ECE-C690: Dependable Computing Midterm Exam

Transcription

1 ECE-C690: Dependable Computing Midterm Exam February 6, 2009 The midterm is due in class Monday, February 9, Answer all questions. You are not allowed to collaborate with others. 1. (10 points) Assume a triple modular redundant (TMR) system in which faults are NOT independent. On average, a given replica suffers a fault every N cycles. However, if a given replica has a fault, then the other two replicas have a 25% greater chance of being faulty themselves. Assume that the voter is perfect. What is the mean time (in cycles) to a system failure, that is, more than one fault in a given cycle? How does this compare to the case with independent faults? 1

2 2. (10 points) Consider the following system organization. In this scheme, the spare module a can replace a 1 2 V 3 only module 1 and no other. Assume that the voter V and switching circuits are perfect, and answer the following questions: If the reliability of a module is R, what is the reliability of of the overall system? Compare the above answer to the reliability of a conventional hybrid system with a TMR core and a single spare that can replace any failed component. 2

3 3. (30 points) Consider the following flight control system for a helicopter. The system has dual-redundant processors and dual-redundant interface units (called remote terminals). Two buses are used in the system and each bus is also dual redundant. The interesting part of the system is the navigation equipment. The aircraft can be completely navigated using the Inertial Navigation System (INS). If the INS fails, the aircraft can be navigated using the combination of the doppler and the altitude heading and reference system (AHRS). The system contains three AHRS units, of which only one is needed. This is an example of functional redundancy where the data from the AHRS can be used to replace the INS, if the INS fails. Also, both buses are required for the system to function properly regardless of which navigation mode is being employed. Answer the following questions. Draw the reliability block diagram of the system and calculate the reliability of the system for a onehour flight using the MTTF values given below. Assume that the exponential failure law applies and that the fault coverage of the comparators/voters is perfect. Equipment MTTF Processing unit 2000 hours Remote terminal 3500 hours AHRS 1000 hours INS 1000 hours Doppler 500 hours Bus 5000 Repeat the above problem, but this time incorporate a coverage factor for fault detection and reconfiguration of the processing units. Using the same failure rate data, determine the approximate fault coverage value that is required to obtain a reliability (at the end of one hour) of Determine the availability of the system when the coverage is perfect. Assume that the MTTR varies from one hour to two weeks and plot the availability as a function of the MTTR. Compare this availability to that which can be achieved if the INS was not included in the system, and the navigation depended completely on the AHRS and the doppler. 3

4 4. (20 points) Use the D and PODEM algorithms to generate tests for the primary input line x 5 stuck at 1. s/1 4

5 5. (10 points) The following figure shows a checker for a 2-of-4 code checker. The function of this checker is to verify that the input code word has exactly two 1s. So, a valid input codeword to the circuit has exactly two 1s. The valid output codeword is (z 1, z 2 ) = (0, 1) or (z 1, z 2 ) = (1, 0), that is z 1 and z 2 will be complements of each other if a valid input codeword is presented to the circuit. Prove that the above circuit is totally self checking. Explain your answer clearly. 5

6 6. (20 points) A duplex system consists of two active units and a comparator. Assume that each unit has a failure rate of λ and a repair rate of µ. The outputs of the two active units are compared, and when a mismatch is detected, a procedure to locate the faulty unit is performed. The probability that upon a failure, the faulty unit is correctly identified and the fault-free unit continues to run properly is given by the coverage factor c. When a coverage failure occurs, the entire system fails and both units have to be repaired (at a rate µ each). When the repair of one unit is complete, the system becomes operational and the repair of the second unit continues, allowing the system to return to its original state. Show the Markov model for this duplex system. Derive an expression for the steady-state availability of the system assuming that µ = 2λ. 6