A novel lifetime analysis of repairable systems via Daubechies wavelets

Jingchi Wu (), Tadashi Dohi () and Hiroyuki Okamura ()
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Jingchi Wu: Hiroshima University
Tadashi Dohi: Hiroshima University
Hiroyuki Okamura: Hiroshima University

Annals of Operations Research, 2025, vol. 349, issue 1, No 14, 287-314

Abstract: Abstract It is well-known that minimally repaired systems are characterized by non-homogeneous Poisson processes. When the underlying lifetime distribution function or its associated intensity function is completely known, the statistical inference of the cumulative number of failures/repairs is made through some standard techniques. On the other hand, when the parametric form of the lifetime distribution or the intensity function is not known, non-parametric inference techniques such as non-parametric maximum likelihood estimate (NPMLE) and kernel-based estimates are employed. Since these techniques are based on the underlying lifetime data, the resulting estimates of the cumulative number of failures/repairs with respect to the system operation time are discontinuous and troublesome in assessing the reliability measures such as reliability function and mean time to failure, etc. In this paper, we propose a novel lifetime analysis of the repairable systems via Daubechies wavelets. More specifically, we generalize the seminal Daubechies wavelet estimate by Kuhl and Bhairgond (Winter Simul Conf Proc 1:562–571, 2000) by combining the ideas on NPMLE and KMBs. In both simulation experiments and real data analyses, we investigate applicability of our Daubechies wavelet-based approaches and compare them with the conventional non-parametric methods.

Keywords: Repairable systems; Non-homogeneous poisson processes; Non-parametric inference; Daubechies wavelets; Simulation experiments; Real data analyses (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10479-024-06074-6

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