Weibull statistics standard deviation

First, simple statistical analysis (arithmetic average and standard deviation) was applied to three fibers, namely curaua, ramie, and sisal fibers. In other studies, Weibull analysis program was used to analyze the obtained fracture strength values of different diameters. In both the cases, the results indicated that two types of variation of strength of fibers could be possible. Thinner fibers showed increased... 

Previously, the data presented in Fig. 7 were analyzed in terms of averages and standard deviations to determine lifetime. However, averages and standard deviations do not capture the entire picture when it involves hfetime, so the data need to be reanalyzed using SPLIDA. The results of the SPLIDA analysis are shown in Fig. 9. Not only can SPLIDA provide a hfetime probability distribution for the data in Fig. 7, it can also predict the lifetime of the samples at end-use conditions (70 °C cell temperature and 100% inlet gas relative humidity). When SPLIDA was used for statistical analysis, the following relationships were selected Weibull distribution for lifetime data, Arrhenius relationship for temperature, class relationship for load... 

Figure 5 shows the maximum indentation force and standard deviation as a function of the nnmber of measured silica model aggregates. A constant standard deviation is determined by the inherent distribution of the micromechanical properties of the aggregated system [42], In contrast to the distribution of the micromechanical properties of individual particles or single crystals, which can be described by Weibull statistics [14, 50], the distributions of aggregates can be described by a log-normal distribution [42], Consequently, the specification of the log-normal fit can be used for the characterization of the measured system. 

With such a statistical study, it was found that the Weibull distribution could fit the earthquake data in Taiwan reasonably well. For instance, given a magnitude threshold of 3.0, mean magnitude of 3.442, and standard deviation of 0.398, the corresponding parameters a and fi of the Weibull distribution are 1.11 and 0.46, respectively. With the parameters calibrated with the seismicity, the observation and the model are in a satisfactory agreement in earthquake-size distribution. 

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