Lluís Marco-Almagro

Six Sigma: : hints from practice to overcome difficulties

Six Sigma has proven to be a powerful system for improving quality and productivity. However, the successful implementation of the methodology is not simple, and it is therefore normal – especially in the early phases – to experience problems that may impede taking full advantage of the methodology. We have grouped some of the most frequent ones into four main areas: implementation and organisational aspects, adherence to DMAIC methodology, tools and statistical techniques and implementation of improvements and project closure. For each of them, the paper discusses some of the difficulties and issues that should be taken into account.

Visualizing type II error in normality tests

ABSTRACT A skewed exponential power distribution, with parameters defining kurtosis and skewness, is introduced as a way to visualize Type II error in normality tests. By varying these parameters a mosaic of distributions is built, ranging from double exponential to uniform or from positive to negative exponential; the normal distribution is a particular case located in the center of the mosaic. Using a sequential color scheme, a different color is assigned to each distribution in the mosaic depending on the probability of committing a Type II error. This graph gives a visual representation of the power of the performed test. This way of representing results facilitates the comparison of the power of various tests and the influence of sample size. A script to perform this graphical representation, programmed in the R statistical software, is available online as supplementary material.

Graphical comparison of normality tests for unimodal distribution data

ABSTRACT A methodology is proposed to compare the power of normality tests with a wide variety of alternative unimodal distributions. It is based on the representation of a distribution mosaic in which kurtosis varies vertically and skewness horizontally. The mosaic includes distributions such as exponential, Laplace or uniform, with normal occupying the centre. Simulation is used to determine the probability of a sample from each distribution in the mosaic being accepted as normal. We demonstrate our proposal by applying it to the analysis and comparison of some of the most well-known tests.