Javier M. Moguerza

Measurement System Analysis with R

Measurement system analysis (also known as gage R&R study) identifies and quantifies the sources of variation that influence the measurement system. R&R stands for repeatability and reproducibility. It is a very important matter in Six Sigma, because if the variability of the measurement system is not controlled, then the process cannot be improved. To perform a gage R&R study, several of the individual tools described in other chapters of the book may be used, such as control charts, analysis of variance (ANOVA), and plots. The principal types of studies are crossed studies and nested studies. This chapter shows how to use these tools individually with R and provides an interpretation of the outputs from the SixSigma package for crossed studies.

Six Sigma in a Nutshell

Many total quality management methodologies have been introduced in recent decades. Six Sigma has emerged as a breakthrough methodology. With Six Sigma, we are solving problems and improving processes using as our basis one of the most powerful tools of human development: the scientific method. The basis of the Six Sigma methodology is the DMAIC cycle. It consists of five stages: define, measure, analyze, improve, and control. The roles of people involved in Six Sigma projects are also an important issue. Using martial arts comparisons, these roles can be categorized into Master Black Belts, Black Belts, Green Belts, Yellow Belts, Champions, and Managers. In this chapter, we give an overall view of Six Sigma and a basic description of the interaction between the different elements involved in this methodology.

Statistics and Probability with R

Statistics can be defined as the collection, classification, analysis, and interpretation of data. It is a mathematical discipline traditionally divided into two fields: descriptive statistics and inferential statistics. It makes use of the tools and methods of probability theory. Nowadays, statistics is an interdisciplinary knowledge area, used in any field where data analysis is needed. This chapter deals with descriptive statistics and probability, including central tendency measurements, variability measurements, random variables, and probability distributions, with a special focus on the binomial and normal probability distributions.

Statistical Inference with R

Statistical inference is the branch of statistics whereby we arrive at conclusions about a population through a sample of the population. We can make inferences concerning several issues related to the data, for example, the parameters of the probability distribution, the parameters of a given model that explains the relationship among variables, goodness of fit to a probability distribution, and differences between groups (e.g., regarding the mean or the variance). In Six Sigma projects, improvement is closely linked to the effect that some parameters of the process (input) have on the features of the process (output). Statistical inference provides the necessary scientific basis to achieve the goals of the project and validate its results. This chapter reviews the main tools and techniques to deal with statistical inference using R.

R from the Beginning

R is a system for statistical computing and graphing. It consists of a language and a software environment. R has been widely used for academic and research purposes and is increasingly being deployed in corporate environments. R is a freely available software, under a GNU license, and is supported by the R Development Core Team. The strength of R is its extensibility through the packages developed by the community of R users, available through the CRAN repository, where support is also given. Furthermore, it is available for a wide range of platforms, including Windows, Mac, and Linux. In this chapter, we explain the basic background to help readers get used to R.

Process Mapping with R

Process mapping is a tool to retrieve information about a process. This information will be used in the phases of the Six Sigma project to be discussed later, and many of the measurements, analyses, and conclusions will be based on this information. The result of process mapping is a map of a process. This map stems from the Project Charter and should be modified during the development of the project. Process mapping begins with a top-level map, identifying the inputs and outputs of the process. Then the process is broken down into simpler steps, where parameters and features are identified and classified. This classification will guide the posterior analysis of the relationship between the parameters and the critical to quality features. In this chapter, we describe a method to build process maps and show how to draw and represent them using R.

Pareto Analysis with R

Pareto analysis is a technique that can be used in several stages of a Six Sigma project. In the Measure phase of the design, measure, analyze, improve, and control cycle, we use it to prioritize the possible causes of defects and then focus on the important ones. The basis of Pareto analysis is the Pareto principle, which applies to many processes in real life. Roughly speaking, the Pareto principle states that most effort/benefit (approximately 80%) is due to a limited number of key actions (approximately 20%). It is also known as the 80/20 rule. A search for these key actions is usually made using a Pareto chart, a tool that allows us to see at a glance the results of a Pareto analysis. In this chapter, we show how a Pareto analysis can be applied to detect important improvement opportunities in a Six Sigma project.

Loss Function Analysis with R

Most features defining a product are not usually important to the customer. Only a few of them are critical to quality, in particular, those defining what the customer expects. To meet these expectations, the processes involved in the development of the final product should be correct. This is the Six Sigma way: high-quality processes lead automatically to high-quality products. This is related to the concept of cost of quality, which is the cost of having a low-quality product (from the customer’s perspective). Some managers still think that this concept is equivalent to total quality cost, which corresponds to the amount of money expended in implementing quality methodologies and improving processes. To avoid misunderstandings, we will refer to the cost of quality as the cost of poor quality. The cost of poor quality will result in a quantifiable loss for the organization and for society in general. This loss can be modeled by a function. In Six Sigma, this function is based on the variability of the process. In this chapter, we will analyze the quality loss function introduced by Taguchi and explain how to use it to calculate the average loss of a process.

Other Tools and Methodologies

In this chapter, we describe other tools and methodologies related to the topic of the book. In this way, we provide for the reader a global view of the advanced possibilities of Six Sigma and R. These tools include failure mode, effects, and criticality analysis (FMECA), design for Six Sigma (DFSS), lean, Gantt charts, and some advanced R reporting issues.

Process Control with R

Engineers usually associate statistical process control (SPC) with a set of charts to monitor whether the outputs of a process are in or out of control. This is the classic approach to quality control (QC) and consists of adjusting processes only when their outputs are out of control. Under this approach, inspection is a standard way to proceed. One of the goals of modern QC is to reduce the need for inspection. The Six Sigma process aims at sustaining the improvements achieved throughout the other stages of the DMAIC cycle. Under the Six Sigma paradigm, control is established over the variables affecting the critical to quality characteristics. In this chapter, we first introduce some concepts of mistake-proofing strategies for process control. Then, control charts and their representation with Rare explained. Finally, other topics related to SPC are touched upon along with the available Rpackages.