A system consists of components and connected in series, as shown in the following schematic illustration. The lifetime in months of component is lognormally distributed with and , and the lifetime in months of component is lognormally distributed with and . The system will function only so long as and both function.

a. Generate, by simulation, a large number (at least 1000) of system lifetimes.

b. Estimate the mean system lifetime.

c. Estimate the probability that the system fails within 2 months.

d. Estimate the 20th percentile of system lifetimes.

e. Construct a normal probability plot of system lifetimes. Is the system lifetime approximately normally distributed?

f. Construct a histogram of the system lifetimes. Is it skewed to the left, skewed to the right, or approximately symmetric?

Solution:

Step 1of 4:

A system consist of components A and B connected in series. The lifetime of component A in months is lognormally distributed with mean =1, and standard deviation =0.5. Similarly the lifetime of component B is lognormally distributed with =2 and =1.

The system will function as long as the both will functions. Let x denote the lifetime of system A and Y denote the lifetime of system B.

Which means the system lifetime can be defined as L= Min (X,Y).