Condition-Based Maintenance of Degrading Assets underIntermittent Accessibility

• When an accessible opportunity arises, intervening now trades off against waiting, which risks further degradation or failure before another opportunity.Corrective maintenance is also subject to accessibility restrictions, potentially prolonging downtime after failure.Source: §1 · p. 2
• The same condition and accessibility status can imply different decisions when the outlook for future opportunities differs.Seasonal and random environmental changes motivate accounting for the accessibility cycle, not just whether maintenance is possible now.Source: §1 · pp. 2–3
• The model treats asset degradation as the physical need for intervention and accessibility as a separate stochastic process governing whether intervention is possible.The formulation is a finite-state Markov decision process minimizing long-run average cost.Source: §1 · pp. 3–4
• For each accessible state, the optimal policy maintains a condition threshold, but that threshold depends on the current accessibility state and its transition dynamics.Stochastic accessibility preserves the threshold structure while making it contingent on future maintenance opportunities.Source: §1 · p. 4
• The numerical study benchmarks the optimal policy against an optimized single-threshold condition-based policy and an optimized age-based policy under the same stochastic accessibility process.It also examines how accessibility dynamics, degradation characteristics, and economic parameters affect optimal thresholds.Source: §1 · p. 4

• Classical maintenance research studies intervention timing under degradation and failure, while later work extends the scope to predictive maintenance, production planning, and optimization.Source: §2 · p. 4
• Structural maintenance policies include condition-based control limits, age-varying thresholds, and policies for settings with production or information complexities.Examples include Elwany et al. (2011), Si et al. (2018), and Liu et al. (2017).Source: §2 · p. 5
• Environmental effects have been modeled through changes to degradation rates or through restrictions and delays affecting maintenance opportunities.The first line changes asset-side degradation dynamics; the second affects when maintenance can occur or the costs of delay.Source: §2 · p. 5
• Prior wind-turbine studies represent weather through disruptions, seasonal conditions, delays, or waiting times, rather than an explicitly evolving accessibility state governing maintenance availability.The paper treats accessibility as a distinct stochastic process and studies how its evolution modifies the condition threshold under a long-run average cost criterion.Source: §2 · p. 6

3.1 Problem Setting and Sequence of Events

• At each decision epoch, condition and accessibility are observed; maintenance is available only in accessible states, and otherwise the asset continues operating and degrading.Preventive maintenance is possible before failure and corrective maintenance after failure; either intervention restores the asset to as-good-as-new.Source: §3.1 · pp. 6–7

3.2.1 State and Action Space

• The system state combines an asset-condition state with an accessibility state, and the available actions depend on accessibility and whether the asset has failed.The asset condition ranges from new through degraded states to failure; maintenance is unavailable in inaccessible states.Source: §3.2.1 · p. 7

3.2.2 Transition Dynamics

• Accessibility evolves as a stochastic process independent of degradation; without maintenance, condition follows its degradation transition, while maintenance resets condition to new.Source: §3.2.2 · pp. 7–8

3.2.3 Cost Structure

• Continuing operation incurs efficiency-loss costs that depend on condition and accessibility, while preventive and corrective maintenance incur accessibility-dependent costs, with corrective maintenance more costly.Costs include direct intervention expense and maintenance-related production losses.Source: §3.1 · p. 7, §3.2.3 · p. 8

3.3 Long-Run Average Cost and Recurrence

• Recurrence assumptions make accessible states reachable and ensure that postponing maintenance leaves a positive-probability path to failure; the resulting stationary-policy chains have one recurrent class.The common post-maintenance state helps connect recurrent behavior across policies, making long-run average cost independent of the initial state.Source: §3.3 · p. 9

4.1 Conditions for Structural Analysis

• The structural analysis requires degradation and operating consequences to preserve condition ordering, with corrective maintenance no cheaper than preventive maintenance.Worse current conditions must not yield stochastically better future conditions; failure-related consequences preserve the ordering through the failed state.Source: §4.1 · p. 10

4.2 Average-Cost Optimality Equation

• The finite-state problem is characterized by an average-cost optimality equation, and the preventive-maintenance value is independent of the current degraded condition.This state independence lets increasing continuation value with degradation yield an ordered maintenance region.Source: §4.2 · p. 11

4.3 Monotonicity of the Bias Function

• The bias function is nondecreasing with degradation because continued operation combines greater current efficiency loss with stochastically worse future conditions, while maintenance restores the same new state.Source: §4.3 · pp. 12–13

4.4 Optimality of Accessibility-Dependent Threshold Policies

• Under Assumptions 1–4, an average-cost-optimal stationary policy uses a condition threshold for each accessible state: maintain at or above it, and continue below it.At threshold K, preventive maintenance is never performed; intervention occurs only after failure.Source: §4.4 · pp. 14–15
• Thresholds can differ across accessible states because current accessibility changes both the immediate intervention tradeoff and the distribution of future opportunities.No threshold decision is needed when the asset is inaccessible, since maintenance cannot be performed there.Source: §4.4 · p. 15

4.5 Threshold Policy Representation

• The optimal stationary policy can be represented by one condition threshold per accessible state rather than a separate action for every state.Source: §4.5 · p. 15

5 Numerical Study

• The experiments examine how stochastic and seasonal accessibility affect condition-based maintenance decisions in an offshore wind setting.The motivating accessibility process reflects weather and sea conditions with annual seasonality and period-to-period uncertainty.Source: §5 · p. 16
• The study compares the optimal policy with optimized constant-threshold and age-based policies under the same stochastic accessibility process.Source: §5 · p. 16
• Sensitivity analyses vary accessibility, degradation, and economic characteristics to assess their effects on threshold levels and seasonal variation.Source: §5 · p. 16

5.1.1 Degradation Process

• A Gamma process models monotone cumulative degradation, with failure absorbing absent maintenance in the discrete condition-state model.The Gamma-process specification is used only for the numerical experiments.Source: §5.1.1 · p. 16

5.1.2 Accessibility Process

• Accessibility is modeled as a two-state Markov process with persistence and seasonal variation, distinguishing accessible from inaccessible weeks.Its parameters control persistence, seasonality amplitude, and the week of peak accessibility.Source: §5.1.2 · p. 17

5.1.3 Parameterization

• The base case uses 11 condition states and a mean time to failure of 80 weeks with a 35-week standard deviation.The preventive and corrective maintenance costs are $150,000 and $750,000, respectively; operating cost increases with degradation and is substantially higher at failure.Source: §5.1.3 · pp. 17–18
• The parameter values are selected for computational experiments, including a 52-week accessibility cycle with persistence 0.55, seasonality amplitude 0.40, and peak accessibility in week 30.Source: §5.1 · p. 16, §5.1.3 · p. 19

5.2 Base-Case Analysis

• The optimal threshold is generally higher when accessibility is favorable and expected to persist or improve, and lower when future accessibility is expected to worsen.A lower threshold means using the current opportunity before access becomes more limited.Source: §5.2 · p. 19
• Weeks 16 and 44 have the same one-week accessibility probability (0.50), but thresholds of 5 and 3, respectively, because their later accessibility outlooks differ.Access is expected to improve after week 16 but worsen after week 44.Source: §5.2 · p. 20
• Stochastic accessibility preserves the condition-threshold structure but makes the threshold state-dependent and forward-looking.Decisions reflect asset condition, current accessibility, and future maintenance opportunities.Source: §5.2 · p. 20

5.3 Value of Informed Decisions

• The optimized age-based benchmark schedules preventive maintenance after a fixed elapsed time and selects 24 weeks as its maintenance age.The age is chosen to minimize long-run average cost over candidate ages from 4 to 44 weeks.Source: §5.3 · p. 20
• The optimized constant-threshold benchmark observes condition but uses one threshold year-round, with threshold 4 selected to minimize long-run average cost.This comparison isolates the value of adapting condition-based decisions to accessibility.Source: §5.3 · p. 20
• The optimal policy reduces long-run average cost from $9323.0 to $6157.7 versus the age-based policy, a 33.95% improvement.Corrective-maintenance frequency falls from 0.075 to 0.038 events per year.Source: §5.3 · p. 21, Table 2 · p. 21
• Relative to the constant-threshold policy, the optimal policy reduces long-run average cost from $6435.0 to $6157.7, a 4.31% improvement.Both policies use degradation state and face the same accessibility restrictions; the optimal policy adapts its threshold to accessibility and future opportunities.Source: §5.3 · pp. 21–22, Table 2 · p. 21
• The combined comparisons reduce long-run average cost from $9323.0 to $6435.0 by incorporating condition information, then to $6157.7 by adapting thresholds to accessibility.The latter savings come from lower operating and preventive maintenance cost rates that more than offset a small increase in corrective-maintenance cost.Source: §5.3 · p. 22
• Across the shared 150-week simulation, the optimal policy lowers its threshold to 3 during weeks 43–51 and performs preventive maintenance in week 46, before extended inaccessibility.The constant-threshold policy, with fixed threshold 4, skips the available week-46 opportunity and subsequently fails; the age-based policy performs preventive maintenance in the new condition state.Source: §5.3 · p. 22

5.4 Sensitivity Analysis

• Sensitivity analysis varies one parameter at a time while holding the others fixed, then recomputes optimal thresholds over the 52-week cycle.The varied parameters cover accessibility, degradation, and economic characteristics.Source: §5.4 · pp. 22, 24

5.4.1 Accessibility Characteristics

• Stronger weather persistence makes thresholds slightly lower in unfavorable periods and higher in favorable periods, while stronger seasonality widens this contrast.With weak seasonality (∆= 0.30), the threshold is nearly constant; stronger persistence also makes the policy more responsive to the accessibility outlook.Source: §5.4.1 · p. 24

5.4.2 Degradation Characteristics

• Shorter mean time to failure lowers optimal thresholds, while greater uncertainty in time to failure increases their variation across the seasonal accessibility cycle.Faster degradation calls for earlier intervention, and greater degradation uncertainty makes the policy respond more strongly to accessibility changes.Source: §5.4.2 · p. 25

5.4.3 Economic Characteristics

• Lower preventive-maintenance costs and higher efficiency-loss multipliers both lower optimal thresholds, favoring intervention at less-degraded conditions.Higher preventive-maintenance costs shift thresholds toward more degraded states; greater efficiency losses make continued operation in degraded states more costly.Source: §5.4.3 · p. 26

6 Conclusion

• The optimal policy retains a condition threshold, but its level varies with accessibility because future opportunities affect whether to intervene now or wait.The same current accessibility can imply different thresholds when the outlook for future opportunities differs.Source: §6 · p. 28
• 4.31% lower long-run average cost than the optimized constant-threshold policy, and 33.95% lower than the optimized age-based policy, were achieved by the optimal policy.It also required fewer preventive interventions and experienced substantially fewer corrective interventions than the age-based policy.Source: §6 · p. 28
• Stronger weather persistence and seasonality increase threshold differentiation, while faster degradation prompts earlier intervention and greater time-to-failure uncertainty increases responsiveness to accessibility.Lower preventive costs and higher degradation-related operating losses favor earlier intervention; higher preventive costs and lower operating losses support postponement.Source: §6 · p. 28
• The optimal threshold is not universal: it changes with accessibility, degradation, and economic conditions, and failing to adapt can increase long-run cost.Source: §6 · p. 29
• Future extensions include competing assets, multi-period maintenance durations, imperfect maintenance, and partially observed condition.These features would allow accessibility-aware maintenance to be studied in richer operational environments.Source: §6 · p. 29