Median ranks

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... 

Fig. 2. Rank range runs for 184 watersheds according to species richness of six taxonomic groups as indicators. The dots along the lines show the position of the median rank for the watershed...

Therefore, the focus shifts from indicator to landscape unit (watershed in this case). Statistics are computed on the set of rank values for each landscape unit (watershed). Statistics needed for the present operation are minimum rank, maximum rank, and median rank. These become three derived observational variables for each landscape unit (watershed). Given these preparatory computations, the operations for rank range sequencing are as follows ... 

Managers may also be interested in the comparative differences between perspectives provided by rank summary statistics such as median rank, mean rank, and midrange of ranks. The rank range approach can also provide an interesting alternative for conducting such comparative analysis. The statistics of interest can be treated as second-order multiple indicators for the units instead of using the indicator data from which the statistics were derived. Poset Cl level and rank range analyses are then conducted in a parallel manner to the procedures described above. It would not be informative, however, to consider the end-member elimination effects in this... 

It has been reported that consensus scoring is generally preferable to the use of a single scoring function [92]. Furthermore, the median rank is more suitable than the average rank in consensus scoring because the former is less sensitive to outliers [93]. 

A discussion of the derivation of the failure probability from the numbers of failures (particularly for relatively small numbers) will be found in Refs. 21 and 22. Thi.s probability is not generally equal to the ratio of the number failed to the total number but to the "median rank" probability. A widely accepted close approximation to this is... 

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. 

Table 7. Median rank of composite leaf springs.

Leaf spring no. Life (cycles) Median rank Reliability (%)... 

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... 

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