PERFORMANCE EVALUATION OF MULTIHEAD WEIGHERS BY MATHEMATICAL MODELING

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  • 組合せ計量機の数理モデル化による性能評価

Abstract

<p> In food manufacturing, multihead weighers are commonly used to fill bags with the right amount of products, where the weights of contents vary widely such as bell peppers and potato chips. Multihead weighers feed a few quantity of contents into about ten small boxes, called hoppers, and find a combination of hoppers to satisfy the right range of the total weight. The yield rate and the operating rate of these machines are primary interests to operators. This paper presents a simple mathematical model of multihead weighers, and discusses the probability to get the right amount of product. Specifically, we calculate the probability of the existence of a combination of hoppers to satisfy the right range of the total weight regarding the number of hoppers, the means and the variances of the weights, where we assume that the weights of contents in hoppers independently follow an identical normal distribution. The calculation is not easy in the combinatorial sense, and this paper employs the Monte Carlo method taking accuracy assurance into consideration. We calculate the probabilities exhaustively regarding the number of hoppers, the mean value and the variance of weight, then compare the result with the real data. Our result supports an empirical knowledge that the larger variance of contents, the better operating rate.</p>

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