At a computer disk drive factory, inspectors randomly pick a product from production lines to detect a failure. If the production lines are normal, this failure rate q0 = 10−3 . However occasionally some problems occur in the lines, in which case the rate goes up to q1 = 10−1 . Let Hi denote the hypothesis that the failure rate is qi . Every morning, an inspector chooses drives at random from the previous day’s production and tests them. If a failure occurs too soon, the company stops production and checks the critical part of the process. Production line problems occur about once every 4 days, so we will say P(H1) = 0.25 = 1 − P(H0).1. Based on N, the number of drives tested up to and including the first failure, design a MAP test.
2. Calculate the probability of ‘false alarm’ (i. e. our MAP test computed in previous part concludes that the rate is q1 wrongly) and the probability of ‘missed detection? (i. e. our MAP test fails on detect that the rate is q1).
3. Based on this, calculate the probability of detection error Pe?