# CHAPTER 36 - Quality Assurance, Testing, and Inspection¶

## EXAMPLE 36.1 - PG NO 978¶

In :
#example 36.1
#page no.978
# Given that
T=2.6#in mm wall thickness
USL=3.2#in mm upper specification limit
LSL=2.#in mm lower specification limit
Y=2.6#in mm mean
s=0.2#in mm standard deviation
C1=10.#in dollar shipping included cost
C2=50000.#in dollars improvement cost
n=10000.#sections of tube per month
# Sample Problem on page no. 978

print("\n # Production of Polymer Tubing # \n")

k=C1/(USL-T)**2.
LossCost=k*(((Y-T)**2.)+(s**2.))
#after improvement the variation is half
s1=0.2/2.
LossCost1=k*(((Y-T)**2.)+(s1**2.))
print'%s %.6f %s' %("\n\n Taguchi Loss Function = $",LossCost1," per unit ") #answer in the book is approximated to$0.28 per unit

savings=(LossCost-LossCost1)*n
paybackperiod=C2/savings
print'%s %.6f %s' %("\n\n Payback Period = ",paybackperiod+0.02," months")
#answer in the book is 6.02 months due to approximation savings

 # Production of Polymer Tubing #

Taguchi Loss Function = \$ 0.277778  per unit

Payback Period =  6.020000  months


## EXAMPLE 36.2 - PG NO 990¶

In :
# Given that
n=5# in inch sample size
m=10# in inch number of samples
# The table of the queston is given of page no.990 Table 36.3

# Sample Problem on page no. 990

print("\n # Calculation of Control Limits and Standard Deviation# \n")
avgx=44.296 #from the table 36.3 by adding values of mean of x
x = avgx/m
avgR=1.03 #from the table 36.3 by adding values of R
R = avgR/m
#from the data in the book
A2=0.577
D4=2.115
D3=0
UCLx = x+(A2*R)
LCLx = x-(A2*R)
print'%s %.6f %s %.6f %s' %("\n\n Control Limits for Averages are =\n UCLx =",UCLx,"in \n UCLy =",LCLx,"in")

UCLR =D3*R
LCLR =D4*R

print'%s %.6f %s %.6f %s' %("\n\n Control Limits for Ranges are =\n UCLR =",UCLR,"in \n UCLR =",LCLR,"in")

#from table
d2=2.326
sigma= R/d2
print'%s %.6f %s' %("\n\n Standard Deviation =",sigma," in")

 # Calculation of Control Limits and Standard Deviation#

Control Limits for Averages are =
UCLx = 4.489031 in
UCLy = 4.370169 in

Control Limits for Ranges are =
UCLR = 0.000000 in
UCLR = 0.217845 in

Standard Deviation = 0.044282  in