I have four redundant components as follows:
a)Has a life that is normally distributed with a mean of 95 hour and a standard deviation of 15 hours.
b)Has a constant hazard rate with a MTBF equal to 125 hours.
c)Has a life that is Weibull distributed with a shape parameter equal to 1.6 and a characteristic life equal to 135 hours? ( = 0 )
d)Has a constant hazard rate with a MTBF equal to 114 hours. What is the reliability of the system after 100 hours of life, and after 150 hours of life?
a)
Reliability after 100 hrs is given by
R(100) = P[Z > (x − )/]
= P[Z > (100 − 95)/15]
= P[Z > 0.33)
= 0.3707 (from Z values table)
b) Hazard rate is constant for Exponential Distribution and is given by
MTBF (Maximum time before failure) = 1/ = 125 hrs
Thus, = 1/125
Reliability R = e− = e−100/125 = 0.45
c) For Weibull Distribution, reliability is given by
R(t) = e−[(t −)/] ^
Here, = 1.6, = 0
Thus, R(t) = 0
d)
Hazard rate is constant for Exponential Distribution and is given by
MTBF (Maximum time before failure) = 1/ = 114 hrs
Thus, = 1/114
Reliability R = e− = e−100/114 = 0.416
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