Estimation procedures for partially accelerated life test model based on unified hybrid censored sample from the Gompertz distribution

• Autorzy: Lone Showkat Ahmad , Panahi Hanieh

Identyfikatory

DOI

10.17531/ein.2022.3.4

• Języki publikacji: EN

Abstrakty

EN

The accelerated life testing is the key methodology of evaluating product reliability rapidly. This paper presents statistical inference of Gompertz distribution based on unified hybrid censored data under constant-stress partially accelerated life test (CSPALT) model. We apply the stochastic expectation-maximization algorithm to estimate the CSPALT parameters and to reduce computational complexity. It is shown that the maximum likelihood estimates exist uniquely. Asymptotic confidence intervals and confidence intervals using bootstrap-p and bootstrap-t methods are constructed. Moreover the maximum product of spacing (MPS) and maximum a posteriori (MAP) estimates of the model parameters and accelerated factor are discussed. The performances of the various estimators of the CSPALT parameters are compared through the simulation study. In summary, the MAP estimates perform superior than MLEs (or MPSs) with respect to the smallest MSE values.

Słowa kluczowe

EN

constant-stress; maximum a posteriori; maximum product of spacing; stochastic EM algorithm; unified hybrid censoring

• Wydawca: Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne
• Czasopismo: Eksploatacja i Niezawodność
• Rocznik: 2022
• Tom: Vol. 24, no. 3
• Strony: 427--436
• Opis fizyczny: Bibliogr. 28 poz., rys., tab.

Twórcy

autor

Lone Showkat Ahmad

• Saudi Electronic University, Department of Basic Sciences, College of Science and Theoretical Studies, (Jeddah-M), Riyadh11673, Kingdom of Saudi Arabia

• https://orcid.org/0000-0001-7149-3314

autor

Panahi Hanieh

• Department of Mathematics and Statistics, Lahijan branch, Islamic Azad University, Lahijan, Iran

• https://orcid.org/0000-0003-2431-1463

Bibliografia

• 1. Aljohani HM, Alfar NM. Estimations with step-stress partially accelerated life tests for competing risks Burr XII lifetime model under type-II censored data. Alexandria Engineering Journal 2020; 59: 1171-1180, https://doi.org/10.1016/j.aej.2020.01.022.
• 2. Alshenawy RA. New one parameter distribution: properties and estimation with applications to complete and type II censored data. J Taibah Univ Sci. 2020; 14: 11-18, https://doi.org/10.1080/16583655.2019.1698276.
• 3. Asadi S, Panahi H, Swarup C, Lone SA. Inference on adaptive progressive hybrid censored accelerated life test for Gompertz distribution and its evaluation for virus-containing micro droplets data. Alexandria Engineering Journal 2022; 61: 10071-10084, https://doi.org/10.1016/j.aej.2022.02.061.
• 4. Balakrishnan N, Rasouli A, Farsipour SN. Exact likelihood inference based on an unified hybrid censored sample from the exponential distribution. J Stat Comput Simul 2008; 78:475-488, https://doi.org/10.1080/00949650601158336.
• 5. Bing L, Zhong-Zhan Z. Statistical analysis for constant-stress partially accelerated life test with interval censored data. Chin. Quart. J. of Math 2019; 34:1-13.
• 6. Celik N, Guloksuz CT. A new lifetime distribution. Eksploatacja i Niezawodnosc - Maintenance and Reliability. 2017; 19 (4): 634-639, https://doi.org/10.17531/ein.2017.4.18.
• 7. Chandrasekar B, Childs A, Balakrishnan N. Exact likelihood inference for the exponential distribution under generalized Type-I and Type-II hybrid censoring, Nav Res Logis 2004; 51: 994-1004, https://doi.org/10.1002/nav.20038.
• 8. Cheng RCH, Amin NAK. Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B 1983; 45(3):394-403, https://doi.org/10.1111/j.2517-6161.1983.tb01268.x.
• 9. Childs A, Chandrasekar B, Balakrishnan N, Kundu D. Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution, Annals of the Institute of Statistical Mathematics 2003; 55(2):319-330, https://doi.org/10.1007/BF02530502.
• 10. Chiou K-C, Chen K-S, Lifetime performance evaluation model based on quick response thinking. Eksploatacja i Niezawodnosc- Maintenance and Reliability 2022; 24 (1): 1-6, http://doi.org/10.17531/ein.2022.1.1.
• 11. Di R, Wang P, He C, Guo Z. Constrained Adjusted Maximum a Posteriori Estimation of Bayesian Network Parameters Entropy, 2021; 23:1283, https://doi.org/10.3390/e23101283.
• 12. Eliwa MS, El-Morshedy M. Bivariate odd Weibull-G family of distributions: properties, Bayesian and non-Bayesian estimation with bootstrap confidence intervals and application, J Taibah Univ Sci 2020; 14:331-345, https://doi.org/10.1080/16583655.2020.1741919.
• 13. Ferreira LA, Silva JL. Parameter estimation for Weibull distribution with right censored data using EM algorithm. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2017; 19 (2): 310-315, https://doi.org/10.17531/ein.2017.2.20.
• 14. Ghafil WK. Maximum Likelihood and Bayesian Estimation of Rayleigh with Partly Interval-Censored Case-I Data, Neuro Quantology 2020; 18(5):26-28, https://doi.org/10.14704/nq.2020.18.5.NQ20163.
• 15. Ghazal MGM, Hasaballah HM. Bayesian Prediction based on unified hybrid censored data from the exponentiated Rayleigh distribution, J. Stat. Appl. Pro. Lett 2018; 5:103-118, https://doi.org/10.18576/jsapl/050301.
• 16. Gwag J, Lee K. Estimation of the scale parameter of the half logistic distribution under unified hybrid censored sample, Journal of the Korean Data & Information Science Society 2018; 29:13-25, https://doi.org/10.7465/jkdi.2018.29.1.13.
• 17. Hassan AS, Al-Thobety AK. Optimal design of failure step stress partially accelerated life tests with type II censored inverted Weibull data. International Journal of Engineering Research and Applications 2012; 2:3242-3253.
• 18. Jeon YE, Kang SB. Estimation of the Rayleigh distribution under unified hybrid censoring, Austrian Journal of Statistics 2021; 50:59-73, https://doi.org/10.17713/ajs.v50i1.990.
• 19. Lin CT, Hsu YY, Lee SY, Balakrishnan N. Inference on constant stress accelerated life tests for log-location-scale lifetime distributions with type-I hybrid censoring. Journal of statistical computation and simulation, 2019; 89:720-749, https://doi.org/10.1080/00949655.2019.1571591.
• 20. Lone SA, Rahman A. Step stress partially accelerated life testing plan for competing risk using adaptive type-i progressive hybrid censoring. Pakistan J Stat 2017; 33: 237-248, https://doi.org/10.1007/978-981-10-5699-4_8.
• 21. Lone SA, Panahi H, Shah I. Bayesian prediction interval for a constant-stress partially accelerated life test model under censored data, Journal of Taibah University for Science 2021; 15(1):1178-1187, https://doi.org/10.1080/16583655.2021.2023847.
• 22. Maiti K, Kayal S, Estimation of stress-strength reliability following extended Chen distribution, International Journal of Reliability, Quality and Safety Engineering 2021, https://doi.org/10.1142/S0218539321500467.
• 23. Panahi H. Estimation of the Burr type III distribution with application in unified hybrid censored sample of fracture toughness, Journal of Applied Statistics 2017; 14:2575-2592, https://doi.org/10.1080/02664763.2016.1258549.
• 24. Panahi H, Asadi P. Estimating the parameters of a generalized inverted exponential distribution based on adaptive type II hybrid progressive censoring with application, Journal of Statistics and Management Systems 2022; 25:433-455, https://doi.org/10.1080/09720510.2021.1892259.
• 25. Wiranto A, Kurniawan A, Fitria DA, Chamidah SN. Estimation of type I censored exponential distribution parameters using objective Bayesian and bootstrap methods (case study of chronic kidney failure patients), Journal of Physics: Conference Series 2019; 012060, https://doi.org/10.1088/1742-6596/1397/1/012060.
• 26. Yang Y-H, Wang K-S. Study of the characteristics about insulation damage based on the accelerated life tests, Eksploatacja i Niezawodnosc - Maintenance and Reliability 2013; 15 (4): 325-331.
• 27. Yazgan C, Gürler C, Esemen M, Sevinc B, Fuzzy stress-strength reliability for weighted exponential distribution, Quality and Reliability Engineering International 2021, https://doi.org/10.1002/qre.3000.
• 28. Zheng D, Fang X. Exact confidence limits for the acceleration factor under constant-stress partially accelerated life tests with type-I censoring, IEEE Transactions on Reliability 2018; 67:92-104, https://doi.org/10.1109/TR.2017.2747762.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).