Asked by Ajayi Oluwagbemileke on Jul 15, 2024
Verified
Consider a product with three components in series, with reliabilities of 0.90, 0.80, and 0.99 for components A, B, and C, respectively. Furthermore, component B uses a backup that also has a reliability of 0.80. What is the reliability of the system?
A) 0.50000
B) 0.71280
C) 0.80000
D) 0.85536
E) 3.49000
Reliabilities
Reliability refers to the consistency and dependability of a system or process to perform its intended function under specified conditions over a certain period.
Backup
The act of copying data, files, or systems to a secondary location for preservation in case of failure or loss of the original.
- Understand the concept and calculation of reliability for products with components in series and parallel arrangements.
- Apply reliability calculations to both theoretical and practical scenarios, including systems with backups and different configurations.
Verified Answer
LL
Laila LohseJul 18, 2024
Final Answer :
D
Explanation :
The overall reliability of the system can be calculated using the following formula:
R_sys = R_A*R_B*R_C
where R_A, R_B, and R_C are the reliabilities of components A, B, and C, respectively. Since component B has a backup with reliability 0.8, the overall reliability of component B becomes:
R_B = 0.8 + 0.2*0.8 = 0.96
Using this value and the given values for R_A and R_C, we get:
R_sys = 0.9 * 0.96 * 0.99 = 0.85536
Therefore, the reliability of the system is 0.85536. The correct choice is D.
R_sys = R_A*R_B*R_C
where R_A, R_B, and R_C are the reliabilities of components A, B, and C, respectively. Since component B has a backup with reliability 0.8, the overall reliability of component B becomes:
R_B = 0.8 + 0.2*0.8 = 0.96
Using this value and the given values for R_A and R_C, we get:
R_sys = 0.9 * 0.96 * 0.99 = 0.85536
Therefore, the reliability of the system is 0.85536. The correct choice is D.
Learning Objectives
- Understand the concept and calculation of reliability for products with components in series and parallel arrangements.
- Apply reliability calculations to both theoretical and practical scenarios, including systems with backups and different configurations.