Median Rank for Multiple Censored Data

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This example validates the median rank calculation for multiple censored data.

Data Source

Table 3.1 on page 78 in 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 from 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=2xMON_{i}\cdot F_{0.5,m,n}\,\! }[/math] is the 50 percentile of a F distribution with degree of freedom of m and n.