Vehicle Maintenance Cost Prediction using Bayesian Regression in ML

Fleet‑management teams must forecast each vehicle’s next maintenance cost before scheduling service, using early-life indicators such as vehicle age, odometer reading, engine hours, prior maintenance costs, and usage intensity. Maintenance costs tend to increase nonlinearly with age and usage (e.g., via exponential wear-out), and uncertainty arises from variability in driving conditions and fluctuations in repair costs. By applying Bayesian Regression, we obtain not only a point estimate of expected cost but also a credible interval that quantifies our uncertainty—enabling data-driven budgeting and proactive parts procurement.

Libraries Required

import pandas as pd                             # data manipulation  
import numpy as np                              # numerical ops  
  
import matplotlib.pyplot as plt                 # plotting  
import seaborn as sns                           # visualization  

import pymc3 as pm                              # Bayesian modeling  
import arviz as az                              # posterior analysis  

from sklearn.model_selection import train_test_split  
from sklearn.preprocessing import StandardScaler  
from sklearn.metrics import mean_absolute_error  

Dataset

Logistics Vehicle Maintenance History Dataset

Step-by-Step Code Implementation

Import Libraries & Load Data

import pandas as pd

# Load dataset
df = pd.read_csv("data/logistics-vehicle-maintenance-history-dataset.csv")

# Preview relevant columns
df.head()[[
    'Age','Mileage','EngineHours','PrevMaintenanceCost','MaintenanceCost'
]]

Preprocessing & Train/Test Split

from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

# Select features and target
X = df[['Age','Mileage','EngineHours','PrevMaintenanceCost']].values
y = df['MaintenanceCost'].values  # USD

# Chronological or random split
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42
)

# Standardize predictors for stable MCMC sampling
scaler = StandardScaler().fit(X_train)
X_train_s = scaler.transform(X_train)
X_test_s  = scaler.transform(X_test)

Define & Fit Bayesian Regression Model

• Priors (α,β,σ): We use broad normal priors for intercepts and slopes to remain weakly informative, reflecting substantial uncertainty about cost drivers.
• Model: μ = α + β·X_standardized captures a linear—but uncertainty‑quantified—relationship between cost and features.
• Likelihood: Observed costs are assumed to be normally distributed around μ with standard deviation σ.
• Sampling: MCMC draws (2,000 post‑tuning) with target_accept=0.9 ensure stable exploration of the posterior.

import pymc3 as pm

with pm.Model() as model:
    # Priors: intercept α and weights β
    α = pm.Normal("α", mu=0, sigma=100)
    β = pm.Normal("β", mu=0, sigma=50, shape=X_train_s.shape[1])
    σ = pm.HalfNormal("σ", sigma=50)
    
    # Linear predictor
    μ = α + pm.math.dot(X_train_s, β)
    
    # Likelihood
    Y_obs = pm.Normal("Y_obs", mu=μ, sigma=σ, observed=y_train)
    
    # MCMC sampling
    trace = pm.sample(
        draws=2000, tune=1000,
        target_accept=0.9,
        return_inferencedata=True
    )

Posterior Analysis & Point Predictions

• Posterior predictive: We generate predicted costs for new inputs and derive high-probability (HPD) credible intervals to quantify forecast uncertainty.
• Point estimates & MAE: Posterior means of α and β yield point forecasts; MAE on the hold‑out set quantifies average prediction error.

import arviz as az

# Summarize posterior distributions
az.summary(trace, round_to=2)

# Posterior predictive sampling
with model:
    ppc = pm.sample_posterior_predictive(trace, var_names=["Y_obs"])

# Compute posterior means for α and β
α_post = trace.posterior["α"].mean().item()
β_post = trace.posterior["β"].mean(dim=["chain","draw"]).values

# Point predictions on test set
y_pred = α_post + X_test_s.dot(β_post)

# Evaluate mean absolute error
mae = mean_absolute_error(y_test, y_pred)
print(f"Test MAE: ${mae:.2f}")

Visualise Predictions & Credible Intervals

Plotting cost vs mileage (holding other features fixed) with credible bands illustrates both expected cost trend and our uncertainty, guiding risk‑aware maintenance budgeting.

# Example: vary Mileage, hold others at median
mile_grid = np.linspace(X_train_s[:,1].min(), X_train_s[:,1].max(), 100)
grid = np.column_stack([
    np.full_like(mile_grid, X_train_s[:,0].mean()),  # Age
    mile_grid,
    np.full_like(mile_grid, X_train_s[:,2].mean()),  # EngineHours
    np.full_like(mile_grid, X_train_s[:,3].mean())   # PrevCost
])

with model:
    pm.set_data({"X": grid})
    ppc_grid = pm.sample_posterior_predictive(trace, var_names=["Y_obs"])

preds = ppc_grid["Y_obs"]
mean_pred = preds.mean(axis=0)
hpd = az.hdi(preds, hdi_prob=0.94)

# Transform mileage back
mile_orig = scaler.inverse_transform(
    np.column_stack([np.zeros_like(mile_grid), grid[:,1:],])
)[:,1]

plt.figure(figsize=(8,5))
plt.plot(mile_orig, mean_pred, label="Posterior mean")
plt.fill_between(mile_orig, hpd[:,0], hpd[:,1], alpha=0.3, label="94% CI")
plt.scatter(scaler.inverse_transform(X_test_s)[:,1], y_test,
            color="k", alpha=0.5, label="Test data")
plt.xlabel("Mileage")
plt.ylabel("Maintenance Cost (USD)")
plt.title("Bayesian Regression: Cost vs. Mileage")
plt.legend()
plt.show()

Summary

By leveraging Bayesian Regression for vehicle maintenance cost forecasting, we achieve:

1. Point estimates of upcoming maintenance spending based on early indicators (age, mileage, engine hours).

2. Credible intervals that reflect uncertainty from usage variability and repair‐price fluctuations.

3. Actionable insights: fleet managers can budget with upper and lower bounds, proactively schedule parts procurement, and identify vehicles with high forecasting uncertainty for closer monitoring.