Decision support for life extension of technical systems through virtual age modelling

https://doi.org/10.1016/j.ress.2013.02.002Get rights and content

Abstract

This article presents a virtual age model for decision support regarding life extension of ageing repairable systems. The aim of the model is to evaluate different life extension decision alternatives and their impact on the future performance of the system. The model can be applied to systems operated continuously (e.g., process systems) and systems operated on demand (e.g., safety systems). Deterioration and efficiency of imperfect maintenance is assessed when there is limited or no degradation data, and only failure and maintenance data is available. Systems that are in operation can be studied, meaning that the systems may be degraded. The current degradation is represented by a “current virtual age”, which is calculated from recorded maintenance data. The model parameters are estimated with the maximum likelihood method. A case study illustrates the application of the model for life extension of two fire water pumps in an oil and gas facility. The performance of the pump system is assessed with respect to number of failures, safety unavailability and costs during the life extension period.

Highlights

► Life extension assessment of technical systems using virtual age model is proposed. ► A virtual age model is generalised for systems in stand-by and continuous operation. ► The concept of current virtual age describes technical condition of the system. ► Different decision alternatives for life extension can be easily analysed. ► The decision process is improved even when only scarce failure data is available.

Introduction

Many of the oil and gas (O&G) facilities on the Norwegian Continental Shelf are approaching or have exceeded their original design lifetime. However, improvements in extraction technologies and high energy prices have created new opportunities for prolonging the operation of the installations. This has led O&G companies to focus on extending the life of these ageing facilities. Life extension requires sufficient reliability and safety during the additional years of operation. This may be challenging because practically all the technical systems in O&G facilities are subject to ageing and deterioration, and many systems have been in operation for more than 20 years. This means that the systems may be degraded even if they are still operative. In addition, degradation rates may increase during the life extension period and therefore influence negatively the reliability and safety of the systems. Hence, ageing and the degradation level should be included into reliability models for analysing the system performance and assessing a possible life extension, since they will provide valuable information for the decision process. Unfortunately, quantification of ageing and degradation is often not straightforward, due to lack of data.

The modelling of maintenance is also important for studying the performance of repairable systems in O&G facilities. A system is repairable when maintenance actions can bring it back to operation after a failure has occurred. The basic assumptions on maintenance efficiency for repairable systems are that after maintenance the system is As Bad As Old (ABAO or minimal maintenance), or As Good As New (AGAN or perfect maintenance). However, ABAO and AGAN assumptions may not represent the actual maintenance performed to the equipment. In general, components installed in O&G facilities are maintained with both imperfect preventive maintenance (PM) and imperfect corrective maintenance (CM). Imperfect maintenance refers to maintenance actions that partially restore the condition of the component. Hence, models capable of combining both types of imperfect maintenance are more realistic.

This article presents a virtual age model for assessing the life extension of ageing repairable systems which are imperfectly maintained with CM and PM. The virtual age model can be used for life extension assessment of systems operated continuously (e.g., process systems) and systems operated on demand (e.g., safety systems). The main purpose of the model is to study feasible life extension decision alternatives and the consequential future performance of the system. The different decision alternatives may include: (i) replacement, (ii) overhauling, (iii) modification of the system, or (iv) keeping the system in operation without any changes (which is denominated use-up in this article). These decision alternatives are included in the model as maintenance actions performed in addition to the regular PM and CM actions. In this article, imperfect CM refers to maintenance actions performed after the occurrence of a failure to bring the equipment back to operation and partially restore its condition. Furthermore, imperfect PM refers to periodically performed maintenance actions that restore to some extent the component's condition (i.e., does not include inspections or condition based maintenance).

Several imperfect maintenance models have been proposed in the literature. Reviews of imperfect maintenance models are given, for example, by Pham and Wang [1] and Nakagawa [2]. Among them, virtual age models are one of the most commonly used classes of models. Kijima [3] proposed two models that differentiate between the system's age, which is the time elapsed since the system was new, and the virtual age or effective age of the system, which represents its technical condition when compared to a new system. Virtual age models assume that maintenance actions reduce the virtual age of the system, and increasing failure intensities are normally used to describe deterioration. Most imperfect maintenance models consider only one type of maintenance, and this is also the case for virtual age models. Various authors have used the concept of virtual age for modelling either imperfect CM or imperfect PM, for instance Makis and Jardine [4], Doyen and Gaudoin [5], Shirmohammadi et al. [6] and Sheu et al. [7]. However, few authors have combined CM and PM in imperfect maintenance models, normally using virtual age models for describing both types of maintenance. Some examples are Jack [8], and Doyen and Gaudoin [9], who proposed virtual age models which consider imperfect periodic PM and imperfect CM; Doyen and Gaudoin [10] who used a virtual age model which includes imperfect condition-based PM and imperfect CM; and Ramírez and Utne [11] who suggested a virtual age model with imperfect periodic PM and imperfect CM for life extension assessment of ageing systems operated continuously.

Virtual age models are normally applied to systems operated continuously for which failures are detected and repaired immediately, and are not commonly used for components operated on demand. Current practical methods used for assessing the reliability of safety systems assume that the component or system is restored to AGAN condition after a functional test or an inspection is performed, such as IEC 61508 [12] or the PDS method [13]. This assumption makes sense when the components are subject to random failures only (i.e., the failure rate is constant), and when components are not subject to degradation. However, for repairable components whose technical condition worsens due to degradation, a functional test just verifies whether the component is functioning or not, but it does not improve its technical condition. Consequently, some authors have proposed models that make more realistic assumptions, for instance, [14], [15], [16], [17]. However, none consider the use of virtual age models for assessing the life extension of safety systems.

This article extends the model in [11] and introduces a virtual age model that can be applied to both systems operated continuously and safety systems operated on demand. The main difference is that failures in systems operated continuously are detected and repaired immediately, while failures in safety systems are normally detected and repaired after a functional test has revealed the failure. Hence, safety systems require performing functional tests in addition to CM and PM. Functional tests do not have any impact on the component's condition, but they are necessary in order to reveal hidden failures. The model can be applied to components that have been in operation and are already degraded, meaning that the component's condition at the time of analysis is not AGAN. The current degradation is taken into account by using the current virtual age. In the article, real maintenance data from a fire water pump system installed in an O&G facility is used to estimate the model parameters, and obtain a probability distribution describing the current virtual age. Furthermore, the virtual age model is applied to the fire water pump system, which is a two-component parallel system, for assessing the life extension.

The article is organised as follows: Existing virtual age models combining CM and PM are discussed in Section 2. Section 3 introduces the virtual age model developed in this study. Section 4 presents an approach for including the current degradation of a system or component in the virtual age model. Section 5 discusses the application of the model with real maintenance data and estimation of statistical parameters. A case study is presented in Section 6. Finally, conclusions are given in Section 7.

Section snippets

Virtual age models for CM and PM

In the literature, virtual age models considering both imperfect CM and imperfect PM are normally based on arithmetic reduction of age (ARA) models [5], and adopt one of the following approaches:

  • 1.

    Maintenance reduces the virtual age an amount proportional to its value just before maintenance (ARA CM-ARA PM model) [9], [10].

  • 2.

    Maintenance reduces the virtual age an amount proportional to the supplement of age accumulated since the last maintenance action (ARA1 CM-ARA1 PM model) [8], [9], [10].

In

The virtual age model

The model in this article combines imperfect PM and imperfect CM, and uses an increasing failure intensity to describe ageing of the system or component. The time horizon is assumed to be finite, and therefore the feasibility of different decision alternatives has to be studied for the life extension. These assumptions are realistic, for instance, for complex mechanical equipment, since this type of components normally suffer deterioration, are maintained imperfectly, and cost derived from

Effect of the current virtual age in the model

The current virtual age Vcurrent represents the degradation of a component at present time, and therefore relates to its current technical condition. While the failure intensity normally describes the behaviour of various similar components, the current virtual age is related to the specific component under study. In general terms, the current virtual age depends on the CM and PM actions performed in the past, and the previous maintenance efficiency. The current virtual age also depends on the

Parameter estimation for the virtual age model

The maximum likelihood is a common method for estimating the parameters of the virtual age model from historical maintenance data. The likelihood function is obtained from the following expression [20]:L(θ|T1,,Tk)=i=1iCMkztexp(i=1kTi1TiztdtTkTztdt)where θ=(λ, β, ρPM, ρCM) denotes the parameters of the model, zt is the failure intensity at time t, and T is the latest operating time of a component after the last maintenance action k. In (16), it is assumed that the time when a failure

Case study

The system under study consists of two fire water pumps driven by diesel engines and working in parallel. This is a safety system on stand-by operation and it is started on demand. The case study intends to demonstrate the applicability of the model for extending the life of a real system, and illustrate that a better informed decision making is achieved based on the results obtained.

Monte Carlo simulation is used to assess the future performance of the component because there is no closed-form

Conclusions

This article presents a virtual age model for assessing the life extension of ageing repairable systems. The model takes into account CM and periodic PM including functional tests for stand-by safety equipment. Using the concept of current virtual age, the model can be applied to components that are not new, i.e., are degraded to some extent, but which may be kept in operation for some additional years. The aim of the model is to analyse the future performance of a system or component for

Acknowledgements

The authors are grateful to Gassco and MARINTEK for the cooperation and support facilitated through the Gassco research programme on ageing management. The authors would also like to thank Arvid Næss and the reviewers for the valuable comments which greatly improved the paper.

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      Nevertheless, a more realistic assumption for many systems is the Imperfect Repair (IR), meaning that the system returns to an intermediate state between MR and PR. Models based on such assumption have been studied by several authors, among them Kijima et al. [18], Brown and Proschan [6], Malik [22], Shin et al. [34], Yanez et al. [41], Pan and Rigdon [26], Corset et al. [9] and more recently, Ramírez and Utne [31], Pandey et al. [27], Yevkin and Krivtsov [42], and Tanwar et al. [37]. The former has introduced the idea of virtual age.

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      The virtual age model assumes that an imperfect repair reduces a maintained system’s physical age (therein called virtual age) by an amount proportional to the physical age just before the maintenance, or by an amount proportional to the additional age accumulated since the last maintenance. Many researchers have used the concept of virtual age for modelling imperfect corrective maintenance and/or imperfect preventive maintenance; see, among others, Doyen and Gaudoin (2011), Bouguerra, Chelbi, and Rezg (2012), Dijoux and Idee (2013), Ramirez and Utne (2013), Ahmadi (2014) and Ramirez and Utne (2015). Another commonly used class of imperfect maintenance models is the improvement factor model introduced by Malik (1979).

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      Maintenance efficiency ρ=1 is equivalent to a renewal, ρ=0 is a maintenance action which has no effect on the system׳s condition (i.e., minimal repair), 0<ρ<1 is an efficient maintenance action, and ρ<0 is a harmful maintenance action. We refer the reader to Ramírez and Utne [13] for a detailed calculation of the reduction of virtual age vCMi−1, vCBMi−1, and vTBMi−1 in the model. Fig. 5 shows an example of the failure intensity trajectory for a system in stand-by operation with λ=0.078, β=2.95, Q=0.645, ρCM=0.55, ρCBM=0.15, ρTBM=0.175, TBM interval τ=6 years, and functional test interval θ=3 months.

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      While the above models accommodate imperfect maintenance with outcomes somewhere between perfect and minimal repair, Malik [12] introduced the concept of improvement factor in the maintenance scheduling problem. In a recent development Pedro et al. [13] extend the model with continuously operated and stand-by system, for the life extension decision. Authors have done various assessments for number of failures, costs and safety unavailability with a case study for a life extension period.

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