Question

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?

Answer #1

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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