phase of the lifespan of a unit, it also leads to reduced uncertainty in the lifetime distribution for future decisions. As a consequence, preventive can be scheduled more effectively during the remaining lifespan of the unit. In this chapter we investigate the cost benefits over the entire lifespan of a unit, and identify under what circumstances these benefits are largest. The benefit of condition-based compared with time-based strongly depends on the behavior of the deterioration process, the severity of failures, the required setup time, the accuracy of the condition measurements, and the amount of randomness in the deterioration level at which failure occurs. In Chapter 4, we start with a review of studies that compare condition-based with time-based. Furthermore, we review studies that consider the aforementioned practical factors that influence the relative performance of CBM. It turns out that, although both condition-based and time-based have received ample attention in the scientific literature, few studies compare them. Moreover, existing studies that do provide a comparison only consider a few examples; general insights on how the performances of the policies depend on the various characteristics are generally lacking. Therefore, we continue in Chapter 4 with a numerical analysis that does provide insights on the effects of the various characteristics. This analysis is based on simulations of a single unit that deteriorates gradually over time and that is monitored continuously. In Chapter 5, we consider scheduling for a multi-unit system. The specific setting that we consider is that of a system consisting of multiple critical and identical units with economic dependence. Each unit contains a sensor that provides either one signal (alarm) or two signals (alert, alarm). Such systems with only a small number of deterioration states instead of continuous deterioration levels are

8 Introduction 7 very common in industry. Because of the criticality of the units, always has to be performed within a fixed time period after an alarm in order to prevent an impending failure. As a consequence, benefits cannot be obtained by delaying activities. However, due to the economic dependencies between the units, it can be beneficial to cluster actions. We will evaluate the cost performance of two clustering policies and compare it with the policy that does not cluster any activities. Furthermore, we derive general insights on the effects of the number of units, the cost structure, and the mean times until alert and alarm signals. Journal publications The chapters in this thesis are based on the following journal publications. Chapter 2: De Jonge, B., W. Klingenberg, R. H. Teunter, T. Tinga Optimum strategy under uncertainty in the lifetime distribution. Reliability Engineering and System Safety Chapter 3: De Jonge, B., A. S. Dijkstra, W. Romeijnders Cost benefits of postponing timebased under lifetime distribution uncertainty. Reliability Engineering and System Safety Chapter 4: De Jonge, B., R. H. Teunter, T. Tinga The influence of practical factors on the benefits of condition-based over time-based. Reliability Engineering and System Safety Chapter 5: De Jonge, B., W. Klingenberg, R. H. Teunter, T. Tinga Reducing costs by clustering activities for multiple critical units. Reliability Engineering and System Safety

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