Design of experiments tutorial pdf

ASQ has created a design of experiments template Excel available for free download and use. Begin your DOE with three steps:. Conduct and analyze up to three factors and their interactions by downloading the design of experiments template Excel. More complex studies can be performed with DOE. The above 2-factor example is used for illustrative purposes. Cart Total: Checkout. Learn About Quality.

Magazines and Journals search. Quality Glossary Definition: Design of experiments Design of experiments DOE is defined as a branch of applied statistics that deals with planning, conducting, analyzing, and interpreting controlled tests to evaluate the factors that control the value of a parameter or group of parameters.

Blocking: When randomizing a factor is impossible or too costly, blocking lets you restrict randomization by carrying out all of the trials with one setting of the factor and then all the trials with the other setting.

Randomization: Refers to the order in which the trials of an experiment are performed. A randomized sequence helps eliminate effects of unknown or uncontrolled variables. Replication: Repetition of a complete experimental treatment, including the setup. A well-performed experiment may provide answers to questions such as: What are the key factors in a process? At what settings would the process deliver acceptable performance? What are the key, main, and interaction effects in the process? What settings would bring about less variation in the output?

A repetitive approach to gaining knowledge is encouraged, typically involving these consecutive steps: A screening design that narrows the field of variables under assessment. A "full factorial" design that studies the response of every combination of factors and factor levels, and an attempt to zone in on a region of values where the process is close to optimization.

A response surface designed to model the response. Begin your DOE with three steps: Acquire a full understanding of the inputs and outputs being investigated. A process flowchart or process map can be helpful. Consult with subject matter experts as necessary.

One of the most straight-forward methods to evaluate a new process method is to plot the results on an SPC chart that also includes historical data from the baseline process, with established control limits.

Then apply the standard rules to evaluate out-of-control conditions to see if the process has been shifted. You may need to collect several sub-groups worth of data in order to make a determination, although a single sub-group could fall outside of the existing control limits.

You can link to the Statistical Process Control charts module of the Toolbox for help. An alternative to the control chart approach is to use the F-test F-ratio to compare the means of alternate treatments. This is done automatically by the ANOVA Analysis of Variance function of statistical software, but we will illustrate the calculation using the following example: A commuter wanted to find a quicker route home from work.

There were two alternatives to bypass traffic bottlenecks. The commuter timed the trip home over a month and a half, recording ten data points for each alternative. The data are shown below along with the mean for each route treatment , and the variance for each route:.

To determine whether the difference in treatment means is due to random chance or a statistically significant different process, an ANOVA F-test is performed. The F-test analysis is the basis for model evaluation of both single factor and multi-factor experiments. This analysis is commonly output as an ANOVA table by statistical analysis software, as illustrated by the table below:. The most important output of the table is the F-ratio 3.

The F-ratio is equivalent to the Mean Square variation between the groups treatments, or routes home in our example of The Model F-ratio of 3. The p-value 'Probability of exceeding the observed F-ratio assuming no significant differences among the means' of 0.

In other words, the three routes differ significantly in terms of the time taken to reach home from work. The following graph Figure 4 shows 'Simultaneous Pairwise Difference' Confidence Intervals for each pair of differences among the treatment means.

If an interval includes the value of zero meaning 'zero difference' , the corresponding pair of means do NOT differ significantly. You can use these intervals to identify which of the three routes is different and by how much. The intervals contain the likely values of differences of treatment means , and respectively, each of which is likely to contain the true population mean difference in 95 out of samples.

Notice the second interval does not include the value of zero; the means of routes 1 A and 3 C differ significantly. In fact, all values included in the 1, 3 interval are positive, so we can say that route 1 A has a longer commute time associated with it compared to route 3 C.

Other statistical approaches to the comparison of two or more treatments are available through the online statistics handbook - Chapter Multi-factor experiments are designed to evaluate multiple factors set at multiple levels.

One approach is called a Full Factorial experiment, in which each factor is tested at each level in every possible combination with the other factors and their levels. Full factorial experiments that study all paired interactions can be economic and practical if there are few factors and only 2 or 3 levels per factor.

The advantage is that all paired interactions can be studied. However, the number of runs goes up exponentially as additional factors are added. Experiments with many factors can quickly become unwieldy and costly to execute, as shown by the chart below:. To study higher numbers of factors and interactions, Fractional Factorial designs can be used to reduce the number of runs by evaluating only a subset of all possible combinations of the factors.

These designs are very cost effective, but the study of interactions between factors is limited, so the experimental layout must be decided before the experiment can be run during the experiment design phase. You can also use EngineRoom , MoreSteam's online statistical tool, to design and analyze several popular designed experiments. The application includes tutorials on planning and executing full, fractional and general factorial designs.

Start a day free trial today. Genichi Taguchi is a Japanese statistician and Deming prize winner who pioneered techniques to improve quality through Robust Design of products and production processes. Taguchi developed fractional factorial experimental designs that use a very limited number of experimental runs. The specifics of Taguchi experimental design are beyond the scope of this tutorial, however, it is useful to understand Taguchi's Loss Function, which is the foundation of his quality improvement philosophy.

Traditional thinking is that any part or product within specification is equally fit for use. In that case, loss cost from poor quality occurs only outside the specification Figure 5.

However, Taguchi makes the point that a part marginally within the specification is really little better than a part marginally outside the specification. As such, Taguchi describes a continuous Loss Function that increases as a part deviates from the target, or nominal value Figure 6. The Loss Function stipulates that society's loss due to poorly performing products is proportional to the square of the deviation of the performance characteristic from its target value.

Taguchi adds this cost to society consumers of poor quality to the production cost of the product to arrive at the total loss cost. Designed experiments are an advanced and powerful analysis tool during projects.

An effective experimenter can filter out noise and discover significant process factors. The factors can then be used to control response properties in a process and teams can then engineer a process to the exact specification their product or service requires. A well built experiment can save not only project time but also solve critical problems which have remained unseen in processes.

Specifically, interactions of factors can be observed and evaluated. Ultimately, teams will learn what factors matter and what factors do not. MoreSteam uses "cookies" to allow registered users to access and utilize their MoreSteam account. We also use cookies to analyze how users navigate and utilize the Site. We use that information for the purpose of managing content and providing you with a better visitor experience.

We do not use any type of profiling, targeting, or advertising cookies on any of our Sites. Detailed information on the use of cookies on the moresteam. By using this Site you consent to the use of cookies. Introduction The term experiment is defined as the systematic procedure carried out under controlled conditions in order to discover an unknown effect, to test or establish a hypothesis, or to illustrate a known effect. Preparation If you do not have a general knowledge of statistics, review the Histogram , Statistical Process Control , and Regression and Correlation Analysis modules of the Toolbox prior to working with this module.

Components of Experimental Design Consider the following diagram of a cake-baking process Figure 1. There are three aspects of the process that are analyzed by a designed experiment: Factors , or inputs to the process.

Factors can be classified as either controllable or uncontrollable variables. In this case, the controllable factors are the ingredients for the cake and the oven that the cake is baked in. The controllable variables will be referred to throughout the material as factors. Note that the ingredients list was shortened for this example - there could be many other ingredients that have a significant bearing on the end result oil, water, flavoring, etc.

Likewise, there could be other types of factors, such as the mixing method or tools, the sequence of mixing, or even the people involved. People are generally considered a Noise Factor see the glossary - an uncontrollable factor that causes variability under normal operating conditions, but we can control it during the experiment using blocking and randomization.

Levels , or settings of each factor in the study. Examples include the oven temperature setting and the particular amounts of sugar, flour, and eggs chosen for evaluation. Response , or output of the experiment. In the case of cake baking, the taste, consistency, and appearance of the cake are measurable outcomes potentially influenced by the factors and their respective levels.