A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls.

The percentile value is used to look at the variability in results and can be used to assess the risk of a particular scenario.

For example we have 10 simulation runs where production based availability has been estimated to be in a ranked order:
  • 10 → Run 3: 0.99
  • 9 → Run 8: 0.98
  • 8 → Run 1: 0.98
  • 7 → Run 2: 0.96
  • 6 → Run 9: 0.93
  • 5 → Run 6: 0.93
  • 4 → Run 5: 0.91
  • 3 → Run 10: 0.90
  • 2 → Run 4: 0.89
  • 1 → Run 7: 0.88
Finding the P-value is done using the nearest-rank method. After ranking the results from smallest to larges the ordinal rank of the percentile you want to find.
P10 ordinal rank = (10/100) x 10 = 1
P10 value = 0.88
P90 ordinal rank = (90/100) x 10 = 9
P90 value = 0.98
P45 ordinal rank = (45/100) x 10 = 4.5 → rounded to nearest → 5
P45 value = 0.93