Predictive modeling of reliability engineering data using a new version of the flexible Weibull model

Walid Emam; Ghadah Alomani; Walid Emam; Ghadah Alomani

doi:10.3934/mbe.2023436

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 9948-9964. doi: 10.3934/mbe.2023436

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Predictive modeling of reliability engineering data using a new version of the flexible Weibull model

Walid Emam ^{1
,
,},
Ghadah Alomani ²

1.
Department of Statistics and Operation Research, Faculty of Science, King Saud University, P.O.Box 2455, Riyadh 11451, Saudi Arabia
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Academic Editor: Xiaodi Li

Received: 11 December 2022 Revised: 04 February 2023 Accepted: 20 February 2023 Published: 27 March 2023

The combined-unified hybrid sampling approach was introduced as a general model that combines the unified hybrid censoring sampling approach and the combined hybrid censoring approach into a unified approach. In this paper, we apply this censoring sampling approach to improve the estimation of the parameter via a novel five-parameter expansion distribution, which we call the generalized Weibull-modified Weibull model. The new distribution contains five parameters and is therefore very flexible in terms of accommodating different types of data. The new distribution provides graphs of the probability density function, e.g., symmetric or right skewed. The graph of the risk function can have a shape similar to a monomer of the increasing or decreasing model. Using the Monte Carlo method, the maximum likelihood approach is used in the estimation procedure. The Copula model was used to discuss the two marginal univariate distributions. The asymptotic confidence intervals of the parameters were developed. We present some simulation results to validate the theoretical results. Finally, a data set with failure times for 50 electronic components was analyzed to illustrate the applicability and potential of the proposed model.
- modified Weibull,
- generalized Weibull,
- maximum likelihood estimation,
- statistical modeling
Citation: Walid Emam, Ghadah Alomani. Predictive modeling of reliability engineering data using a new version of the flexible Weibull model[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 9948-9964. doi: 10.3934/mbe.2023436

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Abstract

The combined-unified hybrid sampling approach was introduced as a general model that combines the unified hybrid censoring sampling approach and the combined hybrid censoring approach into a unified approach. In this paper, we apply this censoring sampling approach to improve the estimation of the parameter via a novel five-parameter expansion distribution, which we call the generalized Weibull-modified Weibull model. The new distribution contains five parameters and is therefore very flexible in terms of accommodating different types of data. The new distribution provides graphs of the probability density function, e.g., symmetric or right skewed. The graph of the risk function can have a shape similar to a monomer of the increasing or decreasing model. Using the Monte Carlo method, the maximum likelihood approach is used in the estimation procedure. The Copula model was used to discuss the two marginal univariate distributions. The asymptotic confidence intervals of the parameters were developed. We present some simulation results to validate the theoretical results. Finally, a data set with failure times for 50 electronic components was analyzed to illustrate the applicability and potential of the proposed model.

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