A signal processor has a reliability of 0.90. Because of the low reliability a redundant signal processor is to be added. However, a signal splitter must be added before the signal processors, and a comparator must be added after the signal processors. Each of these new components has a reliability of 0.95. Does adding a redundant signal processor increase the system reliability

0.9732

Explanation:

A signal splitter must be placed before a processor and a comparator be placed after a processor.

This contains a series combination of a splitter, processor and comparator. Let R1 represent the reliability of the first subsystem and R2 be the reliability of the added redundant system.

Given: R(processor) = 0.9, R(new components) = 0.95 (i.e. splitter, new processor, comparator)

R1 = series combination of splitter, processor and comparator

R1 = R(splitter) × R(processor) × R(comparator) = 0.95 × 0.9 × 0.95 = 0.81225

R2 = series combination of splitter, processor and comparator

R2 = R(splitter) × R(new processor) × R(comparator) = 0.95 × 0.95 × 0.95 = 0.8574

R2 is the redundant system which is connected in parallel with R1, hence:

R(system) = 1 - (1 - R1)(1 - R2) = 1 - (1 - 0.81225)(1 - 0.8574)

R(system) = 0.9732

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