Predictive maintenance (PdM) in the context of Industry 4.0 faces a dual challenge: accurately detecting rare equipment failures (extreme class imbalance), while simultaneously avoiding excessive false alarms that can cause operator fatigue and reduced system trust. Existing machine learning approaches often rely on heuristic decision thresholds or unconstrained cost minimization, which lack explicit control over False Alarm Rate (FAR) and may compromise safety compliance during deployment. A novel framework, Cost-Sensitive Thresholding-based Conformal Light Gradient Boosting Machine (CST-Conformal-LGBM), which integrates algorithm-level cost-sensitive LightGBM training with distribution-free conformal calibration and FAR-constrained thresholding, is proposed to address these challenges. The approach introduces a risk-controlled decision rule that minimizes economic cost when the decision threshold is within a statistically defined safe region. SHAP-based feature attribution and manifold-learning-based diagnostics are integrated to enhance interpretability. Comprehensive experimental evaluation demonstrates that the proposed framework achieves approximately 1.50% FAR on the test set, within the predefined 2% safety constraint, while maintaining competitive operational costs and stable decision performance.