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Unformatted text preview: ESI 6321 APPLIED PROBABILITY METHODS FOR ENGINEERS Homework 7 Spring 2008 Reading material: Sections 17.1 and 17.2 from Hayter (Coursepack II), as well as the course slides. Note: the material in the slides goes beyond the material in Hayter! Problems: 17.1.4, 17.1.5, 17.2.2, as well as the following 3 problems: Problem 1: Consider the system of problem 17.1.2. However, now suppose that the components have the following constant failure rates (where i denotes the failure rate of component i): 1 = 0.01, 2 = 0.10, 3 = 0.01, 4 = 0.05, and 5 = 0.08. Moreover, suppose that components 4 and 5 are configured as standby parallel, with component 4 the primary unit. Provide an expression for the overall system reliability as a function of time. Problem 2: Consider Problem 17.2.7. Note: the parameterization of the Weibull distribution in the coursepack is different from that in the slides: parameters (a,) in the coursepack correspond to m=a and =1/ in the slides. Answer parts (a) and (b). Hint: use the WEIBULL function in Excel and use the Excel Help function to determine the appropriate parameters! Plot the cdf of the time to failure. Plot the reliability and the failure (=hazard) rate as a function of time. Problem 3: 25 observed times (in hours) that a conveyor belt operates before a mechanical malfunction occurs are given in the Excel file ds17.4.1-conveyor-beltmalfunctions.xls. (a) Assume that the failure times can be modeled by an exponential distribution. Then provide an estimate of the failure rate. (b) Assume that the failure times can be modeled by a Weibull distribution. Then provide estimate of the population parameters m and . (Please use the 3rd c.d.f.-estimate provided on slide 66). Due date: March 30, 2008 at 11:59pm Prof. Edwin Romeijn Homework 7 ESI 6321 Applied Probability Methods For Engineers Spring 2008 Submission guidelines: For all questions, please show the full derivation of your answer. All homework solutions are due on the date specified and late assignment submission will not be accepted. It is preferred and highly recommended that homework solutions are submitted electronically through WebCT since that will provide you with a confirmation and a record of when your solutions were submitted. However, faxed submissions will also be accepted at (352) 392-6291. You are allowed to collaborate on homework problems. However, everyone should submit their own unique homework solutions (including, e.g., any Excel spreadsheets when these are required as part of the solutions). Prof. Edwin Romeijn Homework 7 ESI 6321 Applied Probability Methods For Engineers Spring 2008 ...
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- Spring '07