Optimization of test and maintenance of ageing components consisting of multiple items and addressing effectiveness

Document downloaded from: This paper must be cited as: The final publication is available at Copyright Additional Information http://dx.doi.org/10.1016/j.ress.2016.04.015 http://hdl.handle.net/10251/79776 Elsevier Marton Lluch, I.; Martorell Aigües, P.; Mullor, R.; Sánchez Galdón, AI.; Martorell Alsina, SS. (2016). Optimization of test and maintenance of ageing components consisting of multiple items and addressing effectiveness. Reliability Engineering and System Safety. 153:151158. doi:10.1016/j.ress.2016.04.015 Author’s Accepted Manuscript Optimization of test and maintenance of ageing components consisting of multiple items and addressing effectiveness I. Martón, P. Martorell, R. Mullor, A.I. Sánchez, S. Martorell PII: S0951-8320(16)30043-6 DOI: http://dx.doi.org/10.1016/j.ress.2016.04.015 Reference: RESS5548 To appear in: Reliability Engineering and System Safety Received date: 28 October 2015 Revised date: 5 April 2016 Accepted date: 28 April 2016 Cite this article as: I. Martón, P. Martorell, R. Mullor, A.I. Sánchez and S. Martorell, Optimization of test and maintenance of ageing components consisting of multiple items and addressing effectiveness, Reliability Engineering and System Safety, http://dx.doi.org/10.1016/j.ress.2016.04.015 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. www.elsevier.com/locate/ress ABSTRACT: There are many models in the literature that have been proposed in the last decades aimed at assessing the reliability, availability and maintainability (RAM) of safety equipment, many of them with a focus on their use to assess the risk level of a technological system or to search for appropriate design and/or surveillance and maintenance policies in order to assure that an optimum level of RAM of safety systems is kept during all the plant operational life. This paper proposes a new approach for RAM modelling that accounts for equipment ageing and maintenance and testing effectiveness of equipment consisting of multiple items in an integrated manner. This model is then used to perform the simultaneous optimization of testing and maintenance for ageing equipment consisting of multiple items. An example of application is provided, which considers a simplified High Pressure Injection System (HPIS) of a typical Power Water Reactor (PWR). Basically, this system consists of motor driven pumps (MDP) and motor operated valves (MOV), where both types of components consists of two items each. These components present different failure and cause modes and behaviours, and they also undertake complex test and maintenance activities depending on the item involved. The results of the example of application demonstrate that the optimization algorithm provide the best solutions when the optimization problem is formulated and solved considering full flexibility in the implementation of testing and maintenance activities taking part of such an integrated RAM model. Keywords: Unavailability, costs, multi-objective optimization, ageing, multiple items, imperfect maintenance, testing intervals, maintenance intervals, NPP component. Optimization of test and maintenance of ageing components consisting of multiple items and addressing effectiveness I. Martón1*, P. Martorell1, R. Mullor3, A.I. Sánchez2 , S. Martorell1 1Department of Chemical and Nuclear Engineering. Universitat Politècnica de València, Valencia, Spain 2Department of Statistics and Operational Research. Universitat Politècnica de València, Valencia, Spain 3Department of Statistics and Operational Research. Universidad de Alicante, Alicante, Spain * Corresponding author: I. Martón ([email protected]) * Corresponding author: [email protected] * Corresponding author: [email protected] * Corresponding author: [email protected] artment of Statistics and Operational Research. Universitat Politècnica de València, Valencia, Spain NOTATION 0  Baseline failure rate when the item is new RP Renewal period  Linear ageing rate  Shape factor  Characteristic time  Maintenance effectiveness  Test efficiency  Cyclic or per-demand failure probability D Detected fraction of age-dependent stand-by failure rate U Undetected fraction of age-dependent stand-by failure rate UD Undetected fraction of age-dependent stand-by failure rate that is then detected UU Undetected fraction of age-dependent stand-by failure rate that remains undetected (section 2.1.2) TI Surveillance test interval RI Functional test interval L Life of the item τ Downtime for testing, σ Downtime for preventive maintenance, M Preventive maintenance interval  Downtime for repair  Downtime for replacement uD Unavailability due to detected failures uUD Unavailability due to undetected failures by surveillance testing than are then detected by functional tests uUU Unavailability due to undetected failures by both surveillance and functional tests uT Unavailability due to testing uM Unavailability due to performing preventive maintenance uC Unavailability due to performing corrective maintenance uO Unavailability due to replacement of the item t c Cost contribution as a consequence of performing testing m c Cost contribution as a consequence of performing preventive maintenance c c Cost contribution as consequence of performing corrective maintenance o c Cost contribution associated with replacing 1 INTRODUCTION Many models have been developed in the last decades to assess the reliability, availability and maintainability (RAM) of safety equipment. RAM models are developed mainly to assess the risk level of technological systems and/or with a focus on their use to search for appropriate design and/or surveillance and maintenance policies in order to assure that an optimum level of RAM of safety systems is kept during all the plant operational life [1-3]. Complexity of RAM modelling has evolved along this years in an attempt to capture the equipment behaviour in a more realistic way. For example, most of RAM models that were integrated into standard Probabilistic Safety Assessment (PSA), which is the most used tool for safety and risk management in Nuclear Power Plants (NPPs), do not addresses explicitly neither the effect of equipment ageing nor effectiveness of maintenance and testing programs, which could have a significant impact on the conclusions drawn from PSA studies and applications, particularly when NPP are operated at an advanced age or during long term operation. The reason is that equipment ageing and maintenance effectiveness would most likely result in large uncertainty of current component unreliability and unavailability models that support standard PSA quantification, particularly for aged equipment. Fortunately, these effects are limited often implicitly by adopting a living PSA or at least updating the standard PSA regularly, which is mandatory by current regulation in many countries. In recent years more attention has been paid on modelling explicitly how equipment ageing impacts RAM of safety components and systems. For example, analytical age-dependent unavailability models have been developed adopting linear ageing rates [1], which considers the impact of testing and maintenance activities at least implicitly [2-5]. Nowadays, one can find several proposals in the literature to integrate such a kind of RAM modelling into the so called Ageing PSA (APSA) [6-10]. These studies propose RAM of components should be modelled as a function of the inherent reliability of the component, i.e. component failure rate imposed by design, the component ageing, which degrades the inherent reliability, and the effectiveness of test and maintenance activities, which improve the reliability degraded by ageing, i.e. there is an attempt to return component reliability back to its inherent value eventually, but normally impossible, in case of perfect maintenance activities. In particular, Ref. [6] demonstrates the importance of addressing explicitly the effectiveness of maintenance in managing equipment ageing and test efficiency in detecting hidden failures as this may impact the accurate planning and optimization of testing and maintenance activities based on RAM criteria. This is even more important when the component consists of multiple items, where every item may undertake specific maintenance and testing activities to cope with different degradation mechanisms and failure causes respectively affecting the multiitems component. On the other hand, one can find in the literature an important number of works devoted to the optimization of test and maintenance intervals of safety systems at NPPs , for example using Genetic Algorithms (GAs), which that face either single-objective or multi-objectives adopting RAM plus costs as objectives and/or constraints functions [11-21, 25-30]. Some of them consider the impact of component ageing in the optimization of test and/or maintenance intervals [16-21]. Only several of them considers both test and maintenance interval optimization simultaneously [12, 14, 18, 20]. This paper proposes a new approach for RAM modelling that simultaneously accounts for equipment ageing and maintenance effectiveness and testing efficiency for equipment consisting of multiple items. This model is then used to face the problem of the multi-objective and simultaneous optimization of testing and maintenance intervals for ageing equipment consisting of multiple items. Resolution of such a problem bring a good chance to look for the best balance between component/system availability and cost of the resulting optimal test and maintenance intervals of multiple items components as it is shown in the example of application provided in this paper. The example of application considers a simplified High Pressure Injection System (HPIS) of a typical Pressurized Water Reactor (PWR). Basically, this system consists of ten components: three motor driven pumps (MDP) and seven motor operated valves (MOV). Both component types, MOV and MDP, consist of two items: the motor and pump in the case of the MDP and the actuator and valve in the case of MOV, which are treated separately. These components present different failure modes and behaviours, and also they undertake complex test and maintenance activities, i.e. multiple and different tasks, which depend on the particular item involved. 2 RAM+C MODELS 2.1 Model of a single item 2.1.1 Age-dependent failure rate model incorporating imperfect maintenance As proposed in [6], the integration of testing and maintenance effectiveness was addressed in an improved APSA. For application, specific ageing models for the failure rate need to be used in the equations for the unavailability and cost models to obtain specific numerical results which can be used to analyze the influence of ageing, imperfect maintenance and testing. So, the effect of maintenance on the age of the item and on its reliability is included based on a model of imperfect maintenance. Imperfect maintenance models consider that each maintenance activity reduces the age of the item by some degree, depending on its effectiveness. Among the different models of imperfect maintenance that can be found in the literature, this paper considers the Proportional Age Reduction (PAR) model and the Proportional Age Setback (PAS) model proposed in Refs. [2, 3]. The selection of the most appropriate model in each case depends on the item type, failure mechanism and sort of maintenance activity. In the PAR approach, each maintenance activity is assumed to reduce proportionally the item age gained from the previous maintenance. However, PAS model considers that the maintenance activity reduces proportionally, in a factor of  , the age that the item has immediately before it enters maintenance. In these models, the effect of maintenance is introduced by using an effectiveness parameter  ranging in the interval [0, 1]. If 0  , the previous models simply are reduced to an "As Bad as Old" model (normally corrective maintenance), while if 1  are reduced to an "As Good as New" model (normally overhaul maintenance). For preventive maintenance,  ranges in interval ]0, 1[. In the literature, one can find different component reliability models proposed to address the effect of equipment ageing, such as linear model, Exponential, Weibull, etc [1]. In this work, two reliability models, Weilbull and Linear, and the imperfect maintenance models presented above, PAS and PAR, are considered to model the age-dependent failure rate. Weibull distribution is widely used in reliability and life data analysis to represent equipment ageing with time due to its versatility [3]. Linear distribution is the simplest way to develop an age-dependent reliability model, which assumes that the failure rate has a linear behaviour with component age departing form an initial value. This assumption, when applicable, simplifies the modelling. In addition, one can find in the literature ageing factors proposed for several components in Nuclear Power Plants [1, 9]. According to [2, 3], considering a linear ageing model and imperfect maintenance models can be obtained an averaged standby failure rate, *  , over the item’s life based on a double averaging process [3] which is given by:     )2( ·· 2 0 *  M PAS model (1)       )1)·(1(1··· 2 1 0 * M RP M  PAR model (2) where, 0  is the baseline failure rate when the item is new, M is the maintenance interval, RP is the renewal period and  is the linear ageing rate. According to [3], considering a Weibull ageing model and PAR or PAS model can be obtained an averaged standby failure rate, *  , over the item’s life based on a double averaging process [24] which is given by: ))1(1·( )·( 1 0 *         M PAS model (3)      )·2)·(1·( )·())1·(2·( 0 *    RP MRPM PAR model (4) where,  and  are the shape and scale factors, respectively. Note that the Weibull distribution simplifies to the linear one for shape factor equal to 2 and the scale factor equal to√ ⁄. 2.1.2 Age-dependent failure rate model addressing test efficiency By testing, component failures can be detected that may have occurred since the last test or the time when the component was last known to be operational. The main objective of surveillance test is to detect hidden failures so that the component can be restored to its operational state. For example, as proposed in Ref. [19], it can be seen like a testing coverage of failure mechanisms, where coverage is defined as a share of detected an undetected failures by testing. Alternatively, Ref. [10] defines test efficiency like the probability that a given failure is detected by the test. In both previous cases, test efficiency can be represented by a single parameter η . Ref. [9] and [10] give values of η for test efficiency of several component types. As a result, the consideration of a test efficiency splits the total age-dependent failure rate into two age-dependent failure rate modes: detected and undetected. UD* λλλ  (5) where the test efficiencyranges in the interval [0, 1]. In eqn. (5), the first contribution represents the agedependent failure rate associated with detected failures by testing, D λ , and the second part represents the age-dependent failure rate associated with undetected failures by testing, U λ , which can be derived using the corresponding formulation for * λ using eqn. (1) to eqn. (4). *D ληλ  (6) * 1λη)(λU (7) On the other hand, a large number of critical components overtakes functional tests mostly performed during refuelling of NPP, where the refuelling Interval (RI) ranges between 12 and 24 months, so that typically RI could be set equal to 18 months. The functional test often involves testing full performance of the component capacity, so that it performs very close to real conditions in case of emergency. Then, the efficiency of such a functional test should be very close to one in detecting hidden failures. Similarly to the surveillance tests, in reliability terminology, the functional test intervals (often adopting the RI) are called BAO intervals since the component age coming out of the test is basically the same as the component age going into the functional test, i.e. the component is as old with regard to its age. Thus, critical items for NPP safety may overtake at least two tests: one surveillance test and another functional test. Consequently, to address such a second or refuelling functional test, the undetected agedependent failure rate, given by eqn. (7), should split into two new contributions: detected and undetected after the refuelling functional test, to yield U RI UD ληλ  (8) U RI UU ληλ  )1( (9) where the test efficiency of the refuelling functional testRranges also in the interval [0, 1], but very close to one now. In addition, eqn. (8) represents the age-depended failure rate contribution associated with detected failures only after the refuelling functional test, while eqn. (9) represents the age-dependent failure rate contribution associated with failures that remain undetected even after the refuelling functional test. The formulation proposed in eqns. (5) to (9) can accommodate a number of assumptions made in each application considered. 2.1.3 Unavailability models The unavailability contributions of a single item normally in stand-by are divided into two categories: a) unavailability due to failures, i.e. unreliability effect, and b) unavailability due to testing and maintenance downtimes, named the downtime effect. a) Unreliability contributions Adopting the basis of the formulation of unreliability contributions in Ref. [6] considering the contributions introduced in sections 2.1.1 and 2.1.2, the item unavailability due to unreliability contributions can be evaluated using the following equations : TIλuDD  2 1 (10) RIλuUDUD  2 1 (11) LλρuUUUU  2 1 (12) where uD is the unreliability contribution due to detected failures by surveillance testing, uUD is the unreliability contribution due to undetected failures by surveillance testing that are then detected by a second functional tests and uUU is the unreliability contribution due to undetected failures by both surveillance and functional tests . In addition, the following notation has been used:  = cyclic or per-demand failure probability, D= detected fraction of age-dependent stand-by failure rate (section 2.1.2), UD = undetected fraction of age-dependent stand-by failure rate that is then detected (section 2.1.2), UU = undetected fraction of age-dependent stand-by failure rate that remains undetected (section 2.1.2), TI = surveillance test interval, RI = functional test interval, L = life of the item. Table 4. Decision variables: Test and Maintenance Intervals. Multi-Objective optimization under cost and unavailability criteria has been performed using the nondominated Sorting Genetic Algorithm (NSGA-II) [32] toolbox in Matlab using eqn. (25) as objective function. Relevant parameters used in the optimization process are showed in Table 5. Table 5. NSGA-II parameters Six optimization cases has been developed adopting, in part or as a whole, the set of decision variables presented in Table 4. Lower and upper bounds have been adopted for the decision variables, which allows searching for solutions in the desired domain of feasible ones. Thus, TIi (i = 1,3) must range in the interval [24, 80000] while Mj (j=1,4) must range in the interval [720, 80000]. As said, the initial surveillance test and maintenance intervals are TIi = 2184 and Mj = 4320 ( i=1,3 and j=1,4). Table 6 shows the six optimization problems that have been formulated and solved. All cases adopts the same objective function consisting of both unavailability and costs for the HPIS, which are calculated using reliability and maintenance data showed in Tables 1 to 3, and the initial or optimized values for the decision variables in Table 4 depending on the particular case. The NSGA-II algorithm with the same parameters shown in Table 5 is used for all six cases. Table 6. Cases studied Cases 1 to 3 adopt test efficiency equal to one. This means unavailability of each component resets to the residual value, normally zero, after the surveillance test, i.e. the surveillance test is able to detect whatever hidden failure of the component and therefore it is assumed the component is available after the test provided that the component is not found failed at the test. Cases 4 to 6 considers a test efficiency for each MDP and MOV equal to 0.6 and 0.4, respectively, which are taken from NUREG 5587 [10]. In addition, Case 1 and 4 address surveillance test interval (TI) optimization only. Case 2 and 5 address optimization of both surveillance test intervals (TI) and maintenance intervals (M). Case 3 and 6 address are similar to the previous one. However, now maintenance is grouped either by electrical or by mechanical maintenance, considering that maintenance for each group share the same period. Therefore, now M1 is set equal to M3 and M2 is set equal to M4. Figure 4 and Figure 5 show the results of the optimization process. Figure 4 shows the Pareto Fronts corresponding to Cases 1 to 3. Figure 5 shows the Pareto Fronts corresponding to Cases 4 to 6. Figure 4 shows that better results are obtained when the whole set of TI and M are considered in the decision making of the optimization problem (Cases 2 and 3) as compared to the worst results found for the case where only the set of TI is optimized (Cases 1). The value of unavailability and cost obtained are significantly lower in Cases 2 and 3. In addition, better results are found under Case 2 as compared to Case 3 in terms of optimal unavailability and cost for the HPIS. This means that the best results can be found by including the whole set of decision variables and allowing flexibility in the decision making. Note that in Case 3 maintenance activities are grouped under electrical and mechanical types only and therefore the decision space is reduced. Similar results can be found in Figure 5. On the other hand, by comparing Figures 4 and 5, one can realize the importance of surveillance test efficiency, since the unavailability of the HPIS is underestimated in all cases represented in Figure 4. In addition, when a test efficiency lower than one is considered, which is a more realistic assumption based on data available, there is no so big difference between grouping or not maintenance activities into electrical and mechanical types, see Cases 5 and 6 in Figure 5 as compared to their corresponding Cases 2 and 3 in Figure 4. Figure 4. Pareto Front obtained for Cases 1 to 3 Figure 5. Pareto Front obtained for Cases 4 to 6 7. CONCLUDING REMARKS Many approaches have been suggested in the past to optimize the surveillance test and maintenance intervals of a system based on various analytical unavailability and cost models. Most of these approaches do not consider simultaneously and explicitly the impact of equipment ageing, maintenance effectiveness and surveillance testing efficiency, in particular for components consisting of multiple items. This paper proposes a new approach for RAM modelling that simultaneously accounts for equipment ageing and maintenance effectiveness and testing efficiency for equipment consisting of multiple items. This model is then used to face the problem of the multi-objective and simultaneous optimization of testing and maintenance intervals for ageing equipment consisting of multiple items. The results obtained in the application case show substantial differences, mainly in the assessment of the HPIS system unavailability, when ageing and both maintenance effectiveness and testing efficiency are considered explicitly. Thus, the example of application shows that maintenance effectiveness in managing ageing and test efficiency in detecting hidden failures have a significant impact on the results found, so that, future research should be directed towards the estimation, or even improvement, of maintenance effectiveness and test efficiency and the assessment of their effect on failure causes and failure modes affecting RAM of safety equipment, since they impact the accurate planning and optimization of testing and maintenance activities based on RAM criteria. The results of the example of application demonstrate that the optimization algorithm provide the best solutions when the optimization problem is formulated and solved considering full flexibility in the implementation of testing and maintenance activities taking part of such an integrated RAM model of multiple items components. 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[31] Nelder, J.A.& Mead,R. (1965).ASimplex method for function minimization. Computer Journal, 308–313 [32] Deb, K., PrataP, A., Agarwal, S., Meyarivan, T., A fast and elitist multiobjective genetic algorihtm. NSAG-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197, 2002. ACKNOWLEDGMENTS Authors are grateful to the Spanish Ministry of Science and Innovation for the financial support of this work (Research Project ENE2013-45540-R) and the doctoral fellow (BES-2011-043906) and (BES-2014-067602). Figure. 1. High Pressure Injection (HPIS) system MOTOR DRIVEN PUMP (MDP) MOTOR PUMP FC1M, ... MAINTENANCE ACTIVITIES FC1P, ... FAILURE CAUSES MM MP FM1MDP, ... TESTS FAILURE MODES RI (RI) TI () T1MDP T2MDP MM () MP () Figure 2. Overview of basic interactions for MDP MOTOR OPERATED VALVE (MOV) ACTUATOR VALVE FC1A, ... MAINTENANCE ACTIVITIES FC1V, ... FAILURE CAUSES MA MV FM1MOV, ... TESTS FAILURE MODES RI (RI) TI () T1MOV T2MOV MM () MV () Figure 3. Overview of basic interactions for MOV PUMP A (PA) PUMP B (PB) PUMP C (PC) VALVE 1 (V1) VALVE 2 (V2) VALVE 3 (V3) VALVE 4 (V4) VALVE 5 (V5) VALVE 6 (V6) VALVE 7 (V7) FROM RWST INJECTION PATH A INJECTION PATH B Figure 4. Pareto Front obtained for Cases 1 to 3 Figure 5. Pareto Front obtained for Cases 4 to 6 Table 1. Models and parameters obtained in the estimation process 1,10E+05 1,15E+05 1,20E+05 1,25E+05 1,30E+05 1,35E+05 1,40E+05 1,45E+05 1,50E+05 1,55E+05 1,60E+05 0,000 0,001 0,001 0,002 0,002 0,003 0,003 Cost(x) (€) Unavailability (x) Case 1 Case 2 Case 3 0,00E+00 5,00E+05 1,00E+06 1,50E+06 2,00E+06 2,50E+06 3,00E+06 3,50E+06 4,00E+06 0 0,01 0,02 0,03 0,04 0,05 0,06 Cost (x) (€) Unavailability (x) Case 4 Case 5 Case 6 Motor operated valve (MOV) Motor driven pump (MDP) Valve Actuator Pump Motor Units ρ 1.81E-03 1.25E-05 5.18E-04 1.25E-05 [-] λ0 6.80E-06 7.00E-06 2.30E-05 3.89E-06 [1/h] IM model PAR PAS PAR PAS --  0.76 0.84 0.77 0.29 -- Ageing Model Linear Weibull Linear Weibull --  1.73E-09 -- 2.37E-09 -- [h-2]  -- 4.87 -- 7.47 --  -- 33347 -- 15397 -- Table 2. Data of tests and maintenance for MDP and MOV Motor operated valve (MOV) Motor driven pump (MDP) Valve Actuator Pump Motor Units σ 1 1 10 10 [h] TI 2184 2184 2184 2184 [h]  {1, 0.6} {1, 0.6} {1,0.44} {1,0.44} -- RI 13140 13140 13140 13140 [h] RI 1 1 1 1 -- τ 1 1 4 4 [h]  2,6 2,6 24 24 [h] Γ 6 6 50 50 [h] L 122640 122640 122640 122640 [h] Table 3. Component item cost parameters Units Valve Actuator Pump Motor ct [€/year] 400 400 100 100 cc [€/year] 25920 2880 2808 312 cm [€/year] 7200 800 720 80 co [€/year] 32400 3600 3240 360 Table 4. Decision variables: Test and Maintenance Intervals. Interval Component Item Type of Maintenance/Test Maintenance strategy M1 V1, V2,V3,V4,V5,V6,V7 Valve Mechanical M2 V1, V2,V3,V4,V5,V6,V7 Actuator Electrical M3 PA, PB, PC Pump Mechanical M4 PA, PB, PC Motor Electrical Testing strategy TI1 V1, V2 -- Surveillance Test TI2 V3, V5, PA, PB, PC -- Surveillance Test TI3 V4, V6, V7 -- SurveillanceTest Table 5. NSGA-II parameters Parameter Value Generations 1000 Population Size 100 Crossover rate 2/7 Crossover type Arithmetic Crossover Mutation rate 2/7 Mutation type Gaussian Mutation Stopping criteria Maximum generations number Table 6. Cases studied Case # Test Effectiveness {MDP, MOV) Description Decision variables Case 1 {1,1} TI optimization {TI1, TI2, TI3} Case 2 {1,1} TI and M optimization {TI1, TI2, TI3, M1, M2, M3, M4} Case 3 {1,1} TI and M optimization Maintenance grouped by type of maintenance: electrical or mechanical {TI1, TI2, TI3, M1, M2, M3, M4} being: M1=M3 M2=M4 Case 4 {0.6, 0.4} TI optimization {TI1, TI2, TI3} Case 5 {0.6, 0.4} TI and M optimization {TI, TI2, TI3, M1, M2, M3, M4} Case 6 {0.6, 0.4} TI and M optimization Maintenance grouped by type of maintenance: electrical or mechanical {TI1, TI2, TI3, M1, M2, M3, M4} being: M1=M3 M2=M4 Highlights New approach for RAM modelling Equipment ageing and maintenance effectiveness and testing efficiency explicitly in RAM models Equipment consisting of multiple items Multiple objective optimization problem (MOP) under unavailability and cost criteria Simultaneous optimization of testing and maintenance intervals