An automobile manufacturer warrants the power train of its vehicles for one year

Question

An automobile manufacturer warrants the power train of its vehicles for one year. Empirical data indicate that the time until failure of the power train is exponentially distributed with an average time until failure of 4 years. Suppose the manufacturer's profit on a new car is $1500 and that warranty work on power train failures is $500 for each failure. a) What percentage of cars will experience a power train failure during the warranty period? b) Assuming that the manufacturer provides warranty work on any given vehicle at most once, what is the manufacturer's expected profit per vehicle?

Explanation / Answer

a)

That means the lifetime was less than 1 year.

As

u = 4 years = mean

Then

P(x<t) = 1 - exp(-t/u)

P(x<1) = 1 - exp(-1/4) = 0.221199217 = 22.12% [ANSWER]

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b)

Hence,

E(profit) = 1500*P(no fail) + (1500-500)*P(fail)

As P(fail) = 0.221199217

Then

E(profit) = 1500*(1-0.221199217) + (1500-500)*0.221199217 = 1389.400392 [ANSWER]

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