Neural network modeling with confidence bounds: a case study on the solder paste deposition process

Abstract

The formation of reliable solder joints in electronic assemblies is a critical issue in surface mount manufacturing. Stringent control is placed in the solder paste deposition process to minimize soldering defects and achieve high assembly yield. Time series process modeling of the solder paste quality characteristics using neural networks (NN) is a promising approach that complements traditional control charting schemes deployed on-line. In this paper, we present the study of building a multilayer feedforward neural network for monitoring the solder paste deposition process performance. Modeling via neural networks provides not only useful insights in the process dynamics, it also allows forecasts of future process behavior to be made. Data measurements collected on ball grid array (BGA) and quad flat pack (QFP) packages are used to illustrate the NN technique and the forecast accuracies of the models are summarized. Furthermore, in order to quantify the errors associated with the forecasted point estimates, asymptotically valid prediction intervals are computed using nonlinear regression. Simulation results showed that the prediction intervals constructed give reasonably satisfactory coverage percentages as compared to the nominal confidence levels. Process control using NN with confidence bounds provides more quality information on the performance of the deposition process for better decision making and continuous improvement.Index Terms-Modeling and forecasting, neural networks, nonlinear regression, prediction intervals, process control, solder paste deposition.

Lower Upper Bound Estimation Method for Construction of Neural Network-Based Prediction Intervals

“…Although the generalization power of NN models is improved using this method, the PIs suffer from the fundamental limitation of the delta technique (linearization). The delta method has been applied in many synthetic and real case studies [3], [6], [19], [20], despite this weakness.…”

“…It has been claimed that the bootstrap method generates more reliable PIs than other methods [22]. The main disadvantage of this method is its computational cost for large datasets [6].…”

“…Incorporating the prediction uncertainty into the deterministic approximation generated by NNs improves the reliability and credibility of the predictions [5]. The semiconductor industry [2], surface mount manufacturing [6], electricity load forecasting [7], [8], fatigue lifetime prediction [9], financial services [10], hydrologic case studies [5], transportation [1], and baggage handling systems [3], to name a few, are examples discussing this problem in different domains.…”

“…The main focus of the literature is on the methodologies for the construction of PIs. Quantitative examination of the quality of developed PIs (and also CIs) is often ignored or represented subjectively and ambiguously [1], [6], [7], [9], [15], [25], [27], [28]. In the comparative studies of CI and PI construction methods, the coverage probability has been considered as the only criterion for assessing the quality of the constructed intervals [29].…”

Artificial intelligence for monitoring and supervisory control of process systems

“…Kavchak and Budman (1999) adopted neural networks for non-linear process estimation and control of an exothermic. Ho et al (2001) suggested that using neural networks with confidence bounds could provide more quality information on the performance of the deposition process for better decisionmaking and continuous improvement of a solder paste deposition process. Tsai et al (2002) developed a robust model predictive control architecture using artificial neural networks.…”