Ronald J. M. M. Does

Limiting dilution assays Experimental design and statistical analysis

Two issues in limiting dilution analysis are considered. The first concerns the experimental design: a mathematical algorithm has been developed which calculates the number of replicate culture groups, and the (mean) number of cells per well to be used on the basis of the experimenters a priori information about the unknown frequency. The procedure guarantees useful data if the a priori interval estimate of the frequency to be determined is correct and the cells are willing to grow. The second issue concerns the statistical method to be used for estimation of the unknown frequency. Several methods (minimum chi-square, maximum likelihood and the jackknife version of the maximum likelihood method) have been evaluated with artificial data from extensive Monte Carlo experiments. All three methods were useful in the statistical analysis of data. As a result of these experiments and theoretical considerations the jackknife version of the maximum likelihood estimation procedure is proposed as the statistical procedure of choice. The next best method is the maximum likelihood procedure.

Shewhart-Type Control Charts for Individual Observations

Several options in designing a Shewhart-type control chart for individual observations are discussed. A number of possible estimators of the standard deviation are considered. A two-stage procedure is suggested for retrospective testing. Finally, it is ..

Computer aided design and evaluation of limiting and serial dilution experiments

Two computer programs are presented which can be used for the determination of the design and the statistical evaluation of data in the context of limiting and serial dilution analysis. The first program (DESIGN) gives the experimenter the opportunity to set up different designs, to improve a design according to several suggestions, to make a picture of a design and to evaluate the results of artificial data, obtained from a random experiment corresponding with the chosen design, until (s)he is convinced of having a suitable design for a particular experiment. The second program (EVALUATE) evaluates the experimental data. The design method and the statistical methods used in the programs have been chosen on practical and theoretical grounds.

Lean Six Sigma in financial services

A power train of an automatic transmission adapted to realize a shift stage comprising five forward speeds and one reverse speed by two simple planetary gear sets and seven friction elements to thereby enable compactness and lightness of the automatic transmission, the power train comprising: a combined planetary gear set provided by fixedly connecting a planetary carrier of a first signal pinion planetary gear set to a ring gear of a second single pinion planetary gear set, and by fixedly connecting a ring gear of a first single pinion planetary gear set to a planetary carrier of a second single pinion planetary gear set; three input units for causing an input to be variably initiated to any of three actuating elements out of various actuating elements at the combined planetary gear set; two output units for causing an output to be variably initiated from any of two actuating elements out of various actuating elements at the first single pinion planetary gear set; and two brakes actuating reaction forces between the respective gear sets and transmission housing.

Mixed exponentially weighted moving average-cumulative sum charts for process monitoring

The control chart is a very popular tool of statistical process control. It is used to determine the existence of special cause variation to remove it so that the process may be brought in statistical control. Shewhart-type control charts are sensitive for large disturbances in the process, whereas cumulative sum (CUSUM)–type and exponentially weighted moving average (EWMA)–type control charts are intended to spot small and moderate disturbances. In this article, we proposed a mixed EWMA–CUSUM control chart for detecting a shift in the process mean and evaluated its average run lengths. Comparisons of the proposed control chart were made with some representative control charts including the classical CUSUM, classical EWMA, fast initial response CUSUM, fast initial response EWMA, adaptive CUSUM with EWMA-based shift estimator, weighted CUSUM and runs rules–based CUSUM and EWMA. The comparisons revealed that mixing the two charts makes the proposed scheme even more sensitive to the small shifts in the process mean than the other schemes designed for detecting small shifts. Copyright

Improving the performance of CUSUM charts

The control chart is an important statistical technique that is used to monitor the quality of a process. Shewhart control charts are used to detect larger disturbances in the process parameters, whereas CUSUM and EWMA charts are meant for smaller and moderate changes. Runs rules schemes are generally used to enhance the performance of Shewhart control charts. In this study, we propose two runs rules schemes for the CUSUM charts. The performance of these two schemes is compared with the usual CUSUM, the weighted CUSUM, the fast initial response CUSUM and the usual EWMA schemes. The comparisons revealed that the proposed schemes perform better for small and moderate shifts, whereas they reasonably maintain their efficiency for large shifts as well. Copyright

Design and analysis of control charts for standard deviation with estimated parameters

This paper concerns the design and analysis of the standard deviation control chart with estimated limits. We consider an extensive range of statistics to estimate the in-control standard deviation (Phase I) and design the control chart for real-time process monitoring (Phase II) by determining the factors for the control limits. The Phase II performance of the design schemes is assessed when the Phase I data are uncontaminated and normally distributed as well as when the Phase I data are contaminated. We propose a robust estimation method based on the mean absolute deviation from the median supplemented with a simple screening method. It turns out that this approach is efficient under normality and performs substantially better than the traditional estimators and several robust proposals when contaminations are present.

Control charts for location based on different sampling schemes

Control charts are the most important statistical process control tool for monitoring variations in a process. A number of articles are available in the literature for the X̄ control chart based on simple random sampling, ranked set sampling, median-ranked set sampling (MRSS), extreme-ranked set sampling, double-ranked set sampling, double median-ranked set sampling and median double-ranked set sampling. In this study, we highlight some limitations of the existing ranked set charting structures. Besides, we propose different runs rules-based control charting structures under a variety of sampling strategies. We evaluate the performance of the control charting structures using power curves as a performance criterion. We observe that the proposed merger of varying runs rules schemes with different sampling strategies improve significantly the detection ability of location control charting structures. More specifically, the MRSS performs the best under both single- and double-ranked set strategies with varying runs rules schemes. We also include a real-life example to explain the proposal and highlight its significance for practical data sets.

Shewhart-Type Charts in Nonstandard Situations

Standard textbooks on statistical process control generally offer simple procedures to construct control charts. In many situations the resulting charts are of limited use because the variance components of the process are not adequately taken into account. In this article, an example of this is discussed. The use of an analysis of variance model in constructing more effective control charts is described. Control charts for the mean and linear contrasts are developed, using different estimators of variability. Guidance with respect to construction and evaluation of the charts is provided. The charts are illustrated with the example, and the efficiency is evaluated.

On the Performance of Different Control Charting Rules

In the literature a number of control charting rules are proposed to decide whether a process is in control or out of control. Some issues with these rules will be highlighted in this article. By redefining and listing a set of rules we will evaluate their performance on the X-bar, R, S and S2 charts. Also we will compare the performance of these rules using their power curves to figure out the superior ones. Application of a few of these rules with real data sets will show their detection ability and use for practitioners.