## Abstract

Weighted Linear Regression (WLR) can be used to estimate Weibull

parameters. With WLR, failure data with less variance weigh heavier. These

weights depend on the total number of test objects, which is called the sample

size n, and on the index of the ranked failure data i. The calculation of weights

can be very challenging, particularly for larger sample sizes n and for non-

integer data ranking i, which usually occurs with random censoring. There is a

demand for a light-weight computing method that is also able to deal with non-

integer ranking indices. The present paper discusses an algorithm that is both

suitable for light-weight computing as well as for non-integer ranking indices.

The development of the algorithm is based on asymptotic 3-parameter power

functions that have been successfully employed to describe the estimated

Weibull shape parameter bias and standard deviation that both monotonically

approach zero with increasing sample size n. The weight distributions for given

sample size are not monotonic functions, but there are various asymptotic

aspects that provide leads for a combination of asymptotic 3-parameter power

functions. The developed algorithm incorporates 5 power functions. The per-

formance is checked for sample sizes between 1 and 2000 for the maximum

deviation. Furthermore the weight distribution is checked for very high simi-

larity with the theoretical distribution.

parameters. With WLR, failure data with less variance weigh heavier. These

weights depend on the total number of test objects, which is called the sample

size n, and on the index of the ranked failure data i. The calculation of weights

can be very challenging, particularly for larger sample sizes n and for non-

integer data ranking i, which usually occurs with random censoring. There is a

demand for a light-weight computing method that is also able to deal with non-

integer ranking indices. The present paper discusses an algorithm that is both

suitable for light-weight computing as well as for non-integer ranking indices.

The development of the algorithm is based on asymptotic 3-parameter power

functions that have been successfully employed to describe the estimated

Weibull shape parameter bias and standard deviation that both monotonically

approach zero with increasing sample size n. The weight distributions for given

sample size are not monotonic functions, but there are various asymptotic

aspects that provide leads for a combination of asymptotic 3-parameter power

functions. The developed algorithm incorporates 5 power functions. The per-

formance is checked for sample sizes between 1 and 2000 for the maximum

deviation. Furthermore the weight distribution is checked for very high simi-

larity with the theoretical distribution.

Original language | English |
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Title of host publication | Advanced Computing |

Subtitle of host publication | 11th International Conference, IACC 2021 |

Publisher | Springer Nature |

Pages | 529-541 |

Number of pages | 13 |

ISBN (Electronic) | 978-3-030-95502-1 |

ISBN (Print) | 978-3-030-95501-4 |

DOIs | |

Publication status | Published - 2022 |

Externally published | Yes |

Event | 11th International Advanced Computing Conference - Msida, Malta Duration: 18 Dec 2021 → 19 Dec 2021 |

### Conference

Conference | 11th International Advanced Computing Conference |
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Abbreviated title | IACC 2021 |

Country/Territory | Malta |

City | Msida |

Period | 18/12/21 → 19/12/21 |