Production Process Optimization Model Based on Sequential Probability Ratio Test and Bayesian Update

To improve product quality and control costs, companies need to inspect defect rates of components and handle defective items. Based on hypothesis testing, we set null hypothesis <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{0}$</tex> and alternative hypothesis <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{1}$</tex>, using binomial and normal distribution approximations to calculate sample size and standardized defect rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Z$</tex> to determine whether to reject <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{0}$</tex>. Sequential probability ratio testing is applied to evaluate sample data incrementally, reaching 90% confidence at around 60 samples and 95% confidence at around 290 samples. A minimum-cost model for multi-stage, multi-component production was established. By exhaustive search and combination optimization, the model calculates defect rates and total production costs across each stage and component, identifying the optimal balance between defect rates and costs. The model generates 8192 combinations, considering defect rates, inspection costs, assembly costs, market price, and return loss. Using 0-1 variables for component, semi-finished, and finished product inspection and disassembly status, each strategy's total cost and market loss are calculated. Results show the optimal strategy costs 126 yuan with a 56% defect rate, reducing total production costs. The model further applies a Bayesian update algorithm to dynamically estimate defect rates and adjust strategies in real-time, enabling optimized production flow under defect rate fluctuations. This model provides data support for defect rate control and cost management in the production process.