4. A casting company offers a 1 year warranty for a small aluminum casting. If t

Question

4. A casting company offers a 1 year warranty for a small aluminum casting. If the casting fails during this period it is replaced. The time to failure is well modeled by the following Weibull distribution with B 1,0 8, and x being the time in years: f(x) 0.125 e -0.125x a) What percentage of casting will fail during the warranty period? Answer: b If the manufacturing cost is $60 and the selling price is S115 for a profit per sale of $55. How much does the warranty replacement decrease profit? Without replacement profit is $115-S60 $55. Replacement cost is 0.118($60-$7.05 Answer:

Explanation / Answer

a) f(x) = 0.125*e-0.125x

P(x < 1) = f(1) = 0.125*e-0.125 = 0.1103

b) Probability of failure during warranty period = 0.1103

Probability of of no failure during warranty period = 1 - 0.1103 = 0.8896

Profit without warranty replacement = $55 per sale

Profit without warranty replacement = $55*0.8896 - 0.1103*$7.05 = $48.15   

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