Likelihood Maximization of Lifetime Distributions With Bathtub-Shaped Failure Rate

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2023-06

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Department of Chemical and Metallurgical Engineering

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en

Pages

15

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IEEE Transactions on Reliability, Volume 72, issue 2, pp. 759-773

Abstract

Equipment lifetime distributions with bathtub-shaped failure rate can be fitted to data by the maximum likelihood criterion. In the literature, a commonly used method is to find a point in the parameter space where the partial derivatives of the log-likelihood function are zero. As the log-likelihood function is typically nonconvex, this approach may yield a suboptimal fit. In this work, we maximize the log-likelihood function, using a multistart of 100 optimization procedures, by three nonlinear optimization algorithms: 1) Nelder–Mead with adaptive parameters; 2) sequential least squares quadratic programming (SLSQP); 3) limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm with box constraints (L-BFGS-B). We perform a systematic study of refitting ten key lifetime distributions with bathtub-shaped failure rate from the literature to two widely studied datasets. The multistart nonlinear optimization yields better fits than those reported in the literature in 14 out of 19 distribution-dataset pairs, for which reference parameters are available. Based on the results, if gradient information of the log-likelihood function is available, our recommended optimization algorithm for the purpose is SLSQP.

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Keywords

Additives, Data analysis, Data models, equipment lifetime modeling, Integrated circuits, maximum likelihood estimation, optimization, reliability, Symbols, Systematics, Terminology, Weibull distribution

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DOI

10.1109/TR.2022.3190542

Citation

Ikonen, T J, Corona, F & Harjunkoski, I 2023, 'Likelihood Maximization of Lifetime Distributions With Bathtub-Shaped Failure Rate', IEEE Transactions on Reliability, vol. 72, no. 2, pp. 759-773. https://doi.org/10.1109/TR.2022.3190542

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https://urn.fi/URN:NBN:fi:aalto-202308014557

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[article-cris] Kemian tekniikan korkeakoulu / CHEM