A computer contains 10,000 resistors. When any resistor fails, it is replaced. The cost of replacing a resistor individually is Rs 1 only. If all the resistors are replaced at the same time, the cost per resistor would be reduced to 35 paise. The percentage of surviving resistors say S(t) at the end of month t and the probability of failure P(t) during the month t are as follows: t 0 1 2 3 4 5 6 P(t) 0 0.03 0.07 0.20 0.40 0.15 0.15 What is the optimal replacement plan?

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A computer contains 10,000 resistors. When any resistor fails, it is replaced. The cost of replacing a resistor individually is Rs 1 only. If all the resistors are replaced at the same time, the cost per resistor would be reduced to 35 paise. The percentage of surviving resistors say S(t) at the end of month t and the probability of failure P(t) during the month t are as follows:

t 0 1 2 3 4 5 6
P(t) 0 0.03 0.07 0.20 0.40 0.15 0.15


What is the optimal replacement plan?

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