Question

In: Statistics and Probability

3. Consider the following system made up of functional components in parallel and series. C2 0.80...

3. Consider the following system made up of functional components in parallel and series.

C2

0.80

C1

0.95

C3

0.95

C4

0.80

3-1. (2 points) What is the probability that the system operates? Answer: .  

3-2. (2 points) What is the probability that the system fails due to the components in series? Assume parallel components do not fail. Answer: .

3-3. (2 points) What is the probability that the system fails due to the components in parallel? Assume series components do not fail. Answer: .  

3-4. (2 points) Compute and compare the probabilities that the system fails when the probability that component C1 functions is improved to a value of 0.99 and when the probability that component C3 functions is improved to a value of 0.99. Which improvement increases the system reliability more?

Solutions

Expert Solution


Related Solutions

what is system functional decomposition ? if we add spring and damper in series and parallel
what is system functional decomposition ? if we add spring and damper in series and parallel
Capacitor C1 = 10.0 micro F is connected in series to parallel combination of capacitors C2=7.0...
Capacitor C1 = 10.0 micro F is connected in series to parallel combination of capacitors C2=7.0 microF and C3=7.5 microF. This circuit is connected to a battery delivering V=13.0 V. Find energy stored in capacitor C3 in microJ.
An electrical system consists of 2 components (C1 and C2) functioning independently and are set in...
An electrical system consists of 2 components (C1 and C2) functioning independently and are set in a parallel layout. The failure time of each component follows an exponential distribution with rate 2 every year. Identify the failure density of system if i) the system functions if and only if both components function. Hence, calculate the probability of the system failing in less than 8 months. ii) the system can function only on anyone functioning component. Hence, determine the probability of...
An electrical system consist of 2 components (C1 and C2) functioning independently, and are set in...
An electrical system consist of 2 components (C1 and C2) functioning independently, and are set in a series layout. The failure time of each component follows an exponential distribution with rate 2 in every year.Suppose the system will operate if both components function, and it will fail if any one component fails. calculate i) the probability that the system fails in less than 8 months. ii) the expected time to failure of the system.
For a parallel structure of identical components, the system can succeed if at least one of...
For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fall independently of each other and that each component has a 0.21 probability of failure. (A) Would it be unusual to observe one component fail? Two components? Fill in blanks: It (would,would not) be unusual to observe one component fail, since the probability that one component fails,___is, (less,greater) than 0.05. It (would not, would) be unusual to observe...
Q1: An electrical system consists of 2 components (C1 and C2) functioning independently, and are set...
Q1: An electrical system consists of 2 components (C1 and C2) functioning independently, and are set in a serial layout. The failure time of each component follows an exponential distribution with rate 2 in every year. Thus the system will operate if both components function, and it will fail if any one component fails. (a) Obtain the failure density and distribution of the system (b) Obtain the survival function/distribution of the system. (c) Based on your answer in (a) and...
Task # 3:          Identify Functional and Non-Functional Requirements for the given system description: The proposed...
Task # 3:          Identify Functional and Non-Functional Requirements for the given system description: The proposed software product is the Hospital Patient Info Management System (HPIMS). The system will be used to get the information from the patients and then storing that data for future usage. The current system in use is a paper-based system. It is too slow and cannot provide updated lists of patients within a reasonable timeframe. The intentions of the system are to reduce over-time pay...
A system consisting of two components is subject to a series of shocks that arrive according...
A system consisting of two components is subject to a series of shocks that arrive according to a Poisson process with a rate of one per day. Half the shocks cause no damage, one in ten damages component 1 alone, one in five damages component 2 alone, and the rest damage both components. Note that if only one component is functioning, and a shock occurs that would damage both components, the functioning component is damaged. Compute the probability that the...
Q1) What is not true of signal-transduction pathways? A They are often made-up of a series...
Q1) What is not true of signal-transduction pathways? A They are often made-up of a series of kinases B They transduce signals from water-soluble hormones to stimulate a cellular response C They are typically initiated by the binding of a hormone to a cytoplasmic receptor protein D They allow amplification of a hormonal signals E They allow regulation a hormonal signal by other molecules Q2) When you touch a hot object you automatically pull your hand away as a reflex....
Answer the following two questions in paragraph form: 1. A database system is made up of...
Answer the following two questions in paragraph form: 1. A database system is made up of five major parts. Identify these parts. Provide specifics of what make up these components. 2. A DBMS provides at least nine functions. Identify these functions and provide a brief explanation of each.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT