Fuzzy regression approach to modelling transfer moulding for microchip encapsulation

Transfer moulding is one of the popular processes to perform microchip encapsulation for electronic packages. Existing analytical models, such as generalised Hele–Shaw model, seem to be inadequate to model the process accurately in real world environment due to the complex inter-relationships among the encapsulant properties, process conditions, mould design parameters and overall moulding performance and the inherent fuzziness of the moulding systems. It is quite often that the observed values from the transfer moulding for microchip encapsulation may not be regular. Although statistical regression method could be used to perform the modelling, high degree of fuzziness inherent in transfer moulding systems for microchip encapsulation makes the obtained models having wide possibility range. In this paper, the fuzzy regression concept and its application in modelling transfer moulding for microchip encapsulation are described. Fuzzy regression is a well-known method to deal with the problems with a high degree of fuzziness. Thirty-two experiments were firstly conducted based on an 2iv8−2 experimental plan in this study that involved eight process parameters and three quality characteristics. The experimental settings and results of the 30 experiments were then used to develop three fuzzy linear regression models, which relate various process parameters and the three quality characteristics, respectively. With the use of these models, proper process conditions and prediction range of individual quality measures can be obtained. Two validation tests were carried out to evaluate the developed models. Results of the tests show that the actual values of all the quality measures were found within the corresponding prediction ranges. The calculated prediction errors for the three output measures were all less than 5%.