EXAMPLE 8.9 The failure rates of transistors in a computer are summarized in Table 8.5. Table 8.5 Failure Rates of Transistors in Computers 1 2 3 4 5 6 7 End of week Probability of failure to date 0.07 0.18 0.30 0.48 0.69 0.89 1.00 The cost of replacing an individual failed transistor is Rs. 9. If all the transistors are replaced simultaneously, it would cost Rs. 3.00 per transistor. Any one of the following two options can be followed to replace the transistors: (a) Replace the transistors individually when they fail (individual replacement policy). (b) Replace all the transistors simultaneously at fixed intervals and replace the individual transistors as they fail in service during the fixed interval (group replacement policy). Find out the optimal replacement policy, i.e. individual replacement policy or group replacement policy. If group replacement policy is optimal, then find at what equal intervals should all the transistors be replaced