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42 lines
2.6 KiB
Markdown
42 lines
2.6 KiB
Markdown
# Equipment Level Overhaul Optimization
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This document explains the mathematical theory and implementation used to determine the optimal overhaul interval for individual assets.
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## 1. Theoretical Foundation
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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.
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### Objective Function
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The goal is to find an overhaul interval ($T$) that minimizes the total expected cost amortized over time:
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$$C(T) = \frac{C_{Preventive} + C_{Corrective} \cdot E[N(T)]}{T}$$
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Where:
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* **$T$**: The overhaul interval (e.g., month 12, 24, etc.).
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* **$C_{Preventive}$**: The cost of a planned overhaul (materials, labor, and procurement).
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* **$C_{Corrective}$**: The cost of an unplanned failure (repairs + risk cost of downtime).
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* **$E[N(T)]$**: The expected number of failures occurring in the interval $(0, T]$. This is derived from the **NHPP (Non-Homogeneous Poisson Process)** reliability model.
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## 2. The Cost Balance (The "U-Curve")
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Optimization works by balancing two competing costs:
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1. **Overhaul Cost ($C_{PM}/T$)**: As the interval $T$ increases, the amortized cost of the overhaul decreases (economy of waiting).
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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).
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The point where these two lines intersect typically represents the **Global Minimum** of the total cost curve, known as the **Optimum Overhaul Month**.
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## 3. Implementation Logic
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In the `service.py` engine, the search is performed as follows:
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1. **Failure Projection**: The system fetches reliability prediction data (cumulative failures) for the analysis window.
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2. **Sparepart Simulation**: For every potential month $T$, the system simulates the procurement process to calculate the real $C_{Preventive}$ (including any shortage penalties).
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3. **Cost Amortization**:
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```python
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total_cycle_cost = total_expected_failure_cost + total_preventive_cost
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cput = total_cycle_cost / month_index
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```
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4. **Grid Search**: The system iterates through all months in the analysis window and identifies the index with the lowest `cput` value.
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## 4. Interpretation in UI
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* **Analysis Window Card**: Shows the CPUT value at your currently selected month.
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* **Optimum Target Card**: Shows the month $T$ where the curve is at its lowest point.
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* **Potential Benefit**: Calculated as $CPUT(current) - CPUT(optimum)$. This represents the real monthly cash-flow saving if the maintenance interval is adjusted.
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