# 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:

- [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*.