Academic Journal of Mathematical Sciences, 2024, 5(3); doi: 10.25236/AJMS.2024.050311.
Jingtao Huo1, Min Wang2, Zeyu Chen3
1Polymer Materials and Engineering, Hubei University, Wuhan, China
2Mathematics, Hubei University, Wuhan, China
3Artificial Intelligence, Hubei University, Wuhan, China
As modern industry evolves, the complexity of production and supply chain management increases, making quality control and decision optimisation crucial for competitiveness. This paper addresses these challenges through mathematical modelling and algorithms, focusing on spare parts quality inspection and multi-stage production optimisation. For defective parts detection, a sampling scheme based on hypothesis testing is proposed, calculating minimum sample sizes using binomial and normal approximations—138 samples at 95% confidence and 108 at 90% confidence—effectively reducing inspection costs while ensuring quality. Additionally, a "01 model" is used to optimise multi-stage production decisions, balancing detection and processing costs to minimise overall expenses and maximise profits. Strategic decision-making, as demonstrated by the model, can significantly cut costs and boost profitability. By incorporating Bayesian inference, the study estimates defective rates from sampling data, further refining multi-stage process optimisation and enhancing decision accuracy. This research provides practical tools for quality control and production optimisation, helping enterprises reduce costs, improve profits, and enhance market competitiveness, offering valuable insights for broader industry applications [1].
Binomial distribution, dynamic programming, 0-1 programming, Bayesian inference
Jingtao Huo, Min Wang, Zeyu Chen. Research on Multistage Production Optimization Based on Hypothesis Testing and Bayesian Inference. Academic Journal of Mathematical Sciences (2024) Vol. 5, Issue 3: 75-81. https://doi.org/10.25236/AJMS.2024.050311.
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