Chapter 16: Applications to Reliability and Life Testing

Example, Page-488

In [1]:
# Variable declaration
rel = 0.970
n = 5

# Calculation
from scipy import *
from pylab import *

# Result
print "Riliability of 5 component system: ",round(rel**5,3)
print "Riliability of 10 component system: ",round(rel**10,3)

Riliability of 5 component system:  0.859
Riliability of 10 component system:  0.737

Example, page-489

In [2]:
# Variable declaration
a1 = 0.70
a2 = 0.75

# Calculation
from scipy import *
from pylab import *

a1 = 1-pow((1-a1),3)
a2 = 1-pow((1-a2),2)

riliability = (0.95)*(0.99)*(a1)*(a2)*(0.90)

# Result
print "Riliability: ",round(riliability,3)

Riliability:  0.772

Example, page-495

In [3]:
# Variable declaration
n = 50   # Units
r = 10   # Failed units
v = 20   # Degrees of freedom

# Calculation
from scipy import *
from pylab import *

l = [65,110,380,420,505,580,650,840,910,950]

T = sum(l)+(50-10)*950
U = T/10

X_sq_thr = 31.410         # chi-square theoritical at alpha = 0.05
X_sq_thr1 = 10.851        # chi-square theoritical at alpha = 0.95

# 90% Confidence interval

llim = (2*T)/X_sq_thr
ulim = (2*T)/X_sq_thr1

# Result
print "90% confidence interval(in hours): (",int(round(llim,0)),",",int(round(ulim,0)),") "

90% confidence interval(in hours): ( 2764 , 8001 )

Example, Page-495

In [4]:
# Variable declaration
n = 50   # Units
r = 10   # Failed units
v = 20   # Degrees of freedom

# Calculation
from scipy import *
from pylab import *

l = [65,110,380,420,505,580,650,840,910,950]

U = 1000/0.4
T_prt = sum(l)+(50-10)*950

X_sq_thr = 31.410         # chi-square theoritical at alpha = 0.05
T_thr = (0.5 * U * X_sq_thr)

# Result
print "Practical T value: ",T_prt
if(T_thr > T_prt):
    print "null hypothesis can not be rejected"
    print "Failure rate is greater than 0.40 failure per thousand hours."
else:
    print "null hypothesis must be rejected"
    print "Failure rate is less than 0.40 failure per thousand hours."

Practical T value:  43410
null hypothesis must be rejected
Failure rate is less than 0.40 failure per thousand hours.