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High Cycle Fatigue: A Mechanics of Materials Perspective part 55

High Cycle Fatigue: A Mechanics of Materials Perspective part 55. The nomenclature used in this book may differ somewhat from what is considered standard or common usage. In such instances, this has been noted in a footnote. Additionally, units of measurement are not standard in many cases. While technical publications typically adhere to SI units these days, much of the work published by the engine manufacturers in the United States is presented using English units (pounds, inches, for example), because these are the units used as standard practice in that industry. The graphs and calculations came in those units and no attempt was made to convert. | 526 Appendix D 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 8 specimens 10 specimens 12 specimens 15 specimens 20 specimens 30 specimens 50 specimens 0 0.5 1 1.5 2 Step size a Figure D.6. Proposed correction applied to mean of fatigue strength standard deviations. Figure D.7. Comparison of Dixon-Mood Svensson-Loren correction and proposed correction for N 20 specimens. unbiased. Of course there will be estimates for standard deviation which are both higher and lower than the mean and these estimates will not be corrected to the true value using this correction. Compared to both Dixon-Mood and Svensson-Loren the proposed correction tends to have more scatter though less than Braam-van der Zwaag s correction 8 . Thus in an average sense bias is reduced but for any individual test the results may Appendix D 527 not be improved compared to either Dixon-Mood or Svensson-Loren. The next section will address the means of reducing this scatter. THE USE OF BOOTSTRAPPING Obviously one of the biggest problems inherent in small-sample testing is that statistical scatter can greatly impact results. Use of both the Svensson-Loren correction and the proposed correction increases the already significant scatter inherent in the Dixon-Mood standard deviation estimate. The bootstrapping method was investigated as a possible means to reduce this variance. The bootstrap is a data-based simulation which utilizes multiple random draws from real test data to improve statistical inferences about the underlying population 11 . Essentially the bootstrap method can be summed up by the following conjecture Assuming the test data collected accurately represents the true distribution what other results could have been obtained if the test were repeated The bootstrap algorithm for the staircase application is based on the associated probabilities of failure computed using the number of survivals and failures at each stress level i.e. P-S data . Using these data simulated staircase tests can be .