Modified Chen distribution: Properties, estimation, and applications in reliability analysis
This article proposed a flexible three-parameter distribution known as the modified Chen distribution (MCD). The MCD is capable of modeling failure rates with both monotonic and non-monotonic behaviors, including the bathtub curve commonly used to represent device performance in reliability engineer...
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| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241662 |
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| author | M. G. M. Ghazal |
| author_facet | M. G. M. Ghazal |
| author_sort | M. G. M. Ghazal |
| collection | DOAJ |
| description | This article proposed a flexible three-parameter distribution known as the modified Chen distribution (MCD). The MCD is capable of modeling failure rates with both monotonic and non-monotonic behaviors, including the bathtub curve commonly used to represent device performance in reliability engineering. We examined its statistical properties, such as moments, mean time to failure, mean residual life, Rényi entropy, and order statistics. Model parameters, along with survival and hazard functions, were estimated by utilizing maximum likelihood estimators and two types of bootstrap confidence intervals. Bayesian estimates of the model parameters, along with the survival and hazard functions and their corresponding credible intervals, were derived via the Markov chain Monte Carlo method under balanced squared error loss, balanced linear-exponential loss, and balanced general entropy loss. We also provided a simulated dataset analysis for illustration. Furthermore, the MCD's performance was compared with other popular distributions across two well-known failure time datasets. The findings suggested that the MCD offered the best fit for these datasets, highlighting its potential applicability to real-world problems and its suitability as a model for analyzing and predicting device failure times. |
| format | Article |
| id | doaj-art-2b91ffb62f104dd5a700782778498a63 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-2b91ffb62f104dd5a700782778498a632025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912349063494610.3934/math.20241662Modified Chen distribution: Properties, estimation, and applications in reliability analysisM. G. M. Ghazal0Department of Mathematics, Faculty of Science, Minia University, Minia 61519, EgyptThis article proposed a flexible three-parameter distribution known as the modified Chen distribution (MCD). The MCD is capable of modeling failure rates with both monotonic and non-monotonic behaviors, including the bathtub curve commonly used to represent device performance in reliability engineering. We examined its statistical properties, such as moments, mean time to failure, mean residual life, Rényi entropy, and order statistics. Model parameters, along with survival and hazard functions, were estimated by utilizing maximum likelihood estimators and two types of bootstrap confidence intervals. Bayesian estimates of the model parameters, along with the survival and hazard functions and their corresponding credible intervals, were derived via the Markov chain Monte Carlo method under balanced squared error loss, balanced linear-exponential loss, and balanced general entropy loss. We also provided a simulated dataset analysis for illustration. Furthermore, the MCD's performance was compared with other popular distributions across two well-known failure time datasets. The findings suggested that the MCD offered the best fit for these datasets, highlighting its potential applicability to real-world problems and its suitability as a model for analyzing and predicting device failure times.https://www.aimspress.com/article/doi/10.3934/math.20241662modified chen distributionbathtub-shape hazard ratemaximum likelihood estimatorsbayes estimatorssimulationslifetime data analysis |
| spellingShingle | M. G. M. Ghazal Modified Chen distribution: Properties, estimation, and applications in reliability analysis AIMS Mathematics modified chen distribution bathtub-shape hazard rate maximum likelihood estimators bayes estimators simulations lifetime data analysis |
| title | Modified Chen distribution: Properties, estimation, and applications in reliability analysis |
| title_full | Modified Chen distribution: Properties, estimation, and applications in reliability analysis |
| title_fullStr | Modified Chen distribution: Properties, estimation, and applications in reliability analysis |
| title_full_unstemmed | Modified Chen distribution: Properties, estimation, and applications in reliability analysis |
| title_short | Modified Chen distribution: Properties, estimation, and applications in reliability analysis |
| title_sort | modified chen distribution properties estimation and applications in reliability analysis |
| topic | modified chen distribution bathtub-shape hazard rate maximum likelihood estimators bayes estimators simulations lifetime data analysis |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241662 |
| work_keys_str_mv | AT mgmghazal modifiedchendistributionpropertiesestimationandapplicationsinreliabilityanalysis |