Robust Parameter Design and Process Robustness Studies Robust

Robust Parameter Design and Process Robustness Studies • Robust parameter design (RPD): an approach to product realization activities that emphasizes choosing the levels of controllable factors (parameters) in a process or product to achieve two objectives: • To ensure that the mean of the output response is at a desired level or target • To ensure that the variability around this target value is as small as possible • When an RPD study is conducted on a process, it is usually called a process robustness study • Four operators for layout 1 • Four operators for layout 2 • Developed by Genichi Taguchi (1980 s) 1

Robust Parameter Design and Process Robustness Studies • Before Taguchi, (RPD was often done by overdesign – expensive • Controversy about experimental procedures and data analysis methods (Taguchi’s methods are usually inefficient or ineffective) • Response surface methodology (RSM) was developed as an approach to the RPD problem • Certain types of variables cause variability in the important system response variables (noise variables or uncontrollable variables) 2

Robust Parameter Design and Process Robustness Studies • A robust design problem usually focuses on one or more of the following • Designing systems that are insensitive to environmental factors that can affect performance once the system is deployed in the field • Designing products so that they are insensitive to variability transmitted by the components of the system • Designing processes so that the manufactured product will be as close as possible to the desired target specifications, even though some process variables are impossible to control precisely • Determining the operating conditions for a process so that the critical process characteristics are as close as possible to the desired target values and the variability around this target is minimized 3

Example 14 -2 – Minitab Analysis Table 14 -12 Minitab Balanced ANOVA Analysis of Example 14 -2 Using the Restricted Model 4

The Split-Plot Design 5

The Split-Plot Design • Pulp preparation methods is a hard-to-change factor • Consider an alternate experimental design: – In replicate 1, select a pulp preparation method, prepare a batch – Divide the batch into four sections or samples, and assign one of the temperature levels to each – Repeat for each pulp preparation method – Conduct replicates 2 and 3 similarly 6

The Split-Plot Design • Each replicate (sometimes called blocks) has been divided into three parts, called the whole plots • Pulp preparation methods is the whole plot treatment • Each whole plot has been divided into four subplots or split-plots • Temperature is the subplot treatment • Generally, the hard-to-change factor is assigned to the whole plots • This design requires only 9 batches of pulp (assuming three replicates) 7

The Split-Plot Design Model and Statistical Analysis Table 14 -15 Expected Mean Square Derivation for Split-Plot Design 8

Split-Plot ANOVA Table 14 -14 9

Split-Plot ANOVA Table 14 -16 Analysis of Variance for the Split-Plot Design Using Tensile Strength Data from Table 14 -14 Calculations follow a three-factor ANOVA with one replicate Note the two different error structures; whole plot and subplot 10

Alternate Model for the Split-Plot 11

The Agriculture Heritage of Split-Plot Design • Whole plots: large areas of land • Subplots: smaller areas of land within large areas • Example: Effects of variety, field, and fertilizer on the growth of a crop • One variety is planted in a field (a whole plot) • Each field is divided into subplots with each subplot is treated with one type of fertilizer • Crop varieties: main treatments • Fertilizers: subtreatments 12