Math Problem Statement
In the system above, each component fails with probability 0.64 independently of other components. Compute the systems reliability. Round your answer to five decimal places.
Solution
To compute the system's reliability, we need to determine the probability that the system functions correctly. Given that each component fails with a probability of 0.64, the reliability (the probability that a component does not fail) for each component is:
Assuming the system's overall reliability depends on all components functioning correctly (i.e., it’s a series system), the system's reliability can be calculated as the product of the reliabilities of all the components.
If there are components, then the system's reliability is:
However, since the problem statement does not specify the number of components, we can't compute a specific reliability value. If you provide the number of components in the system, I can give you the exact answer.
Would you like to clarify the number of components, or do you have any other questions?
Here are 5 related questions:
- How does the number of components affect the overall reliability of a system?
- What happens to the reliability of a system if components are arranged in parallel?
- How can we improve the reliability of a system with components that have high failure probabilities?
- What is the difference between a series system and a parallel system in terms of reliability?
- How would adding a redundant component affect the overall system reliability?
Tip: In reliability engineering, parallel systems often have higher overall reliability compared to series systems, as they can tolerate some component failures while still functioning.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Reliability Engineering
Formulas
R_component = 1 - Failure Probability
R_system = R_component^n
Theorems
Series System Reliability Theorem
Suitable Grade Level
Undergraduate
Related Recommendation
System Reliability Calculation with Component Failure Probability 0.64
System Reliability Calculation for Series-Parallel Resistor Network
System Reliability Calculation for Parallel and Series Network Components
Calculate Probability of System Working with Parallel and Series Components
Probability of System Reliability with Parallel and Series Connections