International Journal of Multidisciplinary Futuristic Development

Integrating Reliability, Availability, and Maintainability Analysis into Production Facility Performance Optimization

Susan Ochi Makut1, Festus-Michael Uwagboe2, Henry Chukwuemeka Olisakwe3

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Version of record

This is an author-deposited copy. The version of record was originally published elsewhere: Originally published in International Journal of Multidisciplinary Futuristic Development, Volume 4, Issue 2, 2023. DOI 10.54660/IJMFD.2023.4.2.99-121 . Original source: https://www.transdisciplinaryjournal.com/archives/year-2023.vol-4.issue-2.

Abstract

Reliability, availability and maintainability (RAM) studies of oil and gas production facilities usually assess a design after it has been fixed, not choose it. This study embeds RAM analysis in design optimization for a representative onshore central production facility with seven series subsystems. Eleven decisions were optimized: redundancy and unit sizing for each subsystem, emergency shutdown voting, compressor and turbine spares, and condition-based maintenance. Production efficiency was computed analytically by a multi-state universal generating function, with spare stock-outs and spurious trips represented. All 15,552 designs were enumerated to obtain the exact Pareto front against life-cycle cost. Inputs are representative published values, not field data. The base design achieved 95.3 percent production efficiency, with compression responsible for 2.2 of its 4.7 points of loss. Condition-based maintenance gave the highest return per dollar, and a third compression train the largest absolute gain. A knee design reached 98.1 percent for USD 10.8 million of life-cycle cost. The net-present-value optimum reached 98.7 percent for USD 20.9 million and added USD 60 million. Spares were valuable alone but redundant once a third train was installed. Discrete-event simulation agreed with the analytic model within 0.1 percentage points. Under a factor-of-two uncertainty in failure rates, the optimum had a mean regret of USD 1.1 million, against USD 5.5 million for the knee design.

Keywords: reliabilityavailability and maintainabilityproduction efficiencyuniversal generating functionredundancy allocationspare partscondition-based maintenanceoil and gas facilities

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1. Introduction

Production efficiency, the ratio of actual to potential production, is one of the principal determinants of the value of an oil and gas facility. Each percentage point of production lost to equipment failures, spurious trips and planned shutdowns at a facility producing tens of thousands of barrels of oil equivalent per day represents millions of dollars of deferred revenue each year. The international standard ISO 20815 on production assurance and reliability management sets out how production availability should be analysed and managed through the facility life cycle [1], and the ISO 14224 standard and the Offshore Reliability Data (OREDA) handbook provide the failure data on which such analyses depend [2–4]. Reliability, availability and maintainability (RAM) analysis has been applied to subsea production systems [5, 6], floating production units [7], reciprocating compressor stations [8], gas re-injection plants [9] and offshore platform power systems [10, 11]. Reliability engineering and failure analysis of complex engineering systems more generally [12], and risk-based process engineering frameworks for natural gas infrastructure [13], provide the broader context in which these studies sit.

In practice, RAM studies are often performed late in design to verify that a chosen configuration meets a production availability target, rather than to choose among configurations. Studies of RAM practice describe the use of reliability block diagrams, Monte Carlo simulation and Petri nets to estimate availability and identify critical equipment [14–17], but the design decisions that RAM results should inform, including redundancy, unit sizing, spares, maintenance strategy and safety system architecture, are typically settled separately [18, 19]. Meanwhile, a large literature on redundancy allocation and reliability optimization has developed exact and metaheuristic methods for allocating components in series-parallel systems [20–23], and multi-state reliability theory based on the universal generating function (UGF) has provided efficient ways to compute the performance distribution of systems with capacity-graded units [24–26]. These methods are rarely brought together with the production economics, spare parts and spurious trip behaviour that determine the value of availability at an oil and gas facility.

Three gaps follow. First, optimization studies seldom include the range of levers available to facility engineers, which go beyond component redundancy to unit sizing, spare parts holdings, condition-based maintenance (CBM) and emergency shutdown (ESD) voting [27–29]. Second, interactions between levers, for example between spares and redundancy, are rarely quantified, although they can make an individually attractive measure redundant [27, 30]. Third, the robustness of an optimized design to uncertainty in failure data, which in oil and gas is often generic and sparse, is rarely assessed [31–33].

This paper addresses these gaps with an RAM-based design optimization of a representative onshore central production facility. It makes four contributions. First, it formulates production efficiency as a function of eleven design and support decisions through a multi-state UGF model that includes spare stock-outs, spurious trips and turnarounds. Second, it enumerates all 15,552 designs to obtain the exact Pareto front between production efficiency and life-cycle cost, avoiding the approximation of metaheuristic search [22, 34]. Third, it quantifies the contribution of each subsystem and lever to production loss and the interactions between levers. Fourth, it verifies the analytic model by discrete-event simulation and tests the robustness of the optimal designs to failure-rate uncertainty through regret analysis. Section 2 reviews the literature, Section 3 describes the model, Section 4 presents the results, Section 5 discusses implications and Section 6 concludes.

2. Literature Review

This section reviews RAM and production availability analysis in oil and gas, system modelling methods, safety instrumented systems and common cause failures, redundancy allocation and multi-state systems, spare parts and maintenance optimization, maintainability, prognostics and digital twins, importance measures and resilience, and uncertainty in reliability data. It draws on textbooks and handbooks that establish the foundations of reliability engineering [18, 35, 36] and on the argument that reliability science has distinct foundations linked to risk science [37]. Production availability is treated as the central performance measure for oil and gas facilities, consistent with ISO 20815 and the production assurance literature [1, 14, 38].

2.1. RAM and Production Availability in Oil and Gas

Production regularity assessment for subsea systems dates from the 1980s [38], and RAM analysis was adopted for deepwater subsea developments [5, 39, 40], subsea riser and deepwater system design [41], subsea blowout preventers [42], electrical submersible pumps [43], wellheads [44], distribution systems [6] and high integrity pressure protection systems [45, 46]. Topsides and onshore applications include natural gas compressor plants [47], ammonia plants [48], cogeneration plants [49], gas re-injection [9], production systems under fuzzy Bayesian analysis [50], ship-based carbon dioxide liquefaction [51], LNG fuel gas supply [52], floating production power generation [7], small offshore electric systems [53], offshore platform power [10, 11], oil production systems [54] and surface facilities [55]. Devices, converter topologies and system-level practice for energy efficiency in modern power systems have been reviewed [56], which bears on the power generation and distribution subsystems of production facilities. Quantitative risk assessment of submersible pump components with interval numbers [57], offshore system safety under microbiologically influenced degradation [58], studies of RAM indices for production systems [59, 60], RAM under uncertain data [61], sustainable production processes [62], RAM model development [17], RAMS overviews [63] and integration of RAMS with the safety life cycle [19] complete the picture. Equipment-level studies address compressor reliability from fleet data [64], reciprocating compressor RAM [8], centrifugal compressor maintenance [65], predictive maintenance specifications [66], next-failure prediction [67], efficiency deterioration [68], compressor networks with condition-based maintenance [69, 70], and compressor fault diagnosis [71, 72]. Reliability and integrity management of fired heaters, boilers and furnaces in upstream operations has been reviewed [73], and condition-based maintenance of CALM buoy bearings and swivels [74] and integrity assurance of FSO turret mooring systems [75] have been proposed to raise the availability of offshore crude export. Performance assessment of offshore equipment [76], maintenance criticality offshore [77], failure data analysis with degraded failures [78], competing risks [79], the basic concepts of failure analysis [80], oilfield development optimization under uncertainty [81] and risk assessment data directories [82] provide further context.

2.2. System Modelling Methods

Reliability block diagrams, fault trees, Markov models, Petri nets and Monte Carlo simulation are the main tools for availability modelling. Fault tree analysis has been reviewed [83, 84] and supported by new algorithms [85], analytical simulation tools [86] and time-dependent methods [87]. Petri nets [88] have been applied to dependability [89], production availability [14, 15] and multi-unit maintenance costs [90], and production trees provide a dedicated production availability formalism [16]. Bayesian networks support reliability evaluation [91, 92], compressor fault analysis [65] and dynamic operational reliability [93]. Failure mode and effects analysis has been reviewed [94], and complex systems have been evaluated through dynamic object-oriented methods [95], interval-valued fuzzy approaches [96] and degradation models [97].

2.3. Safety Instrumented Systems, Spurious Trips and

Common Cause Failures Safety instrumented systems (SIS) protect facilities but also cause production loss through spurious trips. Spurious activation in the oil and gas industry [28, 98], spurious activation and operational integrity of redundant SIS [99], MooN voting architectures [100], modelling patterns [101], Markov models [102, 103], analytical formulas with nonconstant failure rates [104], proof testing strategies [105–107], partial testing [108], multi-objective design and testing [109, 110], design optimization with genetic algorithms [111], unavailability of redundant SIS [112], functional analysis [113] and multi-state risk-based maintenance of safety systems [114] have been studied. Common cause failures reduce the value of redundancy and have been analysed using field experience [115], organizational factors [116], alpha factors [117], uncertainties in rates [118], single failure events in multiple groups [119], age-related degradation [120], updating for risk monitoring [121], inter-unit estimation [122], decision diagrams [123], multi-state systems [124, 125], redundant safety systems [126], optimization [127] and the value of redundancy [128].

2.4. Redundancy Allocation and Multi-State Systems

The redundancy allocation problem has been studied since Bellman’s dynamic programming formulation [20]. Exact algorithms [21, 22, 34], multi-objective formulations [23, 129–142], mixed and universal redundancy strategies [143–148], time-dependent failure rates [149], survival signatures [150], load sharing [151], component supplier selection [152], strength redundancy [153], cold standby with inspection [154], k-out-of-n subsystems [155, 156], common cause failures [157], flow networks [158], electrical systems [159], bilevel formulations [160], two-stage approaches [161], particle swarm [162, 163], inventory-redundancy allocation [164] and production-reliability-inventory models [30] have been developed. Physical programming [165] and strategy-space reduction for multi-state maintenance optimization [166] show how large design spaces can be handled. Multi-state systems theory, built on the UGF [24, 167] and its engineering applications [25], has extended reliability to systems whose performance is graded, including extended block diagrams [26], combined stochastic process and UGF [168], weighted k-out-of-n systems [169, 170], three-state systems [171], swarm optimization [172], consecutively connected systems [173–175], dynamic series-parallel systems [176], common bus performance sharing [177, 178], confidence bounds [179], importance measures [180, 181], condition-based maintenance and performance control [182], manufacturing vulnerability [183], distributed generation [184], power reserves [185], critical failure modes [186], degraded systems with minimal repair [187], heterogeneous redundancy [188], phased missions [189, 190], maintenance policies [191, 192] and selective maintenance [193]. Availability of k-out-of-n systems with non-identical components [194], repairable k-out-of-n systems [195], warm standby [196, 197], general time distributions [198], load sharing with switching delays [199], selective maintenance of serial k-out-of-n systems [200] and failure dependencies [201] complete the modelling basis.

2.5. Spare Parts and Maintenance Optimization

Spare parts inventory theory, including the METRIC family of multi-echelon models [202, 203], has been reviewed [204–206] and applied to system availability constraints [207], design-phase reliability [208], repairable stocking and expediting [209], exchangeable-item repair [210], fleet redundancy and spares [27], lateral transshipments [211, 212], demand forecasting [213, 214], emergency warehouses [215], dependent failures [216], time-varying installed bases [217], two-echelon control [218], classification [219], critical spare ordering [220], spare criticality [221], queuing models for aircraft [222], service logistics control towers [223] and the petroleum industry [224]. Models linking inventory availability to plant uptime in energy facilities [29], materials readiness to maintenance-driven supply chain performance [225], and strategic procurement to oil and gas operations [226] connect spares holdings to production, while supply chain risk management for EPC and gas processing projects [227] and supply chain resilience for gas processing plants [228] address disruption of the supply of parts. Joint optimization of maintenance and spares has been studied [229– 232]. Opportunistic and grouping maintenance [233–240], dynamic predictive maintenance for multi-component systems [241], clustering of CBM with redundancy [242], preventive maintenance planning of series-parallel systems [243], genetic algorithm maintenance planning [244–246], maintenance and production interactions [247, 248], dependent two-component systems [249], offshore wind [250, 251], maintenance workforce planning [252, 253], turnaround criticality [254], linking maintenance strategy to performance [255], proactive maintenance cost reduction [256], computerized maintenance management of preventive and corrective work on static equipment [257], incident prevention in maintenance environments [258], maintenance with limited data [259], sustainability of maintenance practices [260] and life-cycle cost under dependent degradation [261] illustrate the breadth of the field.

2.6. Maintainability, Prognostics and Digital Twins

Maintainability determines how quickly failed equipment is returned to service. Lognormal repair time distributions [262, 263], maintainability indices [264], design for maintainability [36, 265], verification standards [266], limited-sample verification [267], clustering-based demonstration [268] and vehicle case studies [269] have been reported, and reliability-centered design that integrates finite element analysis with design failure mode and effects analysis has been proposed for mechanical components [270]. Reliability growth methods, including Crow-AMSAA models and military handbooks, track improvement during development [271–273], and reliability has been treated as a design variable in high-reliability industries [274–276]. Prognostics and health management reduce unplanned downtime [277], through remaining useful life estimation [278–282], multi-component predictive maintenance [283–285], condition-based maintenance with semi-Markov decision processes [286], degradation-threshold-shock models [287], structured replacement [288], fault monitoring [289], alarm-based scheduling [290], grouping [291], deep reinforcement learning for large systems [292], predict-then-optimize approaches [293], scheduling restricted by remaining life [294], safety and efficiency of maintenance strategies [295], the value of information from monitoring [296], condition monitoring filtering [297], predictive maintenance and condition monitoring in power and energy infrastructure [298], data-driven methods for industrial automation and process control [299] and interpretable machine learning for early failure prediction [300]. Non-destructive testing methods for predictive failure analysis [301], NDT-based integrity management of refinery equipment [302], risk-based inspection for fitness-for-service of ageing pressure vessels [303] and non-intrusive inspection that reduces shutdown frequency [304] supply the condition data on which such methods depend. Digital twins support gas turbine degradation prognostics [305], predictive diagnostics at resource-constrained energy sites [306], fault diagnosis [307], fatigue monitoring [308] and nuclear applications [309], and hybrid models have been applied in petroleum systems [310].

2.7. Importance Measures and Resilience

Importance measures, from Birnbaum’s original definition [311] to Fussell-Vesely and risk importance measures [312, 313], identify the components that most affect system performance. Their use in risk-informed decisions [314, 315], differential importance [316], dynamic and dependent systems [317], system-of-systems [318], inventory systems [319] and multi-state systems with external factors [320] has been studied. Resilience extends availability to the recovery from disruptions, with reviews of definitions and measures [321–323], metrics and frameworks [324–328], concepts [329], resilience-based importance measures [330–334], flow-based vulnerability [335], critical infrastructures [336–340], process plants [341], offshore facilities [342, 343], cogeneration [344, 345], mechanical structures [346], enterprises [347] and gas supply networks [348]. Combining system-theoretic process analysis with availability assessment [349] and dynamic risk assessment of deepwater operations [350] link resilience to safety.

2.8. Uncertainty in Reliability Data

Reliability data for oil and gas equipment are often generic, sparse and uncertain. Bayesian priors based on generic data and expert opinion [31], the influence of prior choice [32], rare event risk assessment [351], precursor data [352] and imprecise multi-source fusion [353] address sparse data, and statistical methods from quality engineering [354] and predictive modelling frameworks for forecasting energy yield [355] show how limited operating records can be turned into usable estimates. Sampling-based uncertainty and sensitivity analysis [33, 356], aleatory and epistemic uncertainty [357–359], uncertainty importance measures [360], evidence theory [361, 362], subset simulation [363], derivative-based global sensitivity measures [364], reliability-oriented sensitivity with epistemic uncertainty [365], imprecise probabilities [366], rare event estimation [367] and uncertainty in risk analysis of complex systems [368, 369] provide the methods used to test robustness.

2.9. Research Gap

The literature provides mature methods for RAM modelling, redundancy allocation, multi-state systems, spare parts, maintenance optimization and uncertainty analysis. What is missing is their combination in a design optimization that treats redundancy, unit sizing, spares, maintenance strategy and SIS voting as joint decisions, values availability through production economics, quantifies interactions between levers and tests robustness to data uncertainty, for an oil and gas production facility [1, 27, 32]. The model presented next provides such a combination using an exact multi-state formulation that allows complete enumeration of the design space. Complete enumeration also allows the interactions between levers and the regret of each design under uncertainty to be computed exactly rather than estimated from a sample of designs [22, 34].

3. Methods

This section describes the representative facility, the multi-state availability model, the treatment of spares, CBM, spurious trips and turnarounds, the economic model, the enumeration and selection of designs, the simulation used to verify the analytic model, and the uncertainty analysis. The model follows the production availability principles of ISO 20815 [1], represents subsystems as multi-state elements combined by the UGF [24, 25] and uses data ranges of the kind reported in OREDA and related sources [2, 3, 82]. All parameter values are representative values chosen within published ranges; they are not data from a specific facility, and the results demonstrate the method and the relative value of design options rather than predict the performance of any particular facility.

3.1. Representative Facility

The facility is an onshore central production facility with a design throughput of 60 MMscf/d of gas and 15,000 barrels per day of oil. Its seven subsystems act in series, so that facility capacity at any time is the minimum of the subsystem capacities (Figure 1): inlet separation and slug catching, gas compression, glycol dehydration, oil export pumping, produced water treatment, gas turbine power generation and instrument air and utilities. Each subsystem consists of identical units whose capacities are fractions of design throughput, so that partial failures reduce rather than stop production, as in multi-state models of production systems [183, 184]. When all produced water treatment units are down, production can continue at 30 percent of capacity by diverting water to storage. Demand is at design throughput for the first six years and then declines linearly to 50 percent by year 20, a typical plateau and decline profile [81], and the subsystem structure follows risk-based process engineering practice for natural gas infrastructure [13]. The value of production at full throughput is USD 0.75 million per day. Table 1 lists the subsystem options and reliability parameters.

Fig 1: Series structure of the representative facility, subsystem configuration options and facility-wide decisions.

Table 1: Subsystem configuration options and representative reliability parameters. Code Subsystem Options (units x capacity percent)

Base case Failure rate per unit (per year)

Reference unit cost (USD M)

3.2. Unit Availability, Spares and Condition-Based

Maintenance Each unit alternates between operation and repair. For compression and power generation, a fraction ?????? of failures (15 and 10 percent) requires a major spare such as a compressor cylinder assembly or a turbine hot-section module, with replenishment lead times of 21 and 45 days. If a spare is in stock, repair proceeds normally; otherwise the repair waits for the lead time. With � spares held and Poisson demand, the probability of a stock-out is approximated by the probability that demand during one lead time exceeds the stock, following the logic of repairable inventory models [202, 203] and of inventory availability models for energy facilities [29]:

CBM on compression and power generation units reduces the rate of unplanned failures by 30 percent and the mean repair time by 20 percent, because degradation detected early is repaired in a planned way, consistent with reported benefits of condition monitoring for rotating equipment [66, 69, 74, 277, 298]. CBM costs USD 0.8 million to install and USD 0.1 million per year.

3.3. Multi-State Subsystem and Facility Model

The capacity distribution of a subsystem with ?????? units of capacity ?????? and availability ?????? is obtained by the UGF [24, 25].

with capacities capped at 100 percent of design throughput and replaced by the residual capacity when all units are down. Subsystems in series are composed by the minimum operator:

where �trip and �TA are the fractions of time lost to trips and turnarounds.

3.4. Economic Model and Design Selection

Incremental capital cost of a configuration is the cost of its units relative to the base case, with unit cost scaling with capacity to the power 0.6, plus the cost of spares (USD 1.2 million per compression set and USD 3.0 million per turbine module), ESD upgrade and CBM. Operating costs are 3 percent of incremental capital per year and 5 percent of spares value per year. Incremental life-cycle cost (LCC) is the present value of incremental capital and operating costs, and net present value (NPV) is the present value of production less LCC, both at a 10 percent discount rate over 20 years [261]. The eleven decisions in Table 1 and Figure 1 define 15,552 designs, all of which were evaluated; because the UGF evaluation takes about a quarter of a millisecond, complete enumeration is faster than metaheuristic search and yields the exact Pareto front between production efficiency and LCC [22, 34]. Three designs were selected: the base case (D0), the knee of the Pareto front (D1), defined as the front point with maximum normalized distance from the line joining its extremes, and the NPV-maximizing design (D2).

3.5. Verification by Discrete-Event Simulation

To test the steady-state, independence and exponential repair assumptions of the analytic model, the selected designs were simulated over 20 years in 150 replications with a 2-hour time step. Each unit followed an alternating renewal process with exponential operating times and lognormal repair times with a coefficient of variation of 0.8, consistent with evidence on repair time distributions [262, 263]; spare stock-outs added the lead time with the computed probability; turnarounds occurred in years 2, 6, 10, 14 and 18; and spurious trips occurred as a Poisson process. Monte Carlo simulation of this kind is the standard method for production availability assessment [14, 16, 49].

3.6. Uncertainty and Regret Analysis

Failure rates in oil and gas are uncertain, especially for new facilities with generic data [31, 32]. Each subsystem failure rate was multiplied by an independent lognormal factor with an error factor of 2 (the 95th percentile twice the median), and 500 samples were drawn [33, 357]. For each sample, the production efficiency of the selected designs was computed, and the NPV of all 83 designs on the nominal Pareto front was evaluated to find the best design for that sample. The regret of a design is the difference between the best NPV for the sample and the NPV of the design [360]. A further analysis varied the value of production from USD 0.25 to 1.5 million per day to test how the NPV-optimal design changes with the value of availability.

4. Results

This section reports the base-case losses, the value of individual levers and their interactions, the Pareto front and selected designs, the simulation verification, the robustness to failure-rate uncertainty and the sensitivity to production value. Results are expected values unless stated otherwise. Because the inputs are representative, the ranking and relative size of effects are more informative than absolute values, as in other comparative RAM optimization studies [17]. The analytic results are reported first because they cover every design and every lever; the simulation results in Section 4.4 then check the analytic model for the three selected designs under more realistic repair time distributions.

4.1. Base-Case Production Losses

The base design achieved a production efficiency of 95.3 percent over the life and 94.7 percent during the plateau. Figure 2 decomposes the 4.7 percentage points of loss. Gas compression, with two 50 percent trains each failing about six times a year, caused 2.2 points, almost half the total, because any compressor failure halves throughput during the plateau. Turnarounds caused 0.9 points and spurious trips under 1oo2 ESD voting 0.7 points. Glycol dehydration and produced water treatment, both single-train, caused 0.3 points each, inlet separation 0.1 point and power generation, with 2- out-of-3 turbines, less than 0.1 point. This ranking, in which a frequently failing rotating subsystem without spare capacity dominates, is consistent with RAM studies of compressor stations and gas plants [8, 47, 73].

Fig 2: Production efficiency loss by cause for the base case (D0), knee design (D1) and NPV-optimal design (D2).

4.2. Value of Individual Levers and Their Interactions

Table 2 reports the effect of each lever applied alone to the base case. A third 50 percent compression train gave the largest gain, 2.1 percentage points and USD 45.6 million of NPV. CBM on compression and turbines gave 1.1 points and USD 24.7 million for a life-cycle cost of USD 1.7 million, the highest return per dollar at 14.6. 2oo3 ESD voting gave 0.5 point and USD 9.4 million. One set of compression spares gave 0.4 point and USD 7.2 million, and a second produced water train gave 0.3 point and USD 2.5 million. A second dehydration train broke even, and additional inlet separation, turbines, turbine spares and air compressors destroyed value, because those subsystems already contributed little loss. Removing the standby export pump lost 1.0 point and USD 19.7 million, confirming the value of existing redundancy.

Table 2: Effect of individual levers applied to the base case. Lever Gain in production efficiency (percentage points)

Incremental life-cycle cost (USD M)

NPV gain per dollar of life-cycle cost Third 50 percent compression train 2.12 7.61 45.6 6.0 Condition-based maintenance 1.05 1.69 24.7 14.6 2oo3 ESD voting 0.49 1.50 9.4 6.3 One compression spare set 0.36 1.74 7.2 4.1 Second produced water train 0.27 3.80 2.5 0.7 Second dehydration train 0.29 6.34 0.1 0.0 Second inlet separator 0.13 5.07 -2.2 -0.4 One turbine spare module 0.03 4.34 -3.5 -0.8 Fourth 50 percent turbine 0.08 10.14 -8.1 -0.8 Removal of standby export pump -0.96 -1.52 -19.7 Levers interact. Compression spares, worth USD 7.2 million alone, were not selected in any NPV-optimal design, because once a third compression train is installed, a spare stock-out removes only one of three trains and the facility continues at full capacity; spares and redundancy are substitutes. Conversely, CBM and the third train were complements in the sense that both remained in all high-value designs. Such interactions are invisible when levers are evaluated one at a time, which supports joint optimization of redundancy and spares [27, 30, 164].

4.3. Pareto Front and Selected Designs

Figure 3 shows all 15,552 designs and the exact Pareto front of 83 designs. Production efficiency rises steeply from 94.4 percent for the cheapest design to about 98 percent at USD 10 million of life-cycle cost and then flattens towards a ceiling of 98.8 percent, set by turnarounds and residual trips, which costs USD 54.6 million to reach. Table 3 compares the selected designs. The knee design D1 adds a third compression train, replaces the two 100 percent export pumps with three 50 percent pumps, adopts 2oo3 voting and CBM, and reaches 98.1 percent for USD 10.8 million, adding USD 57.0 million of NPV. The NPV-optimal design D2 adds a third compression train, second dehydration and water trains, 2oo3 voting and CBM, and reaches 98.7 percent for USD 20.9 million, adding USD 60.2 million. The last 0.6 percentage point between D1 and D2 therefore costs USD 10.2 million and adds USD 3.2 million of NPV. In D2, turnarounds account for 0.95 of the 1.3 points of remaining loss (Figure 2). The shape of the front, steep and then flat, is characteristic of redundancy allocation problems in which a few high-importance subsystems dominate the attainable improvement [140, 180].

Fig 3: Production efficiency and incremental life-cycle cost of all 15,552 designs, with the exact Pareto front and the selected designs.

Table 3: Selected designs.

4.4. Verification by Simulation

The discrete-event simulation agreed closely with the analytic model (Table 3 and Figure 4). Mean simulated production efficiency differed from the analytic value by 0.10, 0.07 and 0.01 percentage points for D0, D1 and D2. The small negative bias for D0 reflects the time-step discretization of the many short compressor outages. The simulation also shows the variability of realized performance over a 20-year life: for the base case, the 5th to 95th percentile range spanned 1.2 percentage points, whereas for D2 it spanned 0.2 point, so redundancy reduces both the mean loss and its variability, consistent with evidence that redundancy improves the predictability of production [14, 16].

Fig 4: Distribution of production efficiency over 20 years from discrete-event simulation; dashed lines show the analytic values.

4.5. Robustness to Failure-Rate Uncertainty and

Production Value Figure 5a shows the effect of failure-rate uncertainty. With an error factor of 2 on each subsystem failure rate, the base case had a 90 percent range of production efficiency from 92.6 to 96.5 percent, whereas D1 ranged from 97.5 to 98.3 percent and D2 from 98.4 to 98.7 percent. The regret analysis confirmed that D2 is robust: across 500 samples, its mean regret relative to the best front design for each sample was USD 1.1 million, its 95th percentile USD 3.4 million, and it was within USD 1 million of the best design in 61 percent of samples. The knee design D1 had a mean regret of USD 5.5 million and the base case USD 68.6 million. Figure 5b shows that the NPV-optimal design depends on the value of production. At USD 0.25 million per day, the optimum was D1 without CBM, with 97.9 percent efficiency for USD 9.1 million; at USD 0.5 million per day, it reached 98.4 percent for USD 14.6 million; between USD 0.75 and 1.0 million per day it was D2; and at USD 1.5 million per day a second inlet separator was added, reaching 98.8 percent for USD 26.0 million. The third compression train and 2oo3 voting were selected at every value. The robustness of D2 echoes the finding in the uncertainty analysis literature that decisions should be tested against epistemic uncertainty rather than nominal values alone [357, 360].

Fig 5: (a) Production efficiency under failure-rate uncertainty (box shows quartiles, whiskers 5th and 95th percentiles) and (b) production efficiency and incremental life-cycle cost of the NPV-optimal design as a function of the value of production.

5. Discussion

This section interprets the findings, draws implications for facility design and operation, considers how the method can be applied in practice and sets out its limitations. The discussion is framed by the production assurance principle that availability should be engineered through the life cycle rather than verified at the end of design [1, 19], and by the observation that the value of reliability improvements depends on their interaction with the system in which they are placed [27, 180, 314]. It also considers what the findings mean for brownfield facilities, where the design levers available are narrower than at the design stage [76, 77].

5.1. Principal Findings

Three findings stand out. First, production loss at the base facility was concentrated in a single subsystem. Gas compression, with frequent failures and no spare capacity, caused almost half the loss, and the most valuable measures were those that addressed it directly, a third train and CBM. This concentration is typical of oil and gas facilities, where rotating equipment dominates failure statistics [3, 8, 64], and it explains why RAM-based design choices can add tens of millions of dollars of value while most of the possible additions destroy value. Of the eleven levers, only four added significant value when applied alone, and five reduced NPV. Second, levers interact in ways that single-measure evaluations miss. Spares were valuable in the base design but redundant once a third compression train was installed, because a stock-out then left two trains in service, which still met plateau demand. This substitution between spares and redundancy, and the complementarity between CBM and redundancy, support the joint optimization of reliability, redundancy and spares advocated in the redundancy-inventory literature [27, 30, 164] and contrast with practice in which spares are planned after design is fixed [220, 224]. Third, complete enumeration was both feasible and informative. Because the UGF evaluates a design in a fraction of a millisecond, all 15,552 designs could be evaluated, giving the exact Pareto front and exact regret calculations without the convergence uncertainty of metaheuristic search [22, 34]. The NPV-optimal design was also robust to a factor-of-two uncertainty in failure rates, with a mean regret of USD 1.1 million, whereas the cheaper knee design carried a regret five times larger. Robustness to data uncertainty therefore favoured the more redundant design, a result consistent with the view that redundancy hedges against epistemic uncertainty [32, 357, 360].

5.2. Implications for Practice

For facility designers, the results suggest a sequence of steps. The first is to rank subsystems by their contribution to production loss using a multi-state model and importance measures before choosing any redundancy [180, 181, 311]. The second is to evaluate maintenance strategy and SIS architecture as design levers alongside redundancy, because CBM and 2oo3 voting delivered value at low cost [28, 98, 277]. The third is to optimize spares jointly with redundancy rather than sequentially [27, 207], and to link that plan to materials readiness and procurement lead times in the operating supply chain [225, 226]. The fourth is to test the selected design against failure-rate uncertainty and production value, because a design that is optimal for nominal data may carry large regret if the data are wrong [31, 33].

For operators of existing facilities, the same model supports brownfield decisions. Where adding a compression train is impractical, CBM and spares become the principal levers, and the base-case analysis shows that they recover about 1.4 percentage points together. Turnarounds became the largest residual loss in the optimized designs, which points to turnaround interval and duration optimization as the next frontier once equipment redundancy is adequate [238, 254]. Digital twins that update failure and repair parameters from operating data can keep such models current through the life of the facility [305, 306].

5.3. Application to Real Facilities

The approach requires reliability data for each unit type, repair times, spare lead times, trip rates and production values. Generic data from OREDA or ISO 14224 taxonomies [2, 3] can be updated with site data through Bayesian methods [31, 32, 354], and repair time distributions can be fitted from maintenance records [262, 268]. Where units are not identical or subsystems are not in simple series, the UGF extends to more general structures [26, 169, 176], and where dependencies such as common cause failures or shared maintenance crews matter, Petri nets or simulation can be used to verify the analytic model as was done here [15, 16, 115]. For larger design spaces, exact methods for multi-state redundancy allocation or metaheuristics can replace enumeration [23, 34].

5.4. Limitations

The study has several limitations. All parameters are representative values rather than data from a specific facility. The analytic model assumes independent units in steady state with exponential failures, although the simulation showed that lognormal repair times and finite horizons change the results by at most 0.1 percentage point. Common cause failures, shared repair crews and ageing were not modelled, and all of them would reduce the value of redundancy [115, 128, 252]; disruption of spare supply, which supply chain resilience frameworks for gas processing plants address [228], was also not modelled. The spare parts model uses a single-period stock-out approximation rather than a full inventory model [202]. The effect of CBM was represented by fixed reductions in failure rate and repair time rather than by a degradation model [286, 287]. Finally, safety consequences of trips and failures were not valued, so the analysis addresses production and cost only; in practice, SIS architecture is constrained by safety integrity requirements [103, 107].

6. Conclusion

This study embedded RAM analysis in the design optimization of a representative onshore oil and gas production facility, using a multi-state universal generating function model that included spare stock-outs, spurious trips and turnarounds, and enumerated all 15,552 combinations of eleven redundancy, sizing, spares, maintenance and safety system decisions.

Production loss at the base design was concentrated in gas compression. A third compression train and condition-based maintenance were the most valuable levers, and 2-out-of-3 shutdown voting and compression spares were also valuable when applied alone. Spares became redundant once a third train was installed. The exact Pareto front showed production efficiency rising steeply to about 98 percent for a modest life-cycle cost and then flattening towards a ceiling set by turnarounds. The value-maximizing design reached 98.7 percent and added about USD 60 million of net present value. It agreed with discrete-event simulation within 0.1 percentage point and remained close to optimal under a factor-of-two uncertainty in failure rates. For designers and operators, the results support ranking subsystems by their contribution to production loss, treating maintenance strategy and safety system architecture as design levers, optimizing spares jointly with redundancy and testing designs against data uncertainty. Further work should add common cause failures, shared maintenance resources, ageing and turnaround optimization, and calibrate the model with field data.

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