network modelling and performance
Budget: £10 – £20 GBP
1) State the formula for the reliability of a subsystem and give the 3 main reasons for choosing this probability model.
2) Evaluate the subsystem reliability at the end of a year if the failure rate = 1 per month. Given the subsystem is working at the end of a year, what will be its reliability at the end of another year?
3) a) Explain what is meant by:
• Series systems
• Parallel systems
• Series and parallel combinations
in the reliability sense. State the formulas in each case.
b) i) A series system has 2 subsystems, each with failure rate = 1 per month. Find the system reliability after 6 months.
ii) A parallel system has 2 subsystems, each with failure rate = 1 per month. Find the system reliability after 6 months.
iii) if the series system of (i) and the parallel system of (ii) are in series in the reliability sense, fined the overall reliability after 1 year.
4) With reference to reliability, explain why hardware & software may have to be treated differently, and using diagrams as appropriate, give a reliability ‘model’ for any system (that uses hardware and software) and has two identical copies of the h/w part to improve reliability.
5) Explain what is meant by a “k out of N system” in the reliability sense. Explain the use of the binomial distribution to evaluate reliability in a k out of N system, and evaluate the reliability after 1 year in a k out of N system for which N=4 and k=2, assuming that the subsystem fail rate is 1 per 3 months.
6) A system consists of hardware, replicated 3 times (i.e. there are a total of 4 versions of the hardware), and software, which we assume is common to all hardware. Draw a diagram of the reliability model of such a system.
Evaluate the system reliability after 1 year given the fail rates are as follows: Software: 1 failure per month
Hardware subsystems: fail rate is 6 per year per subsystem.
7) This diagram shows a system (consisting of 7 subsystems) from the Reliability perspective. “Series” runs from L->R, while “parallel” from U->D. Subsystems have MTBFs as follows:
Ss1= 1month, ss2 = 2months, ss3 = 3months, ss4 = 4months, ss5 = 5months, ss6 = 6months, ss7 = 7months. Find the OVERALL system R(t=1year).
2) Evaluate the subsystem reliability at the end of a year if the failure rate = 1 per month. Given the subsystem is working at the end of a year, what will be its reliability at the end of another year?
3) a) Explain what is meant by:
• Series systems
• Parallel systems
• Series and parallel combinations
in the reliability sense. State the formulas in each case.
b) i) A series system has 2 subsystems, each with failure rate = 1 per month. Find the system reliability after 6 months.
ii) A parallel system has 2 subsystems, each with failure rate = 1 per month. Find the system reliability after 6 months.
iii) if the series system of (i) and the parallel system of (ii) are in series in the reliability sense, fined the overall reliability after 1 year.
4) With reference to reliability, explain why hardware & software may have to be treated differently, and using diagrams as appropriate, give a reliability ‘model’ for any system (that uses hardware and software) and has two identical copies of the h/w part to improve reliability.
5) Explain what is meant by a “k out of N system” in the reliability sense. Explain the use of the binomial distribution to evaluate reliability in a k out of N system, and evaluate the reliability after 1 year in a k out of N system for which N=4 and k=2, assuming that the subsystem fail rate is 1 per 3 months.
6) A system consists of hardware, replicated 3 times (i.e. there are a total of 4 versions of the hardware), and software, which we assume is common to all hardware. Draw a diagram of the reliability model of such a system.
Evaluate the system reliability after 1 year given the fail rates are as follows: Software: 1 failure per month
Hardware subsystems: fail rate is 6 per year per subsystem.
7) This diagram shows a system (consisting of 7 subsystems) from the Reliability perspective. “Series” runs from L->R, while “parallel” from U->D. Subsystems have MTBFs as follows:
Ss1= 1month, ss2 = 2months, ss3 = 3months, ss4 = 4months, ss5 = 5months, ss6 = 6months, ss7 = 7months. Find the OVERALL system R(t=1year).