Median Rank for Multiple Censored Data

 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.

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:

$MR_{i}\approx \frac{MON_{i}-0.3}{N+0.4}$

where $MR_{i}\,\!$ is the median rank at the $ith\,\!$ failure time; $MON_{i}\,\!$ is the mean order number; $N\,\!$ 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:

$MR_{i}= \frac{1}{1+\frac{N-MON_{i}+1}{MON_{i}}F_{0.5,m,n}}$

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