Sampling inspection for resubmitted lots

Lot resubmissions are allowed in situations where the original inspection results are suspected or when the supplier is allowed to opt for resampling as per the provisions of the contract etc. This paper examines the situation of resampling of lots and derives the performance measures of a resampling scheme having a single sampling plan for inspection. The usefulness and limitations of resampling of resubmitted lots are also discussed     

Ranked set sampling with concomitant variables

Ranked set sampling is a procedure which may be used to improve the precision of the estimator of the mean. It is useful in cases where the variable of interest is much more difficult to measure than to order. However, even if ordering is difficult, but there is an easily ranked concomitant variable available, then it may be used to “judgment order” the original variable. The amount of increase in the precision of the estimator is dependent upon the correlation between the 2 variables.     

A Distribution-Free Control Chart Based on Order Statistics

In this article, we introduce a new distribution-free Shewhart-type control chart that takes into account the location of a single order statistic of the test sample (such as the median) as well as the number of observations in that test sample that lie between the control limits. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of the chart is that, due to its nonparametric nature, the false alarm rate and in-control run length distribution are the same for all continuous process distributions, and so will be naturally robust. Tables are provided for the implementation of the chart for some typical ARL values and false alarm rates. The empirical study carried out reveals that the new chart is preferable from a robustness point of view in comparison to a classical Shewhart-type chart and also the nonparametric chart of Chakraborti et al. (2004 Chakraborti , S. , van der Laan , P. , van de Wiel , M. A. ( 2004 ). A class of distribution-free control charts . J. Roy. Statist. Soc. Ser. C-Appl. Statist. 53 ( 3 ): 443 – 462 .[Web of Science ®] , [Google Scholar]).     

Mathematical forms of the distribution of the product of two normal variables

This paper finds the mathematical forms of the distribution of the product where x and x follow a bivariate normal distribution In this paper the distribution when PT0 is expressed as an integral, a new, fundamental result. From this general form, six different cases can be distinguished depending on what is known about the parameters and p. The special cases are Aroian $year:1959 and (6) Additionally, we prove that if and as the distribution of the product approaches the Type III distribution. When p=0# Aroian $year:1959 and Aroian and Meeker $year:1977, give tables for various values of 6., 6 . The results in this paper will be used to provide brief tables for p^O in a separate paper     

A generalization of mosteller's test

A generalization of Mosteller's test for slippage of the location parameter is proposed. The distribution of the test statistic under the null hypothesis is obtained and the power of the test is compared with that of Mosteller's test     

Sample-size requirements for confidence bounds of prescribed precision on multivariate normal quantiles

The problem of setting confidence bounds on a central multivariate normal quantile is considered. It is shown that for the setting of exact confidence bounds of specified closeness to the quantile,the required minimum size of a normal sample is large and rises rapidly with the number of variates considered.     

Dirichlet models for square contingency tables

We consider the square contingency tables which arise when the same method of classification is applied twice. The hypothesis of marginal homogeneity is then relevant! and can be tested by various methods Models are discussed which contain marginal homogeneity as a special case. They include a class based on univariate and bivariate Dirichlet distributions. The question of ordered categories is briefly discussed. Applications are made to data on unaided distance vision.     

Minimax property of stein's estimator

Stein's estimator and some other estimators of the mean of a K-variate normal distribution are known to dominate the maximum likelihood estimator under quadratic loss for K > 3, and are therefore minimax. In this paper it is shown that the minimax property of Stein's rule is preserved with respect to a generalized loss function.