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System Maintainability Estimation with Multi-Peak Time Distribution based on the Bayesian Melding Method Cover

System Maintainability Estimation with Multi-Peak Time Distribution based on the Bayesian Melding Method

Measurement Science Review
Volume 25 (2025): Issue 3 (June 2025)
By: Mochao Pei,  Jianping Hao and  Cuijuan Gao  
Open Access
|Jun 2025

Figures & Tables

Fig. 1.

The flowchart of the proposed method.
The flowchart of the proposed method.

Fig. 2.

Illustration of the distribution characteristics of datasets 1, 2 and 3; (a)-(c) Histograms and KDE curves for dataset 1, 2 and 3; (d) Probability plot for dataset 1.
Illustration of the distribution characteristics of datasets 1, 2 and 3; (a)-(c) Histograms and KDE curves for dataset 1, 2 and 3; (d) Probability plot for dataset 1.

Fig. 3.

The p.d.f plots for the prior distributions: (a), (c) and (e) Informative priors for maintenance operations 1, 2 and 4, respectively; (b), (d) and (f) Non-informative priors for maintenance operations 1, 2 and 4, respectively.
The p.d.f plots for the prior distributions: (a), (c) and (e) Informative priors for maintenance operations 1, 2 and 4, respectively; (b), (d) and (f) Non-informative priors for maintenance operations 1, 2 and 4, respectively.

Fig. 4.

Maintainability curves for four estimation methods based on the synthetic data.
Maintainability curves for four estimation methods based on the synthetic data.

Fig. 5.

Illustration for the distribution characteristics of practical data; (a)-(c) Histograms and KDE curves for system level data from PT, the three maintenance operation data from PT, and the data from OT; (d) Probability plot for OT data.
Illustration for the distribution characteristics of practical data; (a)-(c) Histograms and KDE curves for system level data from PT, the three maintenance operation data from PT, and the data from OT; (d) Probability plot for OT data.

Fig. 6.

Maintainability curves for four estimation methods based on practical data.
Maintainability curves for four estimation methods based on practical data.

Hyperparameter estimates for the natural prior distributions_

Hyperparameter source μ^ \hat \mu k̂r̂ λ^ \hat \lambda
System3.22113.061.97
Maintenance operation 133.5518.5049.87
Maintenance operation 274.6214.2175.17
Maintenance operation 444.9016.4545.98

Hyperparameter settings for the non-informative priors_

Number of maintenance operation type μ^ \hat \mu k̂r̂ λ^ \hat \lambda
132.320.81.341
272.420.41.250
443.100.20.18

Parameter settings for maintenance operations_

Number of maintenance operation typeMean parameterVariance parameterSample size
133.4915.07132
275.3564.5924
317.888.33187
444.4523.1396
597.05160.3912
625.2910.81172
7129.12942.914
811.218.98154
958.0039.0653
DOI: https://doi.org/10.2478/msr-2025-0014 | Journal eISSN: 1335-8871
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Language: English
Page range: 110 - 121
Submitted on: Nov 6, 2024
|
Accepted on: Apr 30, 2025
|
Published on: Jun 17, 2025
Published by: Slovak Academy of Sciences, Institute of Measurement Science
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open
Keywords:
maintainability estimation,
Bayesian melding method,
adaptive sampling importance resampling,
mixture prior,
testing and evaluation
Related subjects:
Engineering,
Electrical engineering,
Control engineering, metrology and testing

© 2025 Mochao Pei, Jianping Hao, Cuijuan Gao, published by Slovak Academy of Sciences, Institute of Measurement Science
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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