Median Rank for Multiple Censored Data

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Median Rank for Multiple Censored Data

This example validates the median rank calculation for multiple censored data in Weibull++ standard folios.


Reference Case

Table 3.1 on page 78 in the book Reliability & Life Testing Handbook Vol 2 by Dr. Kececioglu, Prentice-Hall, 1994.


Data

Num. In Stage State F or S Time to Failure
1 F 5100
1 S 9500
1 F 15000
1 S 22000
1 F 40000


Result

Num. In Stage State F or S Time to Failure Median Rank (%)
1 F 5100 12.94
1 S 9500
1 F 15000 36.1
1 S 22000
1 F 40000 70.84


Results in Weibull++

The coordinates of each point in the following plot shows the failure time and the corresponding median rank.


Median Ranks Multiple Censored Data.png


The differences between the results in Weibull++ and the book are due to the method of calculating the median ranks (MR). In the book, the following approximation method is used:

[math]MR_{i}\approx \frac{MON_{i}-0.3}{N+0.4}[/math]


where [math]MR_{i}\,\![/math] is the median rank at the [math]ith\,\![/math] failure time; [math]MON_{i}\,\![/math] is the mean order number; [math]N\,\![/math] is the total samples. For the step by step calculation of mean order number (MON), please refer to the book “Reliability & Life Testing Handbook Vol 2” by Dr. Kececioglu, Prentice-Hall, 1994.


In Weibull++, the following exact method is used:

[math]MR_{i}= \frac{1}{1+\frac{N-MON_{i}+1}{MON_{i}}F_{0.5,m,n}}[/math]


where [math]m=2(N-MON_{i}+1), n=2\times MON_{i}\cdot F_{0.5,m,n}\,\![/math] is the 50 percentile of a F distribution with degree of freedom of m and n.