Asked by Caitlin Saalfrank on Jul 18, 2024
Verified
Suppose that a process is comprised of multiple components, each having a 75% success rate. What is the change in reliability going from a series layout to a parallel layout if the process has 5 components?
A) 0%
B) 100%
C) 76.2%
D) -76.2 %
E) unable to determine
Series Layout
A type of manufacturing process layout where operations or work stations are arranged in a sequence that the product must follow for completion.
Parallel Layout
An arrangement of workstations or machinery where operations are carried out simultaneously, enhancing efficiency and reducing processing time.
- Gain an understanding of the methodology and numerical assessment of reliability in products featuring series and parallel component configurations.
- Execute reliability analyses for theoretical models and actual case studies, encompassing systems featuring alternative backups and multiple configurations.
Verified Answer
AM
Alicia MojarraJul 24, 2024
Final Answer :
C
Explanation :
In a series layout, the reliability is the product of the individual reliabilities, so for 5 components each with a 75% success rate, the overall reliability is 0.755=0.23730.75^5 = 0.23730.755=0.2373 or 23.73%. In a parallel layout, the failure rate is the product of the individual failure rates, so the failure rate for 5 components each with a 25% failure rate (100% - 75%) is 0.255=0.00097656250.25^5 = 0.00097656250.255=0.0009765625 , and the reliability is 1−0.0009765625=0.99902343751 - 0.0009765625 = 0.99902343751−0.0009765625=0.9990234375 or 99.90234375%. The change in reliability is 99.90234375%−23.73%=76.17234375%99.90234375\% - 23.73\% = 76.17234375\%99.90234375%−23.73%=76.17234375% , which rounds to 76.2%.
Learning Objectives
- Gain an understanding of the methodology and numerical assessment of reliability in products featuring series and parallel component configurations.
- Execute reliability analyses for theoretical models and actual case studies, encompassing systems featuring alternative backups and multiple configurations.