A new class of ship is being fielded. Unfortunately, it has a design flaw that e

Question

A new class of ship is being fielded. Unfortunately, it has a design flaw that eventually causes the drive shaft to warp resulting in a total loss of the ship, because it I is too expensive to fix. The drive shaft warping problem occurs once on average every 5,000 days of continuous operations. The Navy is fielding 40 of these ships and would like 90% to still be in service after five years (assume 365 days per year) of continuous operations.

a) Is procuring this ship a good idea?

b) What is the probability that the new class of ship will meet the Navy's goal? Show your work.

Explanation / Answer

Here the problem occur on average 5000 days of continous operations.

so the probability disribution is exponential with Mean = 1/5000

f(t) = (1/5000) e-t/5000

so 5 years means = 5 * 365 = 1825 days

so,

Probability of a ship failure in 1825 days

Pr(t < 1825; 5000 days) = 1 - e-1825/5000 = 0.3058

Here probability of any ship to be failed in 5 years = 0.3058

probability of any ship to be in service after 5 years = 1 - 0.3058 = 0.6942

so number of ships = 40

probability that 90% or atleast 36% would survive

Pr(X >=36 ; 40 ; 0.6942) = 1 - BINOMIAL (x < 36 ; 40 ; 0.6942) = 1 - 0.9980 = 0.0020

so procuring this ship is not at all a good idea as there is very minimal probability that 90% of ships will still be in service after 5 years.

(b) Probability that the new class of ship will meet the Navy's coal is given above.

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