High Cycle Fatigue: A Mechanics of Materials Perspective part 12. 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. | 96 Introduction and Background is discussed based on experimental observations of the type that are classified as all-or-nothing or quantal. While it is generally desirable to have quantitative measurements many cases can be expressed only as occurring or not-occurring. The obvious example with insects is death. The analogous situation with FLSs especially those obtained from staircase type testing is failure or survival run-outs after a certain number of cycles. Not only is it important to analyze the data but the planning of the experiments is equally important. The type of fatigue testing carried out for example the number of tests at each of several stress levels can influence the results. In the application of statistical methods to biological data Fisher 37 suggested that the statistician should be consulted during the planning of an experiment and not only when statistical analysis of the results is required. His advice on experimental design may greatly increase the value of the results eventually obtained whether they be biological experiments or FLS experiments. For the staircase method we can determine the average fatigue limit sc and its standard deviation asc from the equations of Dixon and Mood 35 which are also presented in an ASTM publication 38 . The method is based on a maximum-likelihood estimation MLE and provides approximate formulas to calculate the mean and standard deviation assuming that the FLS follows a Gaussian normal distribution. The equations for the mean and standard deviation are Msc Si 0 s max E i i --- imax .Em i 0 sc 1-62 s provided i 2 max max max E m i2mi - I E imi i 0 i 0 i 0 imax imax i2 max s- imax imax EmJ im - i 0 i 0 imax S im imax - When the quantity above is the mathematics becomes very complicated and a rough approximation can be made using asc 35 . In the above equations s is the step size the parameter i is an integer that denotes the stress level and imax is the The subscript sc .
