# Statistics

Problem 1: Consider three identical items in parallel. What is the system reliability if each item has a reliability of 98%?

Please explain why the exponential function is used for reliability.

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#### Solution Preview

The solution file is attached.

Problem 1: Consider three identical items in parallel. What is the system reliability if each item has a reliability of 98%

Let the three items be A, B and C

P(A fails) = P(B fails) = P(C fails) = 1 - 0.98 = 0.02

P(System works) = 1 - P(System fails)

= 1 - P(All the three items fail)

= 1 - P(A fails and B fails and C fails)

= 1 - (0.02 * 0.02 * 0.02)

= 0.999992

Reliability of the system is 0.999992.

Additional question 1: Please explain to me why the exponential function is used for reliability. I cannot grasp the concept? I know e is an exponential curve, but where lambda and t help out need some answers.

The ...

#### Solution Summary

Systems reliability of three identical items in parallel. The exponential functions are found. A complete, neat and step-by-step solutions are provided in the attached file.