be-optimumoh/docs/overhaul_optimization/equipment_optimization.md

Equipment Level Overhaul Optimization

This document explains the mathematical theory and implementation used to determine the optimal overhaul interval for individual assets.

1. Theoretical Foundation

The optimization model is based on the Expected Total Cost per Unit Time (CPUT) theory, a standard approach in reliability engineering for age-replacement and block-replacement policies.

Objective Function

The goal is to find an overhaul interval (T) that minimizes the total expected cost amortized over time:

C(T) = \frac{C_{Preventive} + C_{Corrective} \cdot E[N(T)]}{T}

Where:

• T: The overhaul interval (e.g., month 12, 24, etc.).
• C_{Preventive}: The cost of a planned overhaul (materials, labor, and procurement).
• C_{Corrective}: The cost of an unplanned failure (repairs + risk cost of downtime).
• E[N(T)]: The expected number of failures occurring in the interval (0, T]. This is derived from the NHPP (Non-Homogeneous Poisson Process) reliability model.

2. The Cost Balance (The "U-Curve")

Optimization works by balancing two competing costs:

1. Overhaul Cost (C_{PM}/T): As the interval T increases, the amortized cost of the overhaul decreases (economy of waiting).
2. Failure Risk (C_{CM} \cdot E[N(T)]/T): As the interval T increases, the probability and expected frequency of failure increase (cost of wear-out).

The point where these two lines intersect typically represents the Global Minimum of the total cost curve, known as the Optimum Overhaul Month.

3. Implementation Logic

In the service.py engine, the search is performed as follows:

1. Failure Projection: The system fetches reliability prediction data (cumulative failures) for the analysis window.
2. Sparepart Simulation: For every potential month T, the system simulates the procurement process to calculate the real C_{Preventive} (including any shortage penalties).
3. Cost Amortization:

   total_cycle_cost = total_expected_failure_cost + total_preventive_cost
   cput = total_cycle_cost / month_index
   

4. Grid Search: The system iterates through all months in the analysis window and identifies the index with the lowest cput value.

4. Interpretation in UI

• Analysis Window Card: Shows the CPUT value at your currently selected month.
• Optimum Target Card: Shows the month T where the curve is at its lowest point.
• Potential Benefit: Calculated as CPUT(current) - CPUT(optimum). This represents the real monthly cash-flow saving if the maintenance interval is adjusted.