Even in the multi-product processes, there are some factors in common among the products. This paper presents the cumulative sum (cusum) control chart for Poisson variables which is applied to the multi-product processes in order to control the factors. The cusum chart is the expanded version of the ordinary cusum chart, which has several reference values. The reference values are determined with correspondence to the main products. Yamada [1] published that the cusum chart was successfully applied to a press process. However, the statistical properties and the design procedure of the cusum chart have not been clearly studied. In this paper we discuss the relations between the ARL (Average Run Length) of the cusum chart for the multi-product process and that of the ordinary cusum chart. On the basis of the discussions, we submit the determination procedure of the parameters in the cusum chart for the multi-product.

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In a two-way analysis of variance, we are confronted with many cases in which it is not enough to test only if there are interaction effects or not. Those are the cases we must consider the alternatives with inequality restrictions to the interaction effects. In this paper, a simple method for constructing a score statistic is proposed, and the usefulness of the proposed statistic is shown by comparing the powers of the proposed score method, other score methods and usual F test against some typical alternatives. Further we indicate that we can construct the score which can be applied for the case of unbalanced replications, which has not been examined yet.

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The operating characteristics and design procedure of single sampling plans by attributes are well documented. This paper considers a double sampling plan which makes the producer's and consumer's risks close to the specified values, and presents a computer algorithm and a simplified procedure for determining the double attribute sampling plans with given two points on the OC curve.

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