CORK INSTITUTE OF TECHNOLOGY INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ Semester 2 Examinations 2010 School: Mechanical & Process Engineering Programme Title: Bachelor of Science (Honours) in Advanced Manufacturing Technology & Bachelor of Science (Honours) in Process Plant Technology. Programme Code: CR_EAMTE_8, CR_EPPTE_8 Module Title: Maintenance & Reliability Module Code: MANU8003 External Examiner(s): Internal Examiner(s): Mr. Neil Kingston, Mr. Joe Phelan Mr. Dan O Brien Instructions: Answer any 3 questions Duration: 2 hours Sitting: Summer 2010 Requirements for this examination: Probability Plotting Paper, Hazard Plotting Paper, Log-Log Paper, Log Tables & Statistical Tables. Note to Candidates: Please check the Programme Title and the Module Title to ensure that you are attempting the correct examination. If in doubt please contact an Invigilator. Page 1 of 11
Q. 1 Reliability Modelling : (a) Differentiate between MTBF and MTTF. (3 marks) (b) The exponential distribution is used to model items with a constant failure rate, Its probability density function, pdf, is given by: x 1 f ( x) = e θ λx = λe, x 0 θ Derive the reliability function and the hazard function from first principles. (10 marks) (c) The equipment in a packaging plant has a failure rate of 0.001/hr. What is the probability of operating for a period of 500hr without failure? (8 marks) (d) Briefly discuss the use of confidence intervals in reliability. (5 marks) (e) In reliability testing to estimate MTBF two situation exist: 1. Type 1 censoring: for which the lower one sided confidence limit is: 2T 2 χ ( α,2r+2) θ 2. Type 2 censoring: for which the lower one sided confidence limit is 2T 2 χ ( α,2r ) θ A unit is tested for a total of 3000hours. When testing was stopped after 3000hr, it was noted that three failures had occurred during testing. Calculate the 90% confidence on the one-sided lower limit for the MTBF (θ) (7 marks) Page 2 of 11
Q. 2 Probability Plotting (a) The cumulative hazard function may be plotted using hazard papers. Discuss the advantages of using this method over Weibull papers. (5 marks) (b) The data below relate to failures of terminations in a sample of 20 semiconductor devices. Each failure results from breaking of either the wire (W) or the bond (B) whichever is the weaker. The specification requirement is that fewer than 1 per cent of terminations shall have strengths of less than 500g. Table 1. Failures of terminations of semiconductor devices. Failure B or W Failure load B or W load (mg) (mg) 550 B 1250 B 750 W 1350 W 950 B 1450 B 950 W 1450 B 1150 W 1450 W 1150 B 1550 B 1150 B 1550 W 1150 W 1550 W 1150 W 1850 W 1250 B 2050 B Estimate Weibull parameters for (i) termination strength, (ii) wire strength, (iii) bond strength. Comment on the results. (12 marks) (c) Briefly describe the Duane model of Reliability Growth (6 marks) (d) A prototype of a repairable system was subjected to a test programme where engineering action is supposedly taken to eliminate causes of failure as they occur. The first 500hrs of running gave failures at 12, 36, 80, 120, 200, 360, 400, 440 and 480hrs. Produce a Duane plot (using the attached log-log paper) to discover whether reliability growth is occurring. (10 marks) Page 3 of 11
Q. 3 Reliability in Design/Human Reliability (a) What is the purpose of an FMEA and explain how it is performed, detailing what information is analysed and the significance of RPN? (8 marks) (b) A pressure vessel is shown in Figure 1 beneath. The safety system consists of 4 valves, which are connected to the tank. The valves will open if the pressure in the tank exceeds a certain level, for example P 0. The contents in the tank will be release to the environment if both valves A 1 and A 2 on line 1 or both valves A 3 and A 4 on line 2 are open. A 2 A 4 A 1 A 3 Figure 1. Arrangement of pressure tank and valves (i) Develop a Fault tree for system failure of the above tank.( i.e. the valves do not open when the pressure in the tank exceeds P 0 state any assumptions) (10 marks) (c) Describe the Robust Design Approach. (8 marks) (d) An operator works on a production transfer line which operates between two tanks. His role is to ensure the correct product is selected for transfer from one tanker to the other; this can be done by operation of the relevant valves which are located remotely. The essential valves must be opened to allow the task to be carried out. The operator possesses average experience in fulfilling this role. The individual is situated in a control room which has a relatively noisy environment and poor lighting. There is a time window of 5 minutes to carry out the required task. Determine the Human Error Probability using the TESEO method. TESEO values are presented in Table 3. (7 marks) Page 4 of 11
Q. 4 Maintenance Management / Inventory Managament (a) Differentiate between TPM and RCM. (6 marks) (b) Discuss the use of Maintenance Time Distributions as a means of predicting time to repair. (8 marks) (c) Spare parts management is divided into slow moving spares and fast moving spares. Describe both policies. (5 marks) (d) In one year, 200 components of similar type were issued out from a store. If the demand for this part was relatively constant: (i) specify an appropriate inventory policy (ii) quantify the policy parameters given the following information: lead time L = 3 weeks order cost C O = 0.80 spares holding cost C H = 0.20/yr. (7 marks) (e) The failure distribution of a component is described by a 2-parameter Weibull distribution, with β = 2.5 and θ = 1000 hours. The cost for a corrective replacement is 6. The cost for a preventive replacement is 1. Estimate the optimum replacement age in order to minimize these costs given T = mθ + δ (7 marks) Page 5 of 11
Figure 2 Hazard Plotting Paper Page 6 of 11
Table 2 Table of Median Ranks Page 7 of 11
Figure 3 Weibull Distribution Function Plotting Paper Page 8 of 11
Figure 4 Log Log Paper Page 9 of 11
Table 3 TESEO Error probabilities TESEO error probabilities Type of activity factor K 1 Simple routine 0.001 Requiring attention, but routine 0.01 Not routine 0.1 Temporary stress factor, for routine activities K 2 Time available, in seconds 2 10 10 1 15 0.5 Temporary stress factor, for nonroutine activities K 2 Time available, in seconds 3 10 30 1 45 0.3 60 0.1 Operator qualities K 3 Carefully selected, highly trained 0.5 Average knowledge and training 1 Little knowledge and training 3 Activity anxiety factor K 4 Situation of grave emergency 3 Situation of potential emergency 2 Normal situation 1 Activity ergonomic factor K 5 Excellent working conditions and a well designed interface 0.7 Good Working conditions and a good interface design 1 Tolerable working conditions and a tolerable interface 3 design Tolerable working conditions and a poor interface design 7 Poor working conditions and a poor interface design 10 Page 10 of 11
Table 4 Optimum Parts Replacement Values for m C f /C p β 1.5 2 2.5 3 4 5 7 10 2.0 2.229 1.091 0.893 0.810 0.766 0.761 0.775 0.803 2.2 1.830 0.981 0.816 0.760 0.731 0.733 0.755 0.788 2.4 1.579 0.899 0.764 0.720 0.702 0.711 0.738 0.777 2.6 1.401 0.834 0.722 0.688 0.679 0.692 0.725 0.766 2.8 1.265 0.782 0.687 0.660 0.659 0.675 0.713 0.758 3.0 1.158 0.738 0.657 0.637 0.642 0.661 0.702 0.749 3.3 1.033 0.684 0.620 0.607 0.619 0.642 0.687 0.739 3.6 0.937 0.641 0.589 0.582 0.600 0.627 0.676 0.730 4.0 0.839 0.594 0.555 0.554 0.579 0.609 0.662 0.719 4.5 0.746 0.547 0.521 0.526 0.557 0.591 0.648 0.708 5 0.676 0.511 0.493 0.503 0.538 0.575 0.635 0.699 6 0.574 0.455 0.450 0.466 0.509 0.550 0.615 0.683 7 0.503 0.414 0.418 0.438 0.486 0.530 0.600 0.671 8 0.451 0.382 0.392 0.416 0.468 0.514 0.587 0.661 9 0.411 0.358 0.372 0.398 0.452 0.500 0.575 0.652 10 0.378 0.337 0.355 0.382 0.439 0.488 0.566 0.645 Page 11 of 11