The process capability indices (CPI) are often used to obtain the information about the production process capability and there are some criteria in determining it, the criteria which are designed for the true values of CPI's. However, since the true values of CPI's are unknown in practice, they are estimated from several data. So the criteria might not be applied to these (point-) estimated values. Confidence intervals for CPI's should be constructed and these results should be taken into consideration. In this paper some useful and practical methods for the interval estimation are given.

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In our previous paper, design procedures for double sampling attributes plans with given two points on the OC curve were presented. The design procedures were based on the least square criterion which makes the producer's and consumer s risks close to the specified values under (special) constraint of c₂=c₃. In this paper, we discuss a general design procedure for the double sampling plans without any special constraints. Samples sizes (n₁, n₂)are obtained as numerical solutions of simultaneous differential equations, and acceptance numbers (c₁, c₂, c₃) are determined according to the inspection cost which contains the sampling cost at the second stage of inspection.

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