Statistical design of experiments

“It’s better to stumble when treading new paths, than getting stuck on old ones." - from China

What is statistical design of experiments?
Statistical design of experiments (DoE) is a process for planning experiments that takes into account that all experiment results involve unavoidable random errors. The random errors are taken into account with statistical methods not only duringthe evaluation, but already at the design of experiment phase, i.e. before the often lengthy and cost-intensive experimental phase begins.

Statistical design of experiment (DoE) pursues several goals in the process:

1. DoE is designed in such a way that minimum experimental effort obtains maximum information. In short: We only want to carry out as many experiments as are actually required to obtain all the necessary information. Exactly the right number of experiments should be carried out – not too many or too few. With regard to optimization, too many experiments mean wasting resources(time, materials, personnel, etc.) and increasing costs. Too few experiments should not be carried out, as this entails the risk that the information required cannot be determined.
2. DoE is the only process with which it is possible to determine interactions.
3. Moreover, DoE isthe only method to find an optimum in the system (material properties, production process, yield, costs, etc.) in a targeted manner.

Benefits ofstatistical design of experiments
The deployment and use of the DoE methodology allows all information about the system to be determined, and this is done in less time than with conventional experimental designs.

The consistent and error-free use of the DoE methodology always leads to considerable timesavings of some weeks to some months.

Outlay for statistical design of experiment
The outlay involved in carrying out experiments using the DoE method is much lower than with other methods such as “trial and error” or OFAT (“One factor at a time”).

The six stages of design of experiment
The beginning of any experimental design consists of the exact definition and description of the task (phase 1). This is followed by analysis, e.g. in the form of a detailed process map (phase 2). The goal of phase 2 is to find all control variables and disturbance variables that affect the system. In phase 3, the influencing variables are evaluated and reduced to a reasonable level. During this process, the cause-effect matrix is used especially. In phase 3, the actual experiment plan is created and evaluated. Only after this planning phase are the preparations for the experimental tasks complete. Phase 4 is then the actual experiment implementation stage which must be carried out according to the previously created plan. This is followed by phase 5 with the evaluation of the determined data (output variables, co-variables, etc.). Graph-based and statistical methods are used here (variance and regression analysis). In phase 6, a repeat trial is then carried out, in order to reproduce and confirm a certain desired material quality, for example.

As a rule, phases 1,2, 3 and 5 are the shortest and therefore most cost-effective phases. The experimental phase 4 is the phase with the highest outlay (time, material, resources, costs, etc.). Good planning (phases 1–3) reduces the outlay involved in phase 4, associated with clear cost reductions.

The training concept
The training concept allows participants to be able to use the tools they have learned directly in their projects at the end of the training. To achieve this goal, for each topic/tool/methodology there is:

• a presentation with PowerPoint slides to facilitate teaching,
• at least one practical example which is explained in detail and calculated with the software used.
• and at least one practical example each, which the participants then calculate themselves, with methodological and technical support from the trainer.

To achieve goals –immediate and direct implementation of DoE in participants’ projects, to obtainmore information whilst also saving time – five days are required, and it may make sense to split the period into two blocks. This is determined by preliminary conversations with the client.

A reduction in outlay leads to the considerable risk that the methods will be inadequately or incorrectly implemented without the necessary training or the data obtained will be incorrectly interpreted. Neither of these is conducive to achieving the desired results, either from the point of view of the customer or from the point of view of the QSW and their trainers.

Content

Day 1:

• Introduction to DoE methodology
• Introduction to the software utilized, Minitab
• Basics of statistics: Location and measures of scatter, normal distribution, probability network
• Graphic tools and data visualization
• Areas of confidence
• Hypothesis test, significance, p-value, apparent effects, actual effects
• Definition of disturbance variables and control variables
• Effects, interactions
• Differentiation and advantages of DoE compared to other methods
• Case examples DoEvs. OFAT: Machine parameters with three input variables

Day 2:

• Variance analysis (ANOVA) with several independent variables
• Regression analysis
• Full factorial experimental designs with blocking, randomization
• Residuals analysis
• Prognosis
• Standard error and mathematical model
• Response surface design (RSD) plans to determine non-linear effects
• Central points
• Orthogonality, rotatability
• Axial points
• Target size optimization
• Contour and effective area diagrams
• Statistical evaluation criteria: Coefficients of determination, PRESS value

Day 3:

• Consolidation of the target optimization (optimization of two target variables simultaneously)
• Super imposed contour diagram
• Confidence and forecast areas
• Partially factorial experimental designs
• With/without blocking
• With/without central points
• Generator and alias structure
• Blending and dissolution
• DoE to be used to reduce scatter in processes
• DoE: Method of the steepest ascent
• EVOP: Evolutionary Operations
• DoE with co-variables (ANCOVA)
• Practical examples: Yield of chemical synthesis reactions, fiber strength of polymer fibers; therapeutic success of drugs

Day 4:

• Process map
• Cause-Effect matrix
• Ishikawa diagrams
• Trend acuteness and sample size
• Handling outliers
• Variable comparison according to Shainin
• Trend analysis
• Practical examples: Coatings, electroplating

Day 5:

• Statistical design of experiments for mixtures and formulations
• Fundamentals of mixture designs
• Simplex Design, degree,
• Variance inflations factor (VIF)
• Results trace diagram according to Cox
• Target size optimization
• Mixture designs with restrictions
• Pseudo components
• Multiple regression analysis
• Practical examples: Elongation of polymer fibers, paint formulations

Examples and extension possibilities for consolidation

• All key words and tools are used with current practical examples.
• If necessary or at the request of the client, the training course can be extended to encompass other important topics: Handling binary output data, logistic regression analysis: One additional day; Taguchi design for robust processes: One additional day

Scope of services

• 5 days
• Extensive training documents in printed format
• Photographic documentation of the flipcharts & workshops being presented
• Practical examples from research, production, quality assurance.
• Hospitality during the breaks, including lunch and beverages

Benefit

• Targeted control of optimal product properties
• Time and cost savings in the development process
• Understanding of cause-effect relationships in complex systems with multiple input variables
• Identification and safe evaluation of main effects and interactions

Group of participants

• Engineers
• Masters inmanufacturing
• Laboratory technicians, developers
• Chemists
• Physicists
• Laboratory and research engineers
• Quality assurance personnel
• and all those who are interested in this method.
• Requirements