Cusum charts for preliminary analysis of individual observations

A preliminary Cusum chart based on individual observations is developed from the uniformly most powerful test for the detection of linear trends. This Cusum chart is compared with several of its competitors which are based on the likelihood ratio test and on transformations of standardized recursive residuals on which for instance the Q-chart methodology is based. It turns out that the new proposed Cusum chart is not only superior in the detection of linear trend out-of-control conditions, but also in the detection of other out-of-control situations. Approximate control limits, determined from simulation, and an example of its use in practice are given for the proposed Cusum chart.Cusum chart;detection of linear trends

Comparison of bias-reducing methods for estimating the parameter in dilution series

Estimation;mathematische statistiek

Multiple-dose design and bias-reducing methods for limiting dilution assays

This paper gives an overview of several (mostly recent) statistical contributions to the theory of Limiting and Serial Dilution Assays (LDA's, SDA's). A simple and useful method is presented for the setup of a design for an LDA or an SDA. This method is based on several user-supplied design parameters, consisting in the researcher's advance information and other parameters inherent to the particular problem. The commonly used Maximum Likelihood (ML) and Minimum Chi-square methods for the estimation of the unknown parameter in an LDA or an SDA are described and compared to several bias-reducing estimation methods, e.g. jackknife and bootstrap versions of the ML method. One particular jackknife version is recommended