# A Modified Bayesian Network Model to Predict Reorder Level of Printed Circuit Board
## 5 Conclusions  
In this paper, the identification of repeated PCB orders for batch production was transformed into a reorder level prediction problem and a modified Bayesian network model with Monte Carlo simulations to study the relationship between different characteristic variables and reorder levels of PCB within six months was established. Reorder frequency was divided into four reorder levels and variables related to a reorder level were specified. Field data was exported and integrated from a PCB manufacturer with 33,542 training samples and 14,484 test samples. Normalization and PCA were employed to reduce differences and redundancy of the datasets, respectively. PCA results indicated that the causes of the reorder level are closely related to seven principal components and the other two variables, i.e., recency and layer number. Entropy minimization based binning method was employed to discretize model variables for the purpose of reducing input type and capturing better performance and results. The modified structure of BN was established by deleting redundant connections between nodes (with weak link strength) and corresponding conditional probability tables based on conditional mutual information and link strength percentage combining with expert experience. This can facilitate the manufacturer to comprehend causal interactions between variables. On this basis, the conditional expected loss was presented for final classification considering different misclassification risk. Monte Carlo simulation was conducted to enable the determination with greater accuracy of a mean and confidence interval for reorder frequency estimations based on the predicted reorder level. The upper limits of reorder frequency are particularly useful for the PCB manufacturer as a basis of each reorder level. The performance of the proposed modified BN was visualized by confusion matrix, evaluated by three indicators, and compared to three advanced methods including TAN, AdaBoost, and ANN. It was found that the modified BN prediction model achieved steady and satisfactory results both for training and test samples with the clearest common sense interpretation. Therefore, the proposed model in this paper is an effective approach to capture the repetition pattern of PCB orders that have seldom been studied before. The established explicit relationship between the variables including extracted factors and the reorder level by the causal network can directly facilitate order selection for batch production that can be conducted according to the decision making step given in Figure 1.  
The main contributions of this work are summarized below. 1. The tricky problem of identifying repeated orders for batch production was transformed into a reorder level prediction problem and then a reorder level prediction model based on modified causal Bayesian network was proposed. From the historically accumulated data in a PCB manufacturer, different characteristic variables were extracted and specified for the model. 2. PCA was employed for data compression and factors extraction. Yet, an entropy minimization based method was presented to discretize variable and extracted factors. They could facilitate data compression, input type reduction, and better classification performance. 3. In order to avoid the defect of TAN BN that easily misses strong links between nodes and generates redundant weak links, CMI and LSP were combined for the establishment of the BN structure. 4. By using Monte Carlo simulations, the confidence upper limits of reorder frequency within six months were determined and the influence of the random nature of reorder was reduced. Further research will be made to design intelligent approaches that can predict and determine reasonable batch production area for each candidate order. Further attempts will also be made to apply this method to similar order-oriented production and develop other intelligent techniques for the repetition pattern excavation. **Author Contributions:** [PERSON] implemented the algorithm and wrote the paper.