This website is intended to give a short introduction into the methods of the qualityTools package. The qualityTools package contains methods associated with the **D** efine (**M**)easure (**A**)nalyze (**I**)mprove and **C** ontrol (i. e. **DMAIC**) problem solving cycle of the Six Sigma Quality Management methodology. Usage of these methods is illustrated with the help of example datasets.

**Define:**Pareto chart**Measure:**Probability-probability/quantile-quantile plots, process capability indices for normal and non-normal distributions and gage repeatability and reproducibility (Gage R&R)**Analyze:**Pareto Chart, Multi-Vari Chart, Dot Plot**Improve:**Full and fractional factorial designs, response surface designs, mixture designs and taguchi designs as well as the desirability approach for simultaneous optimization of more than one response variable. Normal, pareto and lenth plot of effects as well as interaction plots

Working with the qualityTools package is straightforward as you will see in the next few pages. The qualityTools package was initially implemented for teaching purposes in order to serve as a (Six-Sigma)-Toolbox and contains methods that are associated to a problem solving cycle. There are many problem solving cycles around with new ones emerging although most of these new ones take on special aspects. A very popular problem solving cycle is the **PDCA** cycle

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**P**)lan \(\curvearrowright\) - (
**D**)o\(\curvearrowright\) - (
**C**)heck\(\curvearrowright\) - (
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which was made popular by William E. Deming but actually goes back to Walter A. Shewart. As part of the widely known and accepted Six-Sigma-Methodology some enhancements to this problem solving cycle were made and a problem solving cycle consisting of the five phases **Define**, **Measure**, **Analyze**, **Improve** and **Control** emerged.

**Define** Describe the problem and its (financial) consequences. Interdisciplinary workgroups contribute to the problem and its consequences which is the pivotal stage in narrowing down the problem. Process flow diagrams identify crucial process elements (i.e. activities), creativity techniques such as Brainwriting and Brainstorming as well as the SIPOC technique should lead, depending on the future size of the project, to possibly a project charter. Amongst other things, the project charter serves as a descripition of the process, customer's requirements in relation to corporate objectives.

**Measure** Come up with a reasonable plan for collecting the required data and make sure that the measurement systems are capable (i.e. no or known bias and as little system immanent variation contributing to the measurements as possible). **Variation** and **Bias** are the enemy to finding effects. The bigger the background noise the less probable are the chances of success using limited resources for all kinds of experiments. Within the Measure phase a description of the situation is given with the help of process- or gage capability indices i. e. Measurement Systems Analysis - Type I or a Gage R&R Measurement Systems Analysis - Type II .

**Analyze** Try to find the root causes of the problem using various statistical methods such as histograms, regression, correlation, distribution identification, analysis of variance and multi-vari-charts.

**Improve** Use designed experiments i.e. full and fractional factorials, response surface designs, mixture designs, taguchi designs and the desirability concept to find optimal settings or solutions for a problem.

**Control** Once an improvement was achieved it needs to be secured, meaning arrangements need to be implemented in order to secure the level of improvement. Besides proper documentation, the use of statistical process control (i.e. quality-control-charts) can be used to monitor the behavior of a process. Although quite often referred to as **Show Programm for Customers**, SPC is able to help to distinguish between **common causes** and **special causes** in the process behavior.