Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored Data
Estimating the accurate evaluation of product lifetime performance has always been a hot topic in manufacturing industry. This paper, based on the lifetime performance index, focuses on its evaluation when a lower specification limit is given. The progressive first-failure-censored data we discuss h...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-06-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/6/937 |
| _version_ | 1797566261761146880 |
|---|---|
| author | Ying Xie Wenhao Gui |
| author_facet | Ying Xie Wenhao Gui |
| author_sort | Ying Xie |
| collection | DOAJ |
| description | Estimating the accurate evaluation of product lifetime performance has always been a hot topic in manufacturing industry. This paper, based on the lifetime performance index, focuses on its evaluation when a lower specification limit is given. The progressive first-failure-censored data we discuss have a common log-logistic distribution. Both Bayesian and non-Bayesian method are studied. Bayes estimator of the parameters of the log-logistic distribution and the lifetime performance index are obtained using both the Lindley approximation and Monte Carlo Markov Chain methods under symmetric and asymmetric loss functions. As for interval estimation, we apply the maximum likelihood estimator to construct the asymptotic confidence intervals and the Metropolis–Hastings algorithm to establish the highest posterior density credible intervals. Moreover, we analyze a real data set for demonstrative purposes. In addition, different criteria for deciding the optimal censoring scheme have been studied. |
| first_indexed | 2024-03-10T19:25:10Z |
| format | Article |
| id | doaj.art-d4c754a77fd34f60b991da5522bce09a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T19:25:10Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-d4c754a77fd34f60b991da5522bce09a2023-11-20T02:41:58ZengMDPI AGSymmetry2073-89942020-06-0112693710.3390/sym12060937Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored DataYing Xie0Wenhao Gui1Department of Mathematics, Beijing Jiaotong University, Beijing 100044, ChinaDepartment of Mathematics, Beijing Jiaotong University, Beijing 100044, ChinaEstimating the accurate evaluation of product lifetime performance has always been a hot topic in manufacturing industry. This paper, based on the lifetime performance index, focuses on its evaluation when a lower specification limit is given. The progressive first-failure-censored data we discuss have a common log-logistic distribution. Both Bayesian and non-Bayesian method are studied. Bayes estimator of the parameters of the log-logistic distribution and the lifetime performance index are obtained using both the Lindley approximation and Monte Carlo Markov Chain methods under symmetric and asymmetric loss functions. As for interval estimation, we apply the maximum likelihood estimator to construct the asymptotic confidence intervals and the Metropolis–Hastings algorithm to establish the highest posterior density credible intervals. Moreover, we analyze a real data set for demonstrative purposes. In addition, different criteria for deciding the optimal censoring scheme have been studied.https://www.mdpi.com/2073-8994/12/6/937progressive first-failure-censored samplelog-logistic distributionthe lifetime performance indexmaximum likelihood estimationFisher information matrixBayesian analysis |
| spellingShingle | Ying Xie Wenhao Gui Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored Data Symmetry progressive first-failure-censored sample log-logistic distribution the lifetime performance index maximum likelihood estimation Fisher information matrix Bayesian analysis |
| title | Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored Data |
| title_full | Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored Data |
| title_fullStr | Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored Data |
| title_full_unstemmed | Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored Data |
| title_short | Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored Data |
| title_sort | statistical inference of the lifetime performance index with the log logistic distribution based on progressive first failure censored data |
| topic | progressive first-failure-censored sample log-logistic distribution the lifetime performance index maximum likelihood estimation Fisher information matrix Bayesian analysis |
| url | https://www.mdpi.com/2073-8994/12/6/937 |
| work_keys_str_mv | AT yingxie statisticalinferenceofthelifetimeperformanceindexwiththeloglogisticdistributionbasedonprogressivefirstfailurecensoreddata AT wenhaogui statisticalinferenceofthelifetimeperformanceindexwiththeloglogisticdistributionbasedonprogressivefirstfailurecensoreddata |