22 parametric approach (2)

# 22 parametric approach (2) - MFG5350 1 Homework 5 Due Nov...

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Unformatted text preview: MFG5350 1 Homework 5 Due Nov 14 (this Friday) before 5PM MFG5350 2 Make-up Exam Nov 17 (next Monday) 7:30PM - 8:50PM No lecture MFG5350 3 Final Presentation Nov 26 (Wednesday) & Dec 1 (Monday) Final Report Dec 12 (Friday) before 5PM MFG5350 4 Final Exam Dec 8 (Monday) 7:00PM-9:45PM MFG5350 5 Part II: Analysis of Failure Data MFG5350 6 • Parametric Approach • Empirical Method To fit a theoretical distribution (exponential, Weibull, normal, and lognormal distributions) to failure data To derive directly from the failure data, the failure distribution, reliability function or hazard rate function Approaches to Fitting Reliability Distributions to Failure Data MFG5350 7 • Ung rouped versus grouped data Classifications of Failure Data • Complete versus censored data  Ungrouped c omplete data  Grouped c omplete data  Ungrouped censored data  Grouped censored data MFG5350 8 Grouped Censored Data Assume that the failure and censor times have been grouped into k+1 intervals of the form [ t i-1 , t i ), for i = 1, 2, …, k+1 , where t 0 = 0 and t k+1 =  . F i = number of failures in the i th interval C i = number of censored in the i th interval H i = number at risk at time t i-1 : H i = H i-1- F i-1- C i-1 H i ’ = H i – C i / 2 = adjusted number at risk assuming that the censored times occur uniformly over the interval MFG5350 9 Grouped Censored Data 1 ˆ ' 1 ˆ           i i i i R H F R ' i i H F = conditional probability of a failure in the i th interval given survival to time t i-1 Reliability of a unit surviving beyond the i th interval: = conditional probability of surviving the i th interval given survival to time t i-1 ' 1 i i i H F p   MFG5350 10 Grouped Censored Data - Example 200 single-engine aircraft have the following annual failures and removals (censors). Removals resulted from various reasons other than engine failure. Determine the empirical reliability curve.than engine failure....
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22 parametric approach (2) - MFG5350 1 Homework 5 Due Nov...

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