Marshall-Olkin Bilal distribution with associated minification process and acceptance sampling plans

Abstract

In this paper, a new two parameters lifetime distribution, called Marshall-Olkin Bilal distribution is introduced and the structural properties are discussed. The proposed model results from the Marshall and Olkin class of distributions with the baseline model as Bilal distribution. We examined the statistical aspects like moments, quantile function, order statistics and entropy. The hazard function can model increasing and upside-down bathtub shaped data sets. The model parameter estimation is carried out by maximum likelihood estimation and a simulation study is performed. The flexibility of the proposed model is evaluated by two real data sets, compared with the competing models. Its application in time series is studied by the associated autoregressive minification process and the auto-correlation structure is derived. The acceptance sampling plans formulated for the proposed model and the characteristic results are illustrated.

Keywords

• Marshall-Olkin family of distributions
• Bilal distribution
• Hazard rate function
• Minification process
• Acceptance sampling plans

References

1. [1] A. Abd-Elrahman, A new two-parameter lifetime distribution with decreasing, increasing or upside-down bathtub-shaped failure rate, Commun. Stat. Theory Methods 46, 8865-8880, 2017.
2. [2] A. Abd-Elrahman, Utilizing ordered statistics in lifetime distributions production: a new lifetime distribution and applications, J. Probab. Stat. 11, 153-164, 2013.
3. [3] B. Ahmed, M. Ali and H. Yousof, A novel G family for single acceptance sampling plan with application in quality and risk decisions, Ann. Data Sci., 1-19, 2022.
4. [4] M. Ahsan-ul-Haq, M.R. Irshad, E.S. Muhammed Ahammed and R. Maya, New Discrete Bilal Distribution and Associated INAR 1. Process, Lobachevskii J. Math. 44, 3647-3662, 2023.
5. [5] A. Al-Nasser and M. Ahsan-ul-Haq, Acceptance sampling plans from a truncated life test based on the power Lomax distribution with application to manufacturing, Stat. Transit. 22, 1-13, 2021.
6. [6] A. Al-Nasser and B. Alhroub, Acceptance sampling plans using hypergeometric theory for finite population under Q-Weibull distribution, Electron. J. Appl. Stat. 15, 374- 388, 2022.
7. [7] A. Al-Nasser and M. Obeidat, Acceptance sampling plans from truncated life test based on Tsallis q-exponential distribution, J. Appl. Stat. 47, 685-697, 2020.
8. [8] G. Alomani and A. Al-Omari, Single acceptance sampling plans based on truncated lifetime tests for two-parameter Xgamma distribution with real data application, Math. Biosci. Eng. 19, 13321-13336, 2022.

9. [9] A. Al-Omari and A. Al-Nasser, A two parameter quasi Lindley distribution in acceptance sampling plans from truncated life tests, Pakistan J. Stat. Oper. Res. 15, 39-47, 2019.
10. [10] A. Al-Omari, N. Koyuncu and A. Alanzi, New acceptance sampling plans based on truncated life tests for Akash distribution with an application to electric carts data, IEEE Access 8, 201393 - 201403, 2020.
11. [11] R. AlSultan and A. Al-Omari, Zeghdoudi distribution in acceptance sampling plans based on truncated life tests with real data application, Decis. Mak. Appl. Manag. Eng. 6, 432448, 2023.
12. [12] E. Altun, A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models, Mathematica Slovaca 70, 979-994, 2020.
13. [13] E. Altun, M. El-Morshedy and M. Eliwa, A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models, PLoS One 16, 2021.
14. [14] M. Aslam, Design of sampling plan for exponential distribution under neutrosophic statistical interval method, IEEE Access 6, 64153-64158, 2018.
15. [15] R. Barlow, A. Marshall and F. Proschan, Properties of probability distributions with monotone hazard rate, The Annals Of Mathematical Statistics 34, 375-389, 1963.
16. [16] H. Belbachir and M. Benahmed, Two-sided sampling plan for exponential distribution under type II censored samples, Hacet. J. Math. Stat. 51, 327-337, 2022.
17. [17] E. Castillo, Hadi, A. Balakrishnan, N. and J. Sarabia, Extreme Value and Related Models with Applications in Engineering and Science, Wiley Hoboken, 2005.
18. [18] G. Cordeiro, E. Ortega and D. Cunha, The exponentiated generalized class of distributions, Journal Of Data Science 11, 1-27, 2013.
19. [19] M. Ghitany, D. Al-Mutairi, F. Al-Awadhi and M. Al-Burais, Marshall-Olkin extended Lindley distribution and its application, Int. J. Appl. Math. 25, 709-721, 2012.
20. [20] R. Gupta and D. Kundu, Theory and methods: generalized exponential distributions, Aust. N. Z. J. Stat. 41, 173-188, 1999.
21. [21] W. Gui, Marshall-Olkin extended log-logistic distribution and its application in minification processes, Appl. Math. Sci. 7, 3947-3961, 2013.
22. [22] O. Hassan, I. Elbatal, A. Al-Nefaie and A. El-Saeed, Statistical inference of the beta binomial exponential II distribution with application to environmental data, Axioms 11, 740, 2022.
23. [23] P. Jeyadurga and S. Balamurali, A new attribute sampling plan for assuring Weibull distributed lifetime using neutrosophic statistical interval method, Nova Science Publishers, 91-109, 2020.
24. [24] K. Jose and A. Paul, Marshall-Olkin extended Rayleigh distribution and applications, J. Kerala Stat. Assoc. 30, 1-20, 2019.
25. [25] E. Lee and J.Wang, Statistical Methods for Survival Data Analysis, John Wiley, 2003.
26. [26] A. Marshall and I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84, 641-652, 1997.
27. [27] R. Maya, M.R. Irshad, M. Ahammed, and C. Chesneau, The Harris extended Bilal distribution with applications in hydrology and quality control, AppliedMath 3, 221- 242, 2023.
28. [28] R. Maya, M.R. Irshad and S. Arun, Application of Ustatistics in estimation of scale parameter of Bilal distribution, Philipp. Stat. 70, 67-82, 2021.
29. [29] R. Maya, M.R. Irshad and S. Arun, Farlie- Gumbel- Morgenstern bivariate Bilal distribution and its inferential aspects using concomitants of order statistics, J. Prob. statistical Sci. 19, 1-20, 2021.
30. [30] S. Nadarajah, H. Bakouch and R. Tahmasbi, A generalized Lindley distribution, Sankhya B 73, 331-359, 2011.
31. [31] M. Nichols and W. Padgett, A bootstrap control chart for Weibull percentiles, Qual. Reliab. Eng. Int. 22, 141-151, 2006.
32. [32] H. Tripathi, A. Al-Omari, M. Saha and A. Al-anzi, Improved attribute chain sampling plan for Darna distribution, Comput. Syst. Sci. Eng. 38, 382-392, 2021.