Reliability theory
- Inlämningsdatum 16 nov 2016 av 23.59
- Poäng 2
- Lämnar in en filuppladdning
- Filtyper pdf
- Tillgänglig 4 nov 2016 kl 8:00–16 nov 2016 kl 23.59
We will soon start correcting the first home assignments.
The grading will be based on the rubrik below, taking inte account the peer reviews of your reports and the reports themselves.
For full points, 2p, you need 19-24 p, and for one point you need 13-19 p. These points wil be entered in the system during next week, but note that they are not final. We will also check that each group has sent in two good quality peer-reviews. Otherwise one point will be subtracted from the total. If by some technical circumstance, your group has not received two reviews to do, let me know.
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This first assignment will apply Markov chain/process modelling to test reliability of systems under different assumptions and system configurations.
The assignment is described in the following document: home2016nr1.pdf Download home2016nr1.pdf
This home assignment is voluntary. A maximum of two points can be achieved by submitting a written report and performing a peer review. The bonus points are added to the total of your final exam result and are valid for three years.
I want you to work in groups of three persons. If you want help to find team mates I recommend that you make a post, or respond to one, in the discussion area People unassigned to groups.
Matris
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Question 1: 1 point for each correct result: MTTF = 3 month, MTTR = 1/2 month and MTBF = MTTF + MTTR = 3.5 month, Availability = MTTF/MTBF = 6/7
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Question 2: Define the states of the Markov process, two states are sufficient, one for the component working and one for component not working. (1p) The intensity matrix Q = [-1/3 1/3; 2 -2]. Note that the entries may be on a different rows and columns if you switch the states. (1p) . Simulating the process by generating exponentially distributed staytimes in each state (1p). Determining the ergodic estimates of MTTF,MTTR, MTBF and availability (1p). Determining the necessary siimulation time to reach 1% precision should be in the range 500-500000 (1p)
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Question 3: Determining the one-step transition matrix P=[299/300 1/300; 6/300 294/300], Note that the entries may be on a different rows and columns if you switch the states. (1p) . Simulating the process by generating uniform random variables to determine jumps between states (1p). Determining the ergodic estimates of MTTF,MTTR, MTBF and availability (1p). Determining the necessary number of simulation steps to reach 1% precision should be in the range 500-500000 (1p)
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Question 4: Define the states of the Markov process, four states are sufficient, state i corresponding to i components not working. (1p) The intensity matrix Q = [-1 1 0 0; 2 -8/3 2/3 0; 0 2 -7/3 1/3; 0 0 2 -2 ] if you assume that there is only one repair active at each time and the intensity matrix Q = [-1 1 0 0; 2 -8/3 2/3 0; 0 4 -13/3 1/3; 0 0 6 -6 ] if you assume that there is one repair per component active at each time (1p). Simulating the process by generating exponentially distributed staytimes in each state or by determining a discrete time Markov chain and simulating it (1p). Determining the ergodic estimates of MTTF,MTTR, MTBF and availability (1p). Determining the ergodic estimates of MTTF =~ 1, MTTR =~ 0.7, MTBF =~ 1.7 and availability =~0.58 for one repairman and MTTF =~ 1, MTTR =~ 0.6, MTBF =~ 1.6 and availability =~0.6 for one repaiman for each component (1p).
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Question 5: Define the states of the Markov process, three states are sufficient, state i corresponding to i components not working. (1p) The intensity matrix Q = [-2/3 2/3 0; 2 -7/3 1/3 0; 0 2 -2 ] if you assume that there is only one repair active at each time and the intensity matrix Q = [ -2/3 2/3 0; 2 -7/3 1/3; 0 4 -4 ] if you assume that there is one repair per component active at each time (1p). Simulating the process by generating exponentially distributed staytimes in each state or by determining a discrete time Markov chain and simulating it (1p). Determining the ergodic estimates of MTTF,MTTR, MTBF and availability (1p). Determining the ergodic estimates of MTTF =~ 12.2, MTTR =~ 0.5, MTBF =~ 12.7 and availability =~0.96 for one repairman and MTTF =~ 12, MTTR =~ 0.25, MTBF =~ 12.25 and availability =~0.98 for one repairman for each component (1p).
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