Time-reliability optimization of multi-pass underfill dispensing sequences on printed circuit boards: a schedule-dependent reliability model solved by a multiset-permutation binary-addition-tree algorithm
Abstract
Multi-pass underfill dispensing couples cycle time with process reliability because the sequence determines the inter-pass flow times. This paper formulates a tri-objective multiset-permutation routing model that minimises nominal cycle time and additive duration variance while maximising reliability under hard- and soft-dwell policies; reliability combines pass, schedule-dependent flow and travel terms. Under independent durations and deterministic dwell thresholds, the variance measure equals the cycle-time variance under soft dwell and bounds it from above under hard dwell. A multiset-permutation binary-addition-tree algorithm enumerates the feasible routes without duplication and prunes prefixes by dominance. Six instances, including three BeagleBone Black benchmarks, yield reference Pareto fronts, the largest search space of 1.47 × 1012 routes in 38 minutes on 20 CPU cores. Among simulated candidates, the nominally cost-selected routes incur maximum estimated excess costs of USD 0.0014 per board at the modelled duration variability and USD 0.0035 with it doubled. Round-robin dispatch is within 3.7 % of the reference optimum at the tested costs; NSGA-II and simplified swarm optimisation show at most 0.53 % observed cost regret while recovering about 30 % of the largest hard-dwell front. The framework quantifies sequencing trade-offs and heuristic decision regret; physical reliability prediction requires inspection-based calibration.
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BibTeX
@misc{yeh2026timereliability,
title = {{Time-reliability optimization of multi-pass underfill dispensing sequences on printed circuit boards: a schedule-dependent reliability model solved by a multiset-permutation binary-addition-tree algorithm}},
author = {Wei-Chang Yeh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04186},
eprint = {2610.04186},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04186},
}
RIS
TY - UNPB
TI - Time-reliability optimization of multi-pass underfill dispensing sequences on printed circuit boards: a schedule-dependent reliability model solved by a multiset-permutation binary-addition-tree algorithm
AU - Wei-Chang Yeh
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04186
UR - https://arxiv.org/abs/2610.04186
AB - Multi-pass underfill dispensing couples cycle time with process reliability because the sequence determines the inter-pass flow times. This paper formulates a tri-objective multiset-permutation routing model that minimises nominal cycle time and additive duration variance while maximising reliability under hard- and soft-dwell policies; reliability combines pass, schedule-dependent flow and travel terms. Under independent durations and deterministic dwell thresholds, the variance measure equals the cycle-time variance under soft dwell and bounds it from above under hard dwell. A multiset-permutation binary-addition-tree algorithm enumerates the feasible routes without duplication and prunes prefixes by dominance. Six instances, including three BeagleBone Black benchmarks, yield reference Pareto fronts, the largest search space of 1.47 × 10^12 routes in 38 minutes on 20 CPU cores. Among simulated candidates, the nominally cost-selected routes incur maximum estimated excess costs of USD 0.0014 per board at the modelled duration variability and USD 0.0035 with it doubled. Round-robin dispatch is within 3.7 % of the reference optimum at the tested costs; NSGA-II and simplified swarm optimisation show at most 0.53 % observed cost regret while recovering about 30 % of the largest hard-dwell front. The framework quantifies sequencing trade-offs and heuristic decision regret; physical reliability prediction requires inspection-based calibration.
ER -