An system has three major parts with reliabilities of 0.68,0.68,and 0.57.In order to improve the reliability,each component has a backup each with reliability of 0.98.Compute and indicate the composite reliability of the system.
A)0.979
B)0.872
C)0.831
D)0.731

Question

Quizplus · Accepted Answer

The reliability of a system with backup components can be calculated using the formula for parallel systems: $R = 1 - (1 - R_1) \times (1 - R_2)$, where $R_1$ and $R_2$ are the reliabilities of the primary component and its backup, respectively. For each of the three components with backups, we calculate their enhanced reliabilities:1. For the first and second components (each with reliability 0.68 and backup reliability 0.98):   $R_{enhanced} = 1 - (1 - 0.68) \times (1 - 0.98) = 1 - 0.32 \times 0.02 = 1 - 0.0064 = 0.9936$2. For the third component (with reliability 0.57 and backup reliability 0.98):   $R_{enhanced} = 1 - (1 - 0.57) \times (1 - 0.98) = 1 - 0.43 \times 0.02 = 1 - 0.0086 = 0.9914$The overall system reliability, considering it as a series system of the three enhanced components, is the product of their reliabilities:   $R_{system} = 0.9936 \times 0.9936 \times 0.9914 \approx 0.979$Therefore, the composite reliability of the system with backups is approximately 0.979.

An System Has Three Major Parts with Reliabilities of 0