Question

1. A manufacturer of electronic calculator offers a 1-year warranty. If the calculator fails for any reason during this period, it is replaced. The time of failure is modelled by expoential distribution with the prababilty of failure in time t, P(t) = 1 - e ^{- λt}  where λ is failure rate, with mean life of 12 years.

1. What percentage of the calculator will fail by warranty period?
2. The manufacturer cost of calculator is $75, and the profit per sale is $35. How much the profit will be reduced per calculator for warranty replacement.

Answer 1

Ans: Let The Random Variable measure time of Calculator. Given that. pati= F(TLL) = lett failuase of electronic :. To exp( d= t year) as El Tl= 12 = co Tis exponential distribution with no 12 How -a] Calculator will fail by warranty period. = P(TSI) = PC = - 8 1/12 = 0.279956 . Percentage of coltulate fail duning wanenty period = 7.99564 ] Manufacturing cost = $ 75 - Profit pee sole = 35 Let. 100 computer produced then 799561. are fall during je. 7.99 A 8 computea will replaced I fail during warranty period, How Total expenses of 8 computer = 8x 175= 1400 je. Manufacturing wst = 1400 Tatal pofit of 100wmputer should be = 100X 35 = 35,00 But due to 8 compute e fail durry winonty period wanty P Actual profit of 100 womputea = 3500- 1400 tual 100 computer poft - Actual profit of I compute a = 21 ence -Profit will be neduced per calculator wanent replacement for - 35-21