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SMRE Homework 1 Failure Models; Qualitative Analysis 1 A type of safety valve has been shown to exhibit constant failure rate with respect to all failure modes. A field-study has produced a value of MTTF for the valve of 2345 days. Assume that the valve operates in a continuous manner and that the failure modes are independent of each other. a.- Determine the valve failure rate. b.- Determine the probability that the valve will survive for 100 days without failing. 2 Use the relationships summarized on Table 2.1 (p. 20) in your text and the Maple software, to derive all the entries contained in Table 2.2 (p. 64). 3 Failure times of 22 Ball Bearings (in cycles) have been collected. The values are as follows: 1 Time of Failure 17880000 28920000 33000000 41520000 42120000 45600000 48480000 51840000 51960000 54120000 55560000 67800000 68640000 68880000 84120000 93120000 98640000 105120000 105840000 127920000 128040000 173400000 Bearing 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Use the MINITAB software to answer the following questions: a) Compute descriptive statistics for the data, b) Construct the histogram, c) Find good-fitting distributions to the data, d) Select the best fitting distribution(s) and determine the distribution parameters and confidence intervals. e) Use the parameter values of the best fitting distribution and the Maple software to determine analytical expressions for the failure probability distribution function, the survival probability function, the failure rate (hazard) function, the MTTF and the MRL for the bearings. 2 4 United Airlines Flight 232 crashed on July, 19th, 1989 in Sioux City IA after experiencing an unprecedent catastrophic failure. Research the accident to answer the following: a.- Construct an Event Tree with the initiating event being the specific failure that ultimately led to the crash (e.g. Fig. 3.23, p. 110, text). b.- Construct a Fault Tree that could have helped predict the accident (e.g. Fig. 3.19, p. 102, text). c.- Construct a FMECA worksheet (e.g. Fig. 3.13, p. 89, text) that could have helped prevent the accident. 3