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Fifteen assemblies are put on accelerated life test without replacement, and the test is truncated after 4 failures. If the first 4 failures occurred at 16.5, the mean 19.2 20.8, and 37.3 hours, assuming an exponential model, (a) find a 90% confidence interval for the failure rate of such assemblies under these accelerated conditions; (b) test the null hypothesis that the failure rate is 0.004 failure per hour against the alternative that it is less than 0.004, using the 0.01 level of significance.One hundred devices are put on life test and the times to failure (in hours) of the first 10 that fail are 7.0 14.1 18.9 31.6 52.8 80.0 164.5 355.4 451.0 795.1 Assuming a Weibull failure-time distribution, estimate the parameters o and 6 as well as the failure rate at 1,000 hours. How does this value of the failure rate compare with the value we would obtain if we assumed the exponential model?A sample of 200 switches was placed on life test consisting of repeated on-off cycles. The test was terminated after the third failure. The first three failure times were 2,076, 3,667, and 9,102. Find a 95% lower confidence limit for the mean life, in number of cycles, of the switches. Use the exponential model.Suppose that the flight of an aircraft is regarded as a system having the three main components A (aircraft), B (pilot), and C (airport). Suppose, furthermore, that component B can be regarded as a parallel subsystem consisting of 1(captain), 82 (first officer), and 83 (flight engineer); and C is a parallel subsystem consisting of C1 (scheduled airport) and C2 (alternate airport). Under given flight conditions, the reliabilities of components A, 81, 82, 83, C1, and C2 (defined as the probabilities that they can contribute to the successful completion of the scheduled flight) are, respectively, 0.9999, 0.9995, 0.999, 0.20, 0.95, and 0.85. (a) What is the reliability of the system? (b) What is the effect on system reliability of having a flight engineer who is also a trained pilot, so that the reliability of 83 is increased from 0.20 to 0.99? (c) If the flight crew did not have a first officer, what then would be the effect of increasing the reliability of 83 from 0.20 to 0.99? (d) What is the effect of adding a second alternate landing point, C3, with reliability 0.80?\fIn some reliability problems we are concerned only with initial failures, treating a component as if (for all practical purposes) it never fails, once it has survived past a certain time t = o. In a problem like this, it may be reasonable to use the failure rate for 0