1 Chapter 5: Custom Designs 5.1 Custom Design Generation 5.2 Custom Response Surface Designs

2 Chapter 5: Custom Designs 5.1 Custom Design Generation 5.2 Custom Response Surface Designs

Objectives Understand custom designs and how they are generated in JMP. Describe situations for using custom designs. 3

Custom Design Philosophy Build the design to fit the problem instead of fitting the problem into the design. 4

Characteristics of Custom Designs Custom designs provide the most flexibility of all design choices can be used in situations not suitable for classic designs can be used for routine factor screening, split-plot designs, response optimization, experiments with fixed covariate factors, and mixture problems. 5

Custom Design Benefits A custom design can include any kind of factor: continuous, categorical, mixture, blocking, covariate, uncontrolled, or constant any number of levels for the categorical, blocking, or covariate factors any number of factors or combinations of factor levels any combination of effects in the model any number of runs, as long as the number of runs is greater than or equal to the number of terms in the model any randomization restrictions an irregular experimental region. 6

Algorithmic Design Iterative design process Objective criterion for the optimal design –D-optimal –I-optimal 7

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5.01 Quiz Match the optimality criterion with its appropriate objective. 1. D-optimal 2. I-optimal 9 A. To screen for important factors. B. To develop a response surface model and make predictions.

5.01 Quiz – Correct Answer Match the optimality criterion with its appropriate objective. 1. D-optimal 2. I-optimal 1-A, 2-B 10 A. To screen for important factors. B. To develop a response surface model and make predictions.

Custom Design Generation Advantages Custom design generation does not use factorial combinations of design points, which avoids large and inefficient designs does not require a candidate set of design points, which avoids long iterations provides a flexible approach to most problems enables the user to specify the factors, model, and size. 11

Using the Custom Designer This demonstration illustrates the concepts discussed previously. 12

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14 Chapter 5: Custom Designs 5.1 Custom Design Generation 5.2 Custom Response Surface Designs

Objectives Augment an existing experiment for specific effects not originally included in the design to create a response surface model. Design and analyze a custom experiment for a response surface model from the start of the problem. 15

Augmenting a Design Augmentation supports sequential experimentation expands and enhances your initial design raises new questions or indications based on the specific information sought. 16

The Augment Design Platform Replication Addition of center points Foldover design Addition of axial points Optimal augmentation 17

D-Optimal or I-Optimal Augmentation With optimal augmentation, you can add specific effects to the model. find optimal new test runs with respect to this expanded model. group runs into separate blocks. optimally block new runs with respect to original runs change factor ranges. add new constraints. 18

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5.02 Quiz Match the technique for augmentation on the left to a component on the right Replication 2.Addition of center points 3.Foldover design 4.Addition of axial points 5.Optimal augmentation A.removes confounding between main effects and factor interactions B.tests for lack of fit C.reduces variability of effect estimates D.transforms a screening design to a response surface design E.adds points after you include new terms in the model

5.02 Quiz – Correct Answer Match the technique for augmentation on the left to a component on the right Replication 2.Addition of center points 3.Foldover design 4.Addition of axial points 5.Optimal augmentation A.removes confounding between main effects and factor interactions B.tests for lack of fit C.reduces variability of effect estimates D.transforms a screening design to a response surface design E.adds points after you include new terms in the model 1-C, 2-B, 3-A, 4-D, 5-E

Augmentation Example A fractional factorial screening design was used to model the relationship between Yield and four factors of interest: Reactant, Catalyst, Temperature and Pressure. The fractional factorial design had the following aliasing pattern: 22

Initial Findings Temperature is the only detectable main effect; you want to confirm this conclusion. You want to test one two-factor interaction: Reactant*Pressure You want to test all possible quadratic effects. The budget allows 24 runs to be used for screening, optimization, and confirmation. The screening design used 8 runs. This leaves approximately 12 runs for optimization and 4 runs for confirmation. In addition to Yield, Cost must also be considered. Specifically, Cost must be no more than $425, but ideally Cost is no more than $390 per run. This goal is twice as important as the goal for Yield (90%). 23

Augment Design This demonstration illustrates the concepts discussed previously. 24

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Building Custom Designs for RSM The Custom Design platform can be used to build a response surface design ex nihilo. The design can include any type of factor, including blocking factors. There can be any number of runs or factors. 26

Custom Design Example The purpose of this experiment is to choose the best spring for a mechanical design, given the factors Stretch, Brand, and Metallization. The spring must deliver 7±0.5 Newtons of Force when stretched to a displacement of 5 cm. In addition, the Cost must be under $45 per 1000 pieces, but preferably the Cost will be under $30 per 1000 pieces. 27

Custom Design Factors Stretch : continuous range 1-9 cm. Brand : three categorical levels including Acme Springs, eSprings, and Sprung Springs. Metallization : continuous range Blocking : up to 20 runs per jig, up to three jigs. Given that Stretch has 3 possible values (1, 5, 9), Brand has 3 possible values ( Acme, eSprings, Sprung ), and Metallization has 2 possible values (.75, 1.0), there are 3*3*2=18 factor level combinations. There are up to 20 runs per the 3 jigs; the decision is to use 18 runs for each of the 3 jigs for a total of 54 runs. 28

Custom Design for a Response Surface Model This demonstration illustrates the concepts discussed previously. 29

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Exercise This exercise reinforces the concepts discussed previously. 31