Robust parameter design
A robust parameter design, introduced by Genichi Taguchi, is an experimental design used to exploit the interaction between control and uncontrollable noise variables by robustification—finding the settings of the control factors that minimize response variation from uncontrollable factors.
Consider an RPD cake-baking example from Montgomery (2005), where an experimenter wants to improve the quality of cake.
Robust parameter designs seek to minimize the effects of noise factors on quality.
For this example, the manufacturer hopes to minimize the effects in fluctuation of bake time on cake quality, and in doing this the optimal settings for the control factors are required.
RPDs are primarily used in a simulation setting where uncontrollable noise variables are generally easily controlled.
Much like FFDs, RPDs are screening designs and can provide a linear model of the system at hand.
Leoppky, Bingham, and Sitter (2006) used complete search methodology and have listed the best RPDs for 12, 16, and 20 runs.
Because complete search work is so exhaustive, the best designs for larger run sizes are often not readily available.
In that case, other statistical methods may be used to fractionate a Hadamard matrix in such a way that allows only a tolerable amount of aliasing.
Efficient algorithms such as forward selection and backward elimination have been produced for FFDs, but due to the complexity of aliasing introduced by distinguishing control and noise variables, these methods have not yet been proven effective for RPDs.
In 2003, Bingham and Sitter[8] defined maximum resolution and minimum aberration for two-level fractional factorial designs.
As the resolution increases, the level of aliasing becomes less serious because higher order interactions tend to have negligible effects on the response.
Formally, Ye (2003) distinguishes between regular and nonregular designs and states that any polynomial function can be written as If
While Ye developed this indicator function, Bingham and Sitter were working on clarification of resolution and aberration for robust parameter designs.
In 2006, Leoppky, Bingham, and Sitter published the extended word-length pattern and indicator function for robust parameter designs.
However, since RPDs are concerned about noise variables, the CCN interaction is a priority 2.5 effect.
[11] Further investigation of the principles introduced will provide a deeper understanding of design comparison.
[citation needed] For regular fractional factorial designs, the word length will determine what types of aliasing are present.
Word lengths become less simplistic when talking about RPDs because the priority of effects has changed.
This means that any CN interaction bumps that priority up by 0.5; and the word length is obtained by summing each side of the aliasing string.
It is important to understand[citation needed] that in an FFD the differentiation between control and noise would not be taken into account, and this word would be of length 5; but RPDs are concerned with this distinction and even though the word appears to be length 5, design criteria determines priority 4.
After the RPD has been created, the quality of permanent marker is tested at the end of each run.
The manufacturer saves time and money and gets close to the same effect as someone using the marker in extreme weather conditions or elsewhere.
You do not want to risk being understaffed, so you choose to simulate different scenarios to determine the best scheduling solution.
In other words, one can use an RPD to determine how many people are needed on each shift so that the store is not understaffed or overstaffed regardless of the weather conditions or flow of traffic.
RPDs are screening designs and are often used to reduce the number of factors that are thought to have an effect on the response.
