Pere Grima

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.

Experimentation order with good properties for 2k factorial designs

Randomizing the order of experimentation in a factorial design does not always achieve the desired effect of neutralizing the influence of unknown factors. In fact, with some very reasonable assumptions, an important proportion of random orders achieve the same degree of protection as that obtained by experimenting in the design matrix standard order. In addition, randomization can induce a large number of changes in factor levels and thus make experimentation expensive and difficult. De Leon et al. [Experimentation order in factorial designs with 8 or 16 runs, J. Appl. Stat. 32 (2005), pp. 297–313] proposed experimentation orders for designs with eight or 16 runs that combine an excellent level of protection against the influence of unknown factors, with the minimum number of changes in factor levels. This article presents a new methodology to obtain experimentation orders with the desired properties for designs with any number of runs.

A Methodology to Model Water Demand based on the Identification of Homogenous Client Segments. Application to the City of Barcelona

Water management has become a vital concern for both water supply companies and public administrations due to the importance of water for life and current scarcity in many areas. Studies exist that attempt to explain which factors influence water demand. In general, these studies are based on a small sample of consumers and they predict domestic water consumption using ordinary least squares regression models with a small number of socioeconomic variables as predictors, usually: price, population, population density, age, and nationality. We have followed a different approach in two ways; one, in the scope of the study: we have included in the study all consumers of the Barcelona area and as many socioeconomic variables as possible (all the available data from official statistics institutions); and also in the methodology: first, we have segmented clients into homogeneous socioeconomic groups that, as we show later in the Barcelona case, also have homogeneous water consumption habits. This allows for a better understanding of water consumption behaviours and also for better predictions through modeling water consumption in each segment. This is so because the segments’ inner variability is smaller than the general one; thus, the models have a smaller residual variance and allow for more accurate forecasts of water consumption. The methodology was applied to the Barcelona metropolitan area, where it was possible to construct a database including both water consumption and socioeconomic information with more than one million observations. Data quality was a primary concern, and thus a careful exploratory data analysis procedure led to a careful treatment of missing observations and to the detection and correction or removal of anomalies. This has resulted in a stable division of the one million water consumers into 6 homogeneous groups and models for each of the groups. Although the methodology has been developed and applied to the Barcelona area, it is general and thus can be applied to any other region or metropolitan area.

Experimentation order in factorial designs: new findings

Under some very reasonable hypotheses, it becomes evident that randomizing the run order of a factorial experiment does not always neutralize the effect of undesirable factors. Yet, these factors do have an influence on the response, depending on the order in which the experiments are conducted. On the other hand, changing the factor levels is many times costly; therefore it is not reasonable to leave to chance the number of changes necessary. For this reason, run orders that offer the minimum number of factor level changes and at the same time minimize the possible influence of undesirable factors on the experimentation have been sought. Sequences which are known to produce the desired properties in designs with 8 and 16 experiments can be found in the literature. In this paper, we provide the best possible sequences for designs with 32 experiments, as well as sequences that offer excellent properties for designs with 64 and 128 experiments. The method used to find them is based on a mixture of algorithmic searches and an augmentation of smaller designs.

Management by facts: The common ground between total quality management and evidence-based management

It is widely agreed that, whenever possible, managers should base their decisions on scientific knowledge rather than gut feelings or intuitions. There are two main sources of scientific knowledge available to managers: external and internal. External knowledge comes from studies conducted outside the company and it is mainly generated by researchers at universities and business schools; a recent trend, under the name of evidence-based management, tries to potentiate it, despite the fact that as a source of scientific knowledge for management, it has two problems: it is difficult to generate and it is problematic to disseminate among managers. On the other hand, internal knowledge comes from studies conducted on the companys process on which decisions have to be made and by the very same managers that have to make them. The paper argues that this kind of knowledge is easier to generate and use and thus that it has to be potentiated as the main source for scientific decisions; the idea is not new as it is one of the pillars of total quality management and there are methods and techniques of proved efficiency to put it into practice.

Comparison of normal probability plots and dot plots in judging the significance of effects in two level factorial designs

In this article, we present a study carried out to compare the effectiveness of the normal probability plot (NPP) and a simple dot plot in assessing the significance of the effects in experimental designs with factors at two levels (2 k−p designs). Several groups of students who had just completed a course that covered factorial designs were asked to identify the significant effects in a total of 32 situations, 16 of which were represented using NPPs and the other 16 using dot plots. Although the 32 scenarios were said to be different, there were really only 16 different situations, each of which was represented using the two methods to be compared. A simple graphical analysis shows no evidence that there is a difference between the two procedures. However, in designs with 16 runs there are some cases where NPP seems to give slightly better results.

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.

Sustainable Improvement: Six Sigma – Lessons Learned after Five Years of Training and Consulting

A fundamental element for the sustainable long-term success of any organization is an effective improvement program. Six sigma is a powerful improvement methodology that, if correctly implemented, can be an important component of a management system aimed at sustainability. However, a successful implementation of six sigma is not an easy task, in this paper we share our experience after five years of extensive six sigma training and consulting in Spain and South America. We are responsible for a Black Belt open enrollment training and deployment course offered by the Technical University of Catalonia (UPC) in Barcelona, San Sebastian and Santiago de Chile. In addition to presenting some of the lessons learned throughout this experience, we comment on two aspects of the use of the methodology that we believe may affect the future of six sigma: the extent to which statistics must be included in a Black Belt training course and the amount of guidance that needs to be built into both the tools to be used and the DMAIC (define, measure, analyze, improve, control) methodology, in order to obtain the maximum possible benefit with the least possible effort from the six sigma process. We finish with some conclusions.

Twenty-Five Analogies for Explaining Statistical Concepts

The use of analogies is a resource that can be used for transmitting concepts and making classes more enjoyable. This article presents 25 analogies that we use in our introductory statistical courses for introducing concepts and clarifying possible doubts. We have found that these analogies draw students’ attention and reinforce the ideas that we want to transmit.

Which runs to skip in two-level factorial designs when not all can be performed

ABSTRACT When a two-level factorial design allows estimating contrasts that can be considered negligible from scratch, it is possible to omit some runs and later estimate their values by equating to zero the expressions of some of that contrasts. This article presents the combinations of runs to be omitted in 8 and 16 runs two-level factorial designs so that the responses can be estimated in such a way as to produce the least possible impact on the desired properties of the estimated contrasts: low and equal variance and the smallest possible correlation among them.