Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored <i>δ</i> Shock Model
A fresh censored <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> shock model is investigated. The arrival of random shocks follows a general...
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MDPI AG
2023-11-01
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| author | Lina Bian Bo Peng Yong Ye |
| author_facet | Lina Bian Bo Peng Yong Ye |
| author_sort | Lina Bian |
| collection | DOAJ |
| description | A fresh censored <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> shock model is investigated. The arrival of random shocks follows a generalized Pólya process, and the failure mechanism of the system occurs based on the censored <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> shock model. The generalized Pólya process is used for modeling because the generalized Pólya process has excellent properties, including the homogeneous Poisson process, the non-homogeneous Poisson process, and the Pólya process. Thus far, the lifetime properties of the censored <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> shock model under the generalized Pólya process have not been studied. Therefore, for the established generalized Pólya censored <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> shock model, the corresponding reliability function, the upper bound of the reliability function, the mean lifetime, the failure rate, and the class of life distribution are obtained. In addition, a replacement strategy <i>N</i>, based on the number of failures of the system, is considered using a geometric process. We determined the optimal replacement policy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>N</mi><mo>*</mo></msup></semantics></math></inline-formula> by objective function minimization. Finally, a numerical example is presented to verify the rationality of the model. |
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| last_indexed | 2024-03-11T11:25:41Z |
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| spelling | doaj.art-c07873c3a59b488c80d880e691d1b7bb2023-11-10T15:08:17ZengMDPI AGMathematics2227-73902023-11-011121456010.3390/math11214560Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored <i>δ</i> Shock ModelLina Bian0Bo Peng1Yong Ye2College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, ChinaSchool of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, ChinaA fresh censored <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> shock model is investigated. The arrival of random shocks follows a generalized Pólya process, and the failure mechanism of the system occurs based on the censored <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> shock model. The generalized Pólya process is used for modeling because the generalized Pólya process has excellent properties, including the homogeneous Poisson process, the non-homogeneous Poisson process, and the Pólya process. Thus far, the lifetime properties of the censored <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> shock model under the generalized Pólya process have not been studied. Therefore, for the established generalized Pólya censored <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> shock model, the corresponding reliability function, the upper bound of the reliability function, the mean lifetime, the failure rate, and the class of life distribution are obtained. In addition, a replacement strategy <i>N</i>, based on the number of failures of the system, is considered using a geometric process. We determined the optimal replacement policy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>N</mi><mo>*</mo></msup></semantics></math></inline-formula> by objective function minimization. Finally, a numerical example is presented to verify the rationality of the model.https://www.mdpi.com/2227-7390/11/21/4560reliability indicesgeneralized Pólya processcensored δ shock modelfailure rateoptimal replacement policy |
| spellingShingle | Lina Bian Bo Peng Yong Ye Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored <i>δ</i> Shock Model Mathematics reliability indices generalized Pólya process censored δ shock model failure rate optimal replacement policy |
| title | Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored <i>δ</i> Shock Model |
| title_full | Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored <i>δ</i> Shock Model |
| title_fullStr | Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored <i>δ</i> Shock Model |
| title_full_unstemmed | Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored <i>δ</i> Shock Model |
| title_short | Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored <i>δ</i> Shock Model |
| title_sort | reliability analysis and optimal replacement policy for systems with generalized polya censored i δ i shock model |
| topic | reliability indices generalized Pólya process censored δ shock model failure rate optimal replacement policy |
| url | https://www.mdpi.com/2227-7390/11/21/4560 |
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