A group of process plants in an oil refinery are fitted with valves. Over a period of time, the failure pattern of these 400 valves has been observed and it is as follows:

It costs Rs 100 to replace each valve individually. If all the valves are replaced at a time, it costs Rs 50 per valve.
The maintenance department is considering following replacement policies:

(a) to replace all valves simultaneously at fixed intervals, in addition to replacing valves as and when they fail.

(b) to replace valves as and when they fail.
Suggest an optimal replacement policy.

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Month 1 Number of valves failing: 8 22 3 4 5 20 48 104 120 166 7 8 Total 56 32 12 400