The lifetime of a microchip operated at temperature

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When a chip fabrication facility is operating normally, the lifetime of a microchip operated at temperature T , measured in degrees Celsius, is given by an exponential (λ) random variable X with expected value E[X] = 1/λ = (200/T )² years. Occasionally, the chip fabrication plant has contamination problems and the chips tend to fail much more rapidly. To test for contamination problems, each day m chips are subjected to a one-day test at T = 100?C. Based on the number N of chips that fail in one day, design a significance test for the null hypothesis test H₀ that the plant is operating normally.

(a) Suppose the rejection set of the test is R = {N > 0}. Find the significance level of the test as a function of m, the number of chips tested.

(b) How many chips must be tested so that the significance level is α = 0.01.

Reference no: EM131083836

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