Systems Reliability Engineering Assignment: Design for Reliability
Purpose: To learn knowledge and approaches in system reliability design and practice.
Learning objectives covered:
1. Understand and apply reliability concepts and terminology.
2. Understand and apply the basic mathematics involved in reliability engineering.
3. Understand and make use of the relationships amongst the different reliability functions.
4. Model the reliability of systems (including safety systems) using fault tree analysis, reliability block diagrams, and FMECA.
Learning Guides: In order to complete the assignment tasks, you need to read Chapter 5 to Chapter 8 given that you have learnt
While you are reading, you need to understand or answer the following questions:
1. How is system reliability determined? How to calculate the system reliability given that all component and subsystem failure information is clearly known.
2. Know how to calculate reliability of series system, parallel system, combined series-parallel systems.
3. Understand the purpose of using redundancy in system reliability design,
4. What is k-out- of-n redundancy? What is the difference between k-out- of-n:G system and k-outof- n:F system? How to evaluate reliability of a redundant system?
5. What are System Structure Function, Minimal Cuts, and Minimal Paths?
6. Learn Markov chain model in system reliability modelling.
7. Learn what the Static Model is and what the Dynamic Model is in reliability modelling.
8. Know Physics-of Failure models in reliability analysis.
9. Learn reliability design methods and know how to apply them
10. How to specify system reliability? What are the factors that affect the system reliability and lifecycle cost?
11. What are the methods used in Reliability Allocation and how to use them?
12. What is FMEA and how to use it?
13. What is FTA? Know how to conduct a fault tree analysis and know how to evaluate the:
Tasks:
Task 1 - There are a series of machines in a manufacturing line to complete a required manufacture process, see Table 1. The manufacture line is controlled by the Control Centre.
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Table 1 - Machines in a manufacturing line
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Machine & Process Control
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Number of machines in the line
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Minimum No. required
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Distribution of time to failure (in hours)
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Cutting machine
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3
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2
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Weibull (β=2.15, θ=20990)
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Drilling machine
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4
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3
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Weibull (β=2.38, θ=17760)
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Milling machine
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2
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2
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Lognormal (s=0.40, tmed = 17600)
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Multi-axis Machining Centre
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2
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2
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Normal (μ=10958, σ=1250)
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Polishing machines
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4
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3
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Lognormal (s =0.55, tmed=19260)
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Painting machines
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5
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4
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Weibull (β=2.0, θ=31500)
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Control Centre
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1
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1
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Exponential with λ = 0.000015
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Note: β is shape parameter and θ is scale parameter of Weibull distribution; s is shape parameter and tmed is location parameter of Lognormal distribution; μ is mean and σ is standard deviation of Normal distribution.
Assume all machines on the manufacturing line keep operation status unless one fails. Answer the following questions:
1) Construct the reliability block diagram to calculate the probability (reliability) that the manufacturing line can fulfill the required process without failure in a periodical maintenance interval of 6 months?
2) What is the time at which a periodical maintenance is carried out when the probability of the manufacturing line to fulfill the required process without causing the process failure is at 85%?
3) If the probability (reliability) that the manufacturing line can perform well to fulfill the required process without failure in 6 months is required to be 95%, what measure should be taken?
Task 2 - Compare three alternative designs by completing the following table where time is measured in days:
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Alternative
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Distribution
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Rsystem(2 days)
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MTTFsystem (in days)
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Load sharing system with two different units
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Exponential with λ1=030, λ2=0.40, λ*1=0.55, and λ+2=0.65
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Standby system with 3 identical units and no failure in standby; at least 2 units are working, the system works
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Exponential with λ = 0.75
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A 2-out-of-3 system having identical units
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Lognormal (s=0.30, tmed=3.5)
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Note: The distribution rwefers to time to failure distribution of each unit.
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Task 3 - The pilots of Green Airlines which flies the Boeing 797 exclusively are known for their "rough" landings. When the force of the landing exceeds the strength of a wheel strut, a fracture (failure) will occur. The strength of wheel strut is affected by number of landings, v, and described as 650 exp(-0.00132v) psi. Measurements on the force of each landing have determined that the distribution is Weibull with a shape parameter of 1.85 and a scale parameter of 209 psi. Each aircraft averages 3 landings per day.
Answer the following questions:
1) Determine the time (in days) to initial inspection of the landing gear struts to insure no more than a 0.5% chance of a strut fracture (failure). Any fractured struts are then replaced and the inspection interval starts over.
2) If no fracture is found, the struts are inspected again after 60 days. What is the probability of detecting a fracture at the next inspection?
Task 4 - Given the following fault tree:
Answer the following questions:
1) Express the system failure in terms of the basic events using Boolean logic.
2) Find the minimum cut sets. From this analysis, what are the top four basic events that should be the focus of the reliability design effort?
3) If the probability of each basic event is 0.03, estimate the probability of the system failure.
4) If the probability of the system failure is required to be reduced 50 percent based on the result obtained in, consider using redundancy of basic events for achieving the design target. It is required to keep the total number of basic events minimum in all possible solutions. Then, modify the fault tree diagram accordingly to represent your design.
Task 5 - A consumer decides to perform an economic analysis to compare two different automobiles intended for use over the next 10 years. The first auto named Auto_1 averages 23 km per gallon and costs $25,000. Consumer Reports says that the time between failures is gamma with a shape parameter of 2.58 and a scale parameter of 5000 km with an average repair cost of $508. Routine servicing is required every 6000 km at a cost of $130. Trade-in value after 10 years is estimated to be $11,000. The second auto named Auto_2 averages 21 km per gallon and costs $23,000. It has a time between failure distribution that Consumer Reports says is minimum extreme value with a scale parameter of 805 and a location parameter of 9350 km. Average repair cost as advertised is $400. Routine servicing is required every 6500 km at a cost of $145. Trade-in value after 10 years is estimated to be $9500. The consumer averages 18,000 km per year and has an available investment rate of return 4.5 percent. Inflation is expected to average 3.25% in every year over the next decade.
Answer the following:
1) Given the cost of gasoline will be $3.0 per gallon in the first year and it will be increased year by year based on the inflation rate, which automobile should be purchased based only on the economic data provided? Give a short analysis report.
2) How would the life cycle costs compare if the cost of gasoline averages 3.50 (inflation has been considered) a gallon and the automobile is driven 16,000 km/year?