Weibull plots

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. 

Fig. 2 Weibull plot of the filament strength for a test length of 10 cm of a PpPTA yarn yielding a Weibull modulus of 20.6. The average filament strength is 3.2 GPa... 

Weibull plots of various fibre properties, such as the filament count, modulus, elongation at break and the strength, can provide important information on the quality and performance of the manufacturing process. The results can be used to formulate a strategy for the improvement of the yarn properties. 

Other degradation laws can be combined with a Weibull plot, particularly when a lower threshold of, for example, voltage is anticipated. An example of its application to electrical cable insulation lifetime is given in [9]. As well as service failures Weibull plots have proved useful in assessing the failure of fibres and fibre bundles. 

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.

Fig. 6.17 Weibull plot of breakdown data for low-density and high-density...

Figure 5.13. Weibull plot for flexural strength of 3D C/SiC composites [24]...

Figure 4.1 shows a cumulative Weibull plot as being representative of the failure probability of typical femoral heads made from high-purity alumina. The very low data scatter and the high average flexural strength around 600 MPa (d50) attest to both the strength and the extraordinary reliability. 

Figure 4.1 Typical strength distribution of femoral heads made from alumina in a Weibull plot.

Figure 10. Weibull plots of tensile-strength distribution for kilometer lengths of fibers tested in 20-m gauge lengths. In each case one variable was intentionally altered and all others were optimized. (Reproduced with permission from Ref. 6. Copyright 1980 IEEE.)...

Figure 209. Weibull plots for the inactivation of two different lipases in the solid state, a Fraction inactivated. , Pancreatic lipase O, Rhizopus lipase. (Reproduced from Ref. 881 with permission.)...

The use of Weibull plots for design purposes has to be handled with extreme care. As with all extrapolations, a small uncertainty in the slope can result in large uncertainties in the survival probabilities, and hence to increase the confidence level, the data sample has to be sufficiently large N > 100). Furthermore, in the Weibull model, it is implicitly assumed that the material is homogeneous, with a single flaw population that does not change with time. It further assumes that only one failure mechanism is operative and that the defects are randomly distributed and are small relative to the specimen or component size. Needless to say, whenever any of these assumptions is invalid, Eq. (11.23) has to be modified. For instance, bimodal distributions that lead to strong deviations from a linear Weibull plot are not uncommon. 

Figure 11.21 Weibull plot of data shown in Table 11.2. Slope of the line is the Weibull modulus m. The actual survival probability is shown on the right-hand side. At low stresses, S is large (left-hand corner of figure). ...

This is an important result in that it allows for the straightforward construction of an SPT diagram from a Weibull plot (Fig. 11.21). The procedure is as follows (see Worked Example 12.3) ... 

Figure 12.13 Effect of SCG rate exponent n on Weibull plots. The Weibull plots are shifted by 1/n for every decade of life required of the part. Data are the same as plotted in Fig. 11.21, but are converted to a log plot.

Figure 12.17 Effect of strain rate on Weibull plots.

Figure 1. Weibull plots of axial MOR data at room temperature for EX-22 substrates with 350/5.7 O cell and 340/6.3 A cell structure...

Fig. 1 a) Strength data of a silicon nitride ceramic tested in four point bending (4PB) in a Weibull plot and b) the relative frequency distribution of flaw sizes. The data points were determined by fracture experiments. 

Figure 4. Weibull Plots of Yttria and Scandia Zirconias...

Figure 6. Approximate Weibull Plots for various Scandia Zirconias...

A more effective representation of the strength data is possible by using Weibull plots where the measured strength data are reported as a function of failure probability. Here, failure probability was calculated as ... 

Figure 15. Weibull plot of biaxial flexural strength data, Op tor LIST dental porcelain with and without ion exchange. Dotted lines are 95% confidence interval m is Weibull modulus, Uq is characteristic strength, and 05% is fracture stress at 5% fracture probability. Data from [71]...

Shown in Figure 13a and 13b are Weibull plots of typical strength data obtained from the neomesophase based carbon fibers heat-treated at temperatures of 1500°C and 2000 c, respectively. Both sets of fibers have strengths apparently governed by a single flaw population, though not necessarily the same type flaw. Typical flaws observed in these fibers included some surface damage, as well as very small internal pinholes. 

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