Median rank equation

The analysis of the frequeney data is shown in Table 4.12. Note the use of the Median Rank equation, eommonly used for both Weibull distributions. Linear reetifieation equations provided in Appendix X for the 2-parameter Weibull model are used to... 

The pore sizes so measured are arranged in an ascending order. Median ranks are calculated from the following equation ... 

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. 

The rank is indicating the failure probability in percent associated to each result, i.e., the frequency. Since the entire population is never tested, we can only estimate the rank of the sample population. In this respect, several options are available. One of the most common estimate is the median rank, i.e., that rank that is as likely to err on the high side, with respect to the median value, as on the low side. The following equation gives a very good approximation of the estimated median ranks for any sample size n... 

A valid alternative to the median rank is the mean rank, which is given by the equation... 

The slopes of three straight lines are calculated using, for the first slope, the first data point and that immediately following the median, and so on, as shown in Table 21.5. The median of the three slope values is taken as the a term for the linear equation. Then, six values are calculated for the b term where bt — y — ax,. These b( values are then ranked and the median is taken as the b term of the linear equation (Fig. 21.3). 

At first, the slopes of three straight lines are calculated, which pass respectively through the first point and that following immediately the median and so on (Table 22.5). The median of the three calculated slope values is taken as the term a of the linear equation. Then, the six b values are calculated from bj = y, — ax, and also ranked in increasing order. The median will become the term b of the line. 

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