predictive-maintenance-uncertainty-scenario

name	predictive-maintenance-uncertainty-scenario
description	Scenario-based optimization framework for predictive maintenance scheduling under uncertainty. Integrates calendar-based, usage-based, and condition-monitoring (RUL) information into unified finite-horizon decision framework. Use when: (1) optimizing multi-asset maintenance schedules, (2) dealing with uncertain RUL estimates, (3) comparing expected-cost vs tail-risk maintenance policies, (4) integrating heterogeneous maintenance information sources, (5) scenario-based decision making for asset management.
license	Complete terms in LICENSE.txt
metadata	{"arxiv_id":"2605.30222","published":"2026-05-28","authors":"Jerzy Baranowski, Waldemar Bauer","tags":["predictive-maintenance","uncertainty","scenario-optimization","RUL","scheduling","multi-asset","systems-engineering"]}

Predictive Maintenance Optimization under Uncertainty

Scenario-based framework for multi-asset maintenance scheduling that integrates heterogeneous information sources.

Problem Context

Traditional maintenance scheduling approaches treat different information sources separately:

• Calendar-based: Fixed overhaul intervals
• Usage-based: Operating cycle limits
• Condition-monitoring: RUL (Remaining Useful Life) estimates with uncertainty

This framework unifies all three sources into a single optimization problem.

Core Methodology

1. Unified Finite-Horizon Decision Framework

Inputs:

• Multiple assets with different characteristics
• Calendar-based overhaul intervals (τ_cal)
• Usage-based limits with uncertain future cycles (τ_usage)
• RUL estimates with uncertainty distributions (RUL ~ P)

Decision variables:

• Maintenance schedule S = {s₁, s₂, ..., sₙ} for n assets
• Each sᵢ specifies timing and type of maintenance actions

Objective:

• Compare schedules under simulated future scenarios
• Evaluate using expected-cost and tail-risk criteria

2. Scenario Generation

Generate scenarios that capture:

• Uncertain usage patterns (operating cycles)
• RUL uncertainty distributions
• Random failure events
• Cost variations

# Pseudocode for scenario generation
def generate_scenarios(n_assets, n_scenarios):
    scenarios = []
    for i in range(n_scenarios):
        scenario = {
            'usage': sample_usage_patterns(n_assets),
            'rul': sample_rul_distributions(n_assets),
            'failures': sample_failure_events(n_assets),
            'costs': sample_cost_variations()
        }
        scenarios.append(scenario)
    return scenarios

3. Schedule Evaluation

For each candidate schedule S:

def evaluate_schedule(schedule, scenarios):
    costs = []
    for scenario in scenarios:
        cost = compute_schedule_cost(schedule, scenario)
        costs.append(cost)
    
    # Expected cost criterion
    expected_cost = mean(costs)
    
    # Tail-risk criteria
    percentile_95 = percentile(costs, 95)
    percentile_99 = percentile(costs, 99)
    
    return {
        'expected_cost': expected_cost,
        'p95_cost': percentile_95,
        'p99_cost': percentile_99
    }

4. Optimization

Risk-neutral policy:

• Minimize expected_cost across all schedules

Risk-aware policy:

• Minimize tail-risk (p95 or p99) while constraining expected_cost

Key Advantages

1. Integrated approach: Combines calendar, usage, and prognostics information
2. Risk quantification: Explicit handling of uncertainty via scenarios
3. Flexibility: Supports both risk-neutral and risk-aware decisions
4. Multi-asset coordination: Optimizes maintenance across asset portfolio

Implementation Steps

1. Data collection:

   • Gather calendar intervals, usage history, RUL estimates
   • Characterize uncertainty distributions

2. Scenario generation:

   • Define probability distributions for uncertain parameters
   • Generate representative scenarios (100-1000 scenarios typical)

3. Candidate schedules:

   • Generate candidate maintenance schedules
   • Include single-trigger rules as baseline

4. Evaluation:

   • Evaluate each schedule across all scenarios
   • Compute expected-cost and tail-risk metrics

5. Selection:

   • Choose optimal schedule based on risk preference
   • Compare against simpler single-trigger policies

Use Cases

• Industrial equipment: Combined calendar and condition-based maintenance
• Fleet management: Multi-vehicle maintenance coordination
• Infrastructure: Bridge, pipeline, or facility maintenance planning
• Energy systems: Turbine, transformer, or grid component maintenance

Comparison with Traditional Approaches

Approach	Integration	Uncertainty	Risk Quantification
Calendar-only	Single source	Ignored	None
RUL-based	Single source	Partial	Limited
Usage-based	Single source	Partial	Limited
This framework	All three	Explicit	Full

Practical Considerations

• Scenario count: Balance accuracy vs computational cost (typically 100-500)
• Risk preference: Choose tail-risk percentile based on organizational risk tolerance
• Computational complexity: O(n_assets × n_scenarios × n_candidate_schedules)
• Data quality: RUL uncertainty characterization is critical

Related Concepts

• Predictive maintenance: CBM (Condition-Based Maintenance), PHM (Prognostics and Health Management)
• Decision under uncertainty: Robust optimization, stochastic programming
• Risk measures: Value at Risk (VaR), Conditional VaR (CVaR)

Activation Keywords

• predictive maintenance optimization
• maintenance scheduling uncertainty
• scenario-based maintenance
• RUL-based scheduling
• multi-asset maintenance
• risk-aware maintenance planning