Injection Molding Example

DESCRIPTION:

This example is a study of shrinkage of products made by injection molding reported by Engel (1992). The response is the percent shrinkage with nominal is best having target = 2.5% shrinkage. The control factors are from the injection molding process. The noice factors concern the raw materials and ambient conditions.

The control design is the orthogonal array L8 (similar to ff0708) which has 7 experimental factors each at two levels. The design consists of 8 runs and is a 1/16 fraction of the full factorial. The noise design is ff0304. The control and noise designs are combined to form a robust design that has 32 runs.

For more information see Engel (1992) and the chapter on robust design in the documentation.

ARGUMENTS:

A
a control factor indicating the cycle time of the injection molding process.
B
a control factor indicating the mold temperature.
C
a control factor indicating holding pressure.
D
a control factor indicating cavity thickness.
E
a control factor incidating holding time.
G
a control factor indicating injection speed.
H
a control factor indicating gate size.
M
a noise factor indicating percent regrind content of the raw material.
N
a noise factor indicating moisture content of the raw material.
O
a noise factor indicating ambient temperature
shrink
the response variable, the observed percent shrinkage in the molded parts. The target is 2.5% shrinkage.

REFERENCES:

Engel, J. (1992), Modeling variation in industrial experiments, Applied Statistics 41, 579-593.

SOURCE:

Used by permission of Carfax Publishing, Inc.

EXAMPLES:

# This design is already available in S-PLUS under  
# the name mold.df. The following commands were used 
# to create the data frame: 
cont.des <- oa.design(rep(2,7),min.resid.df=0) 
nois.des<-fac.design(rep(2,3),c('M','N','O'), 
     fraction=1/2) 
mold.des <- robust.design(cont.des,nois.des) 
mold.shrink <- c(2.2,0.3,0.5,2.0,3.0,2.1,4.0, 
     2.0,2.3,0.3,2.8,2.0,3.0,3.1,2.2,1.8,2.3, 
     2.7,0.4,1.8,3.0,1.0,4.6,1.9,2.1,2.5,3.1, 
     1.9,3.1,4.2,1.9,1.9) 
mold.df <- cbind(mold.des,shrink=mold.shrink) 
# Sample analysis 
summary(mold.df) 
plot(mold.df) 
mold.sn <- robust.sn(mold.df) 
mold.sn 
plot(mold.sn,"shrink.mean",data.pts=F) 
plot(mold.sn,"shrink.target") 
mold.fac <- fac.aov(mold.sn) 
mold.fac 
summary(mold.fac) 
moldsd.fac <- fac.aov(response=shrink.sd,mold.sn) 
moldsn.fac <- fac.aov(response=shrink.target,mold.sn) 
moldsn2.fac <- fac.aov(response=shrink.meanl,mold.sn) 
pareto(mold.fac) 
pareto(moldsn.fac) 
qqnorm(mold.fac,label=3) 
qqnorm(moldsn.fac) 
acplot(mold.fac) 
acplot(moldsn.fac) 
mold.facs <- fac.aov(shrink.mean~A+C+H,mold.sn) 
pareto(mold.facs, "mse") 
summary(mold.facs) 
newdata <- data.frame(A = seq(-1,1,by=.1), 
     C = rep(-1,21), H = rep(-1,21)) 
print(predict(mold.facs)) 
mold.pred <- predict(mold.facs, newdata, 
     numeric.levels = list(A = c(-1, 1), 
     C = c(-1, 1), H = c(-1, 1))) 
mold.pred