banner
Home > Open Journal Systems

Bayesian and non-Bayesian analysis for the lifetime performance index based on generalized order statistics from Pareto distribution

Amal S. Hassan, Elsayed A. Elsherpieny, Ahmed M. Felifel

Abstract


Modern businesses depend on efficient management and evaluation of product quality performance to assure that they are on the right track, and process capability analysis is used to gauge business performance in practice. Consequently, the lifetime performance index (LPI) , where  is the lower specification limit, is used to gauge a process potential and performance. This paper examines distinct estimators of  under Pareto distribution using generalized order statistics (GOS), which is very helpful in a variety of real-world applications. Results for progressive type II censoring (PTIIC) and first-failure censoring are two particular situations. Using symmetric and asymmetric loss functions, the Bayesian estimator was built, then utilized to produce the  hypothesis testing technique. A simulation study and real data analysis have been investigated to study the behavior of different estimates for  under different schemes, namely PTIIC and the progressive first failure censored scheme.


Keywords


generalized order statistics; Pareto distribution; Bayesian estimator; lifetime performance index

Full Text:

PDF

References


1. Montgomery D. Introduction to Statistical Quality Control. John Wiley & Sons Inc; 1985.

2. Kane VE. Process capability indices. Journal of Quality Technology 1986; 18(1): 41–52. doi: 10.1080/00224065.1986.11978984

3. Hong CW, Wu JW, Cheng CH. Computational procedure of performance assessment of lifetime index of businesses for the Pareto lifetime model with the right type II censored sample. Applied Mathematics and Computation 2007; 184(2): 336–350. doi: 10.1016/j.amc.2006.05.199

4. Hsu BM, Chen BS, Shu MH. Evaluating lifetime performance for the Pareto model with censored information. In: Proceedings of the Second International Conference on Innovative Computing, Information and Control (ICICIC 2007); 5–7 September 2007; Kumamoto, Japan. pp. 79–79.‏

5. Hong CW, Wu JW, Cheng CH. Computational procedure of performance assessment of lifetime index of Pareto lifetime businesses based on confidence interval. Applied Soft Computing 2008; 8(1): 698–705. doi: 10.1016/j.asoc.2007.05.008

6. Lee WC, Wu JW, Lei CL. Evaluating the lifetime performance index for the exponential lifetime products. Applied Mathematical Modelling 2010; 34(5): 1217–1224. doi: 10.1016/j.apm.2009.08.013‏

7. Lee WC. Inferences on the lifetime performance index for Weibull distribution based on censored observations using the max p-value method. International Journal of Systems Science 2011; 42(6): 931–937. doi: 10.1080/00207720903260168

8. Hsu BM, Shu MH, Chen BS. Evaluating lifetime performance for the Pareto model with censored and imprecise information. Journal of Statistical Computation and Simulation 2011; 81(12): 1817–1833. doi: 10.1080/00949655.2010.506439‏

9. Hong CW, Lee WC, Wu JW. Computational procedure of performance assessment of lifetime index of products for the Weibull distribution with the progressive first-failure- censored sampling plan. Journal of Applied Mathematics 2012; 2021: 1–13. doi: 10.1155/2012/717184

10. Ahmadi MV, Doostparast M, Ahmadi J. Estimating the lifetime performance index with Weibull distribution based on progressive first-failure censoring scheme. Journal of Computational and Applied Mathematics 2013; 239: 93–102.‏ doi: 10.1016/j.cam.2012.09.006

11. Wu JW, Hong CW, Lee WC. Computational procedure of lifetime performance index of products for the Burr XII distribution with upper record values. Applied Mathematics and Computation 2014; 227: 701–716. doi: 10.1016/j.amc.2013.11.026

12. Ahmadi MV, Doostparast M, Ahmadi J. Statistical inference for the lifetime performance index based on generalised order statistics from exponential distribution. International Journal of Systems Science 2015; 46(6): 1094–1107.‏ doi: 10.1080/00207721.2013.809611

13. Ahmadi MV, Ahmadi J, Abdi M. Evaluating the lifetime performance index of products based on generalized order statistics from two-parameter exponential model. International Journal of System Assurance Engineering and Management 2019; 10(2): 251–275.‏ doi: 10.1007/s13198-019-00780-2

14. Ahmadi MV, Doostparast M. Pareto analysis for the lifetime performance index of products on the basis of progressively first-failure-censored batches under balanced symmetric and asymmetric loss functions. Journal of Applied Statistics 2019; 46(7): 1196–1227. doi: 10.1080/02664763.2018.1541170

15. Hassan A, Assar S, Selmy A. Assessing the lifetime performance index of burr type III distribution under progressive type II censoring. Pakistan Journal of Statistics and Operation Research 2021; 2021: 633–647. doi: 10.18187/pjsor.v17i3.3635

16. Shaabani J, Jafari AA. Inference on the lifetime performance index of gamma distribution: point and interval estimation. Communications in Statistics-Simulation and Computation 2022; 2022: 1–19. doi: 10.1080/03610918.2022.2045498‏

17. Wu SF, Liu TH, Lai YH, Chang WT. A study on the experimental design for the lifetime performance index of Rayleigh lifetime distribution under progressive type I interval censoring. Mathematics 2022; 10(3): 517.‏ doi: 10.3390/math10030517

18. Kamps U. A concept of generalized order statistics. Journal of Statistical Planning and Inference 1995; 48(1): 1–23.‏ doi: 10.1016/0378-3758(94)00147-N

19. Lehmann EL. Theory of Point Estimation. Springer; 1983.

20. Hogg R, McKean J, Craig A. Introduction to Mathematical Statistics. Pearson Education; 2005.

21. Ahsanullah M. Generalized order statistics from exponential distribution. Journal of Statistical Planning and Inference 2000; 85(1–2): 85–91. doi: 10.1016/S0378-3758(99)00068-3

22. Lehmann EL, Casella G. Theory of Point Estimation, 2nd ed. Springer; 1998.

23. Casella G, Berger RL. Statistical Inference, 2nd ed. Cengage Learning; 2001.

24. Varian H. A Bayesian approach to real estate assessment. In: Savage LJ, Feinberg SE, Zellner A (editors). Studies in Bayesian Econometric and Statistics: In Honor of Leonard J. Savage. North-Holland Pub. Co.; 1975. pp. 195–208.

25. Renjini KR, Abdul Sathar EI, Rajesh G. Bayes estimation of dynamic cumulative residual entropy for Pareto distribution under type-II right censored data. Applied Mathematical Modelling 2016; 40(19–20): 8424–8434. doi: 10.1016/j.apm.2016.04.017




DOI: https://doi.org/10.32629/jai.v7i2.1017

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 Amal S. Hassan, Elsayed A. Elsherpieny, Ahmed M. Felifel

License URL: https://creativecommons.org/licenses/by-nc/4.0/