Assignment 18

Problem

An engineer is interested in the effects of cutting speed A, tool geometry B, and cutting angle C on the life (in hours) of a machine tool. Two levels of each factor are chosen, and one replicate of a 2³ factorial design is run:

1. Assume that the design is run in two blocks.

a) Which effect(s) would you confound with the blocks?

We choose to confound the highest order interaction which is ABC.

b) Propose a design (i.e. assign corner points to blocks)

Block 1 corner points are: (1) AB AC BC

Block 2 corner points are : A B C ABC

2. Assume the design is to be run in four blocks.

a) Which effects would you confound with the blocks?

For 4 blocks run, we have 3 degree of freedom, so we confound all three two-way Interactions, which are AB, AC, BC.

b)Propose a design (i.e. assign corner points to blocks)

Block 1 corner points are: (1), ABC

Block 2 corner points are : A, BC

Block 3 corner points are: B, AC

Block 4 corner points are : AB, C

3. Generate a half normal plot for the collected data

a) Which effects appear to be significant?

library(DoE.base)

## Loading required package: grid

## Loading required package: conf.design

## Registered S3 method overwritten by 'DoE.base':
##   method           from       
##   factorize.factor conf.design

## 
## Attaching package: 'DoE.base'

## The following objects are masked from 'package:stats':
## 
##     aov, lm

## The following object is masked from 'package:graphics':
## 
##     plot.design

## The following object is masked from 'package:base':
## 
##     lengths

tool_life <- c(22, 32, 35, 55, 44, 40, 60, 39)
A <- c(-1,1,-1,1,-1,1,-1,1)
B <- c(-1,-1,1,1,-1,-1,1,1)
C <- c(-1,-1,-1,-1,1,1,1,1)
dat <- data.frame(A,B,C,tool_life)
model <- lm(tool_life~A*B*C,data = dat)
coef(model)

## (Intercept)           A           B           C         A:B         A:C 
##      40.875       0.625       6.375       4.875      -0.875      -6.875 
##         B:C       A:B:C 
##      -2.625      -3.375

halfnormal(model)

## no significant effects

b) Does it appear that the block was significant?

No, the block is not significant.