A MODIFIED TUKEY BOX PLOT APPLIED TO THRESHOLD ANALYSIS: UPPER QUARTILE PARAMETERIZATION

摘要

Current thresholds for condition indicators may be estimated by calculating sample means and then adding a determined number of standard deviations. This approach is based off of a normal distribution which in reality very rarely occurs with the condition indicators of interest. Instead the data follows other distributions that tend to be heavily right skewed with long tails. This approach is also highly susceptible to inflation caused by an unpredictable number of faulted points within the data set. Tukey's boxplot method of adding multiples of the interquartile range to the third quartile is far more robust but fails to adequately characterize distributions with very long tails. A parameter can be developed, however, to account for the increased tail length by dividing the range of the distribution between the 75th and 97.5th percentiles by the range of the data between the 25th and 75th percentiles. Adding this parameter to Tukey's boxplot method extends the inner and outer fences proportionally to the tail length with a very low likelihood of any corruption from faulted data that may exist within the data set. This method can provide an analyst a way to quickly calculate initial threshold values for large data sets without any knowledge of the nature of the distribution.