Chapter 8 269 The equations below show how the Weibull equation can be converted into a linear form, such that a plot of the double logarithm of the reciprocal of survival probability function versus the logarithm of the number of cycles-to-fail yields the shape parameter from the slope, and the characteristic lifetime from the intercept. where 1-F(x) is the probability of surviving x cycles. At this point, there is the need to briefly describe how the collected data is used to produce the cumulative distribution function (F(x)). The most common approach involves the median rank method.6 This involves first ordering cycles-to-fail results for all fibers from lowest to highest. At this point, fibers that survived the fatiguing process, that is, those that did not break upon application of the threshold number of cycles, can also be added to the list. The median rank equation is: Where i is the sample number and n is the total number of samples. While this whole process may appear mathematically intensive, it is especially convenient to set up Excel spreadsheets to perform all data manipulation, plotting and calculations. Reference 7 provides step-by-step instructions for doing this, as well as generating the Survival Probability plots that will be discussed shortly. Table 4 shows an example of how single-fiber fatigue results are treated by this process.