A Quality-Risk-Aware Stochastic Dynamic Programming Model for Blade Replacement Optimization in IC Packaging Singulation
- 1School of Computer Science and Software, Zhaoqing University, Zhaoqing 526061, China
- 2Department of International Business, Ming Chuan University, Taipei 333000, Taiwan
- 3Department of Information Management, Kun Shan University, Tainan 710303, Taiwan
Abstract
Blade degradation in IC packaging singulation processes induces progressive dimensional drift, inflates process variability, and escalates out-of-specification (OOS) risk, thereby coupling equipment condition directly to product quality. Conventional fixed-cycle replacement policies cannot adapt to dynamic production environments characterized by fluctuating production loads, machine vibration, material hardness variation, and unexpected shock disturbances, and therefore either incur excessive replacement expenditure or cause substantial quality losses. This study formulates blade replacement as a finite-horizon sequential decision problem under uncertainty and develops a quality-risk-aware stochastic dynamic optimization model. A discrete-time state-space degradation model is first constructed to describe the joint evolution of blade age and accumulated wear under time-varying manufacturing disturbances. A trend-adjusted process capability index and an analytic OOS probability are then derived to translate the degradation state into quantifiable quality-risk measures. A penalty-augmented cost function combining replacement expenditure, wear-induced operating cost, OOS quality loss, and quality-constraint penalties is minimized, subject to replacement-frequency and minimum-interval constraints, and the resulting Bellman recursion is solved by a scenario-based dynamic programming algorithm over a discretized wear-state grid. Analytical propositions establish the monotonic deterioration of process capability, the monotone escalation of OOS risk with blade wear, the existence of an economic tradeoff between early and delayed replacement, and the weak dominance of the dynamically optimized policy over fixed-cycle rules within the same feasible policy space. Numerical experiments on realistic semiconductor packaging scenarios show that the proposed policy consistently attains the lowest total operational cost relative to fixed-cycle and threshold-based benchmarks, and extensive sensitivity analyses confirm its robustness under varying disturbance levels, cost parameters, and quality requirements.
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BibTeX
@article{fang2026qualityriskaware,
title = {{A Quality-Risk-Aware Stochastic Dynamic Programming Model for Blade Replacement Optimization in IC Packaging Singulation}},
author = {Chih-Chiang Fang and Chin-Chia Hsu and Chun-Wu Yeh},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203670},
url = {https://www.mdpi.com/2227-7390/14/20/3670},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Quality-Risk-Aware Stochastic Dynamic Programming Model for Blade Replacement Optimization in IC Packaging Singulation
AU - Chih-Chiang Fang
AU - Chin-Chia Hsu
AU - Chun-Wu Yeh
PY - 2026
DA - 2026/10/10
JO - Mathematics
DO - 10.3390/math14203670
UR - https://www.mdpi.com/2227-7390/14/20/3670
AB - Blade degradation in IC packaging singulation processes induces progressive dimensional drift, inflates process variability, and escalates out-of-specification (OOS) risk, thereby coupling equipment condition directly to product quality. Conventional fixed-cycle replacement policies cannot adapt to dynamic production environments characterized by fluctuating production loads, machine vibration, material hardness variation, and unexpected shock disturbances, and therefore either incur excessive replacement expenditure or cause substantial quality losses. This study formulates blade replacement as a finite-horizon sequential decision problem under uncertainty and develops a quality-risk-aware stochastic dynamic optimization model. A discrete-time state-space degradation model is first constructed to describe the joint evolution of blade age and accumulated wear under time-varying manufacturing disturbances. A trend-adjusted process capability index and an analytic OOS probability are then derived to translate the degradation state into quantifiable quality-risk measures. A penalty-augmented cost function combining replacement expenditure, wear-induced operating cost, OOS quality loss, and quality-constraint penalties is minimized, subject to replacement-frequency and minimum-interval constraints, and the resulting Bellman recursion is solved by a scenario-based dynamic programming algorithm over a discretized wear-state grid. Analytical propositions establish the monotonic deterioration of process capability, the monotone escalation of OOS risk with blade wear, the existence of an economic tradeoff between early and delayed replacement, and the weak dominance of the dynamically optimized policy over fixed-cycle rules within the same feasible policy space. Numerical experiments on realistic semiconductor packaging scenarios show that the proposed policy consistently attains the lowest total operational cost relative to fixed-cycle and threshold-based benchmarks, and extensive sensitivity analyses confirm its robustness under varying disturbance levels, cost parameters, and quality requirements.
SN - 2227-7390
ER -