Weibull probability plots

Fig. 5. The fast-fracture tensile strengths (inserted table) and Weibull probability plots of AI,0 /Y Als0i2 eutectic libers.

The resulting plots of the cumulative probability F t versus were rearranged according to Eq. 4.16, which gave the Weibull probability plots. 

Weibull probability plots under various thin layer thicknesses. 

Figure 8.27. Weibull probability plot with selected set of parameters. For zero location parameter, a straight line results.

Fig. 18.4. Survival probability plotted on "Weibull probability" axes for samples of volume Vq. This is just Fig. 1 8.3(b) plotted with axes that straighten out the lines of constant m.

The procedure is to fit the population frequency curve as a straight line using the sample moments and parameters of the proposed probability function. The data are then plotted by ordering the data from the largest event to the smallest and using the rank (i) of the event to obtain a probability plotting position. Two of the more common formulas are Weibull... 

In the first instance, when the results were analyzed by simple mean and standard deviation analysis, Amico et al. [16-18] got large relative standard deviatiOTi, indicating limitatimi of this method for the proper characterizatiOTi of the diameter. Then, they used Weibull probability density and cumulative distribution functions [20,56,58] to estimate two parameters, the characteristic life and a dimensionless positive pure number, which were supposed to determine the shape and scale of the distribution curve. For this, they adopted two methods, the maximum likelihood technique, which requires the solution of two nonlinear equations, and the analytical method using the probability plot as mentioned earlier for coir fibers. 

Using the Weibull distribution, plots are made from measured strength data. These data are arranged in ascending order and assigned numbers beginning with 1 and ending with n. The survival probability (or expected life-time) is usually... 

The parameters of the Weibull distribution are calculated using probability plotting (Weibull, 1961). The life cycles of leaf spring are arranged in increasing order and the median rank is calculated using the Equation (3) and are shown in Table 7. 

Fig. 4.12 Weibull probability density functions p(x) plotted for different m values...

Fig. 4.25 Weibull Irdn probability plot of the four amplitude fatigue life data...

As an example of the type of functions possible with just one of the functions, Figure 8.12 shows various Weibull probability density plots for a range of Weibull shape parameters. The ability of this rather simple function to take on many different functional forms is one of the reasons it is frequently used for modeling of reliability data. The shape can range from an exponential like decrease with x to approximate a Gaussian for a shape parameter around 4 and an even more sharply... 

Effect of Weibull Shape Parameter on Probability Plot... 

Suppose, for example, that an estimate based on a Wei-bull fit to the fan data is desired of the fifth percentile of the distribution of time to fan failure. Enter the Weibull plot. Figure 62.6, on the probability scale at the chosen percentage point, 5 per cent. Go vertically down to the fitted line and then horizontally to the time scale where the estimate of the percentile is read and is 14,000 hours. 

An estimate of the probability of failure before some chosen specific time is obtained by the following. Suppose that an estimate is desired of the probability of fan failure before 100,000 hours, based on a Weibull fit to the fan data. Enter the Weibull plot on the vertical time scale at the chosen time, 100,000 hours. Go horizontally to the fitted line and then up to the probability scale where the estimate of the probability of failure is read and is 38 per cent. In other words, an estimated 38 per cent of the fans will fail before they run for 100,000 hours. 

These examples illustrate the application of Weibull plots to service failure data in order to predict the probability of failure before the end of the service life, coupled with a power law to relate time to failure to the applied electric stress (voltage). 

Fig. 6.10 Weibull plot of the cumulative probability of breakdown for a set of polyethylene film samples as a function of time under an applied field of lOOMVnT1 at room temperature.

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