\!\Then a chip fabrication facility is operating no1mally,

Chapter 11, Problem 11.11

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\!\Then a chip fabrication facility is operating no1mally, the lifetime of a inicrochip operated at temperature 1", measured in degrees Celsius, is given by an exponential (.\) random variable X with expected value E[X ) = 1/ .\ = (200 /11) 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 = 1000. Based on the number 1'l of chips that fail in one day, design a significance test for the null hypothesis test Ho that the plant is operating normally. (a) Suppose the rejection set of the test is R = { 1'l > 0}. F ind the significance level of the test as a function of m, the number of chips tested. (b) Ho'v many chips must be tested so that the significance level is a = 0.01. ( c) If we raise the temperattrre of the test, does the number of chips vve need to test increase or decrease?