A system is composed of four parts, J, K, L, and M. All four must function for the system to function. The four component reliabilities are .99, .98, .992, and .998. The designers are considering putting a .80 reliable backup at K. Calculate the change that occurred to the system reliability.

Change that occurred to the system reliability = 0.016

Explanation:

Overall system reliability consisting of 4 components J/K/L/M is

= Reliability of J x Reliability of K x Reliability of L x Reliability of M

= 0.99 X 0.98 X 0.992 X 0.998

= 0.960

Let the subsystem consisting f K along with its back up is Called K1

Thus ,

Reliability of K1 = 1- ( 1 – Reliability of K) x ( 1 – Reliability of Backup )

                             = 1 – ( 1 – 0.98) x ( 1 – 0.80)

                              = 1 – 0.02 x 0.2

                               = 1 – 0.004

                                = 0.996

Thus revised System reliability

= Reliability of J x Reliability of K1 x Reliability of L x Reliability M

= 0.99 X 0.996 X 0.992 X 0.998

= 0.976

Thus, Revised system reliability = 0.976

Thus change in system reliability

= Revised System reliability – Initial system reliability

= 0.976 – 0.960

= 0.016