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Median Rank for Multiple Censored Data
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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
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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:
- [math]\displaystyle{ MR_{i}\approx \frac{MON_{i}-0.3}{N+0.4} }[/math]
where [math]\displaystyle{ MR_{i}\,\! }[/math] is the median rank at the [math]\displaystyle{ ith\,\! }[/math] failure time; [math]\displaystyle{ MON_{i}\,\! }[/math] is the mean order number; [math]\displaystyle{ 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]\displaystyle{ MR_{i}= \frac{1}{1+\frac{N-MON_{i}+1}{MON_{i}}F_{0.5,m,n}} }[/math]
where [math]\displaystyle{ 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.
