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In this paper it is assumed that, using a sample survey, two factors are to be studied, comparisons between the "levels" of the factors are of greatest interest, and there is "interaction" between the factors. Attention is concentrated on situations in which only two levels of each factor are to be compared, but extensions to more complex surveys are discussed. Assuming independent sampling, optimal sample size allocations are obtained. Where these allocations require recourse to programming algorithms, approximate solutions are given. If independent sampling is not feasible, a double sampling procedure is suggested. To indicate how sub-sampling from the first phase sample is to be carried out, a sampling rule (possessing optimal conditional precision properties) is derived. Then, a procedure to determine the optimal first phase sample size is given. Finally, it is demonstrated that this double sampling procedure can be applied to estimation of the (finite) population mean when double sampling with stratification is used. [ABSTRACT FROM AUTHOR]

The author [1], [2] has given an algorithm for finding that stratified allocation which minimizes the posterior variance of the overall population mean subject to a budget constraint under a model in which a normal prior distribution and independent normal sampling distributions were assumed. The budget constraint assumed a variable per unit cost of observation. In the present paper these results are extended to cover the case where there are fixed costs, as well as variable costs, associated with sampling in the ith stratum. The resulting algorithm is noted to be applicable in finding the optimal allocation of sampling effort (with fixed and variable sampling costs) under a variety of distributional assumptions. An interpretation is also given to two and higher stage design questions when there is differential prior information regarding the first stage units. [ABSTRACT FROM AUTHOR]

An algorithm for the determination of the economic design of X-charts based on Duncan's model is described in this paper. This algorithm consists of solving an implicit equation in design variables n (sample size) and k (control limit factor) and an explicit equation for h (sampling interval). The use of this algorithm not only yields the exact optimum but also provides valuable information so that the sensitivity of the optimum loss-cost (L*) can be evaluated. Loss-cost contours are used to discuss the nature of the loss-cost surface and the effect of the design variables. The effect of two parameters, the delay factor (e), and the average time for an assignable cause to occur (1/lambda), on the optimum design is evaluated. Numerical examples are used for illustrations. [ABSTRACT FROM AUTHOR]

This paper is devoted to a discussion of an iterative procedure for obtaining the maximum likelihood estimator of the covariance matrix for multivariate experiments in which measurements on certain components of a normal vector random variable are intentionally omitted in corresponding subgroups of the experimental units. The proposed algorithm, which is based on the Newton-Raphson method, is outlined in detail in Section 5. A special design is included to illustrate the procedure and a few areas of application are indicated. [ABSTRACT FROM AUTHOR]