Estimation of stress-strength reliability for generalized Gompertz distribution under progressive type-II censoring

Abstract

In this study, the stress-strength reliability, $R=P(Y

Keywords

• Bayes estimator
• Lindley’s approximation
• maximum likelihood estimation
• Monte Carlo simulation
• progressive type-II censoring
• stress-strength reliability.

References

1. [1] M.M.E. Abd El-Monsef and W.A.A.E.L. Hassanein, Assessing the lifetime performance index for Kumaraswamy distribution under first-failure progressive censoring scheme for ball bearing revolutions, Qual. Reliab. Eng. Int. 36 (3), 1086-1097, 2020.
2. [1] M.M.E. Abd El-Monsef and W.A.A.E.L. Hassanein, Assessing the lifetime performance index for Kumaraswamy distribution under first-failure progressive censoring scheme for ball bearing revolutions, Qual. Reliab. Eng. Int. 36 (3), 1086-1097, 2020.
3. [2] H.H. Abu-Zinadah and R.A. Bakoban, Bayesian estimation of exponentiated Gompertz distribution under progressive censoring type-II, J. Comput. Theor. Nanosci. 14 (11), 5239-5247, 2017.
4. [2] H.H. Abu-Zinadah and R.A. Bakoban, Bayesian estimation of exponentiated Gompertz distribution under progressive censoring type-II, J. Comput. Theor. Nanosci. 14 (11), 5239-5247, 2017.
5. [3] N. Akdam, İ. Kınacı and B. Saraçoğlu, Statistical inference of stress-strength reliability for the exponential power (EP) distribution based on progressive type-II censored samples, Hacet. J. Math. Stat. 46 (2), 239-253, 2017.
6. [3] N. Akdam, İ. Kınacı and B. Saraçoğlu, Statistical inference of stress-strength reliability for the exponential power (EP) distribution based on progressive type-II censored samples, Hacet. J. Math. Stat. 46 (2), 239-253, 2017.
7. [4] A. Asgharzadeh, Point and interval estimation for a generalized logistic distribution under progressive Type-II censoring, Comm. Statist. Theory Methods 35 (9), 1685- 1702, 2006.
8. [4] A. Asgharzadeh, Point and interval estimation for a generalized logistic distribution under progressive Type-II censoring, Comm. Statist. Theory Methods 35 (9), 1685- 1702, 2006.

9. [5] M.G. Bader and A.M. Priest, Statistical aspects of fiber and bundle strength in hybrid composites, in: T. Hayashi, K. Kawata and S. Umekawa (ed.) Progress in Science and Engineering Composites, Sci. Eng. Compos, (ICCM-IV) Tokyo, 1129–1136, 1982.
10. [5] M.G. Bader and A.M. Priest, Statistical aspects of fiber and bundle strength in hybrid composites, in: T. Hayashi, K. Kawata and S. Umekawa (ed.) Progress in Science and Engineering Composites, Sci. Eng. Compos, (ICCM-IV) Tokyo, 1129–1136, 1982.
11. [6] N. Balakrishnan, Progressive censoring methodology: an appraisal, (with discussions), Test 16 (2), 211-296, 2007.
12. [6] N. Balakrishnan, Progressive censoring methodology: an appraisal, (with discussions), Test 16 (2), 211-296, 2007.
13. [7] N. Balakrishnan and R. Aggarwala, Progressive Censoring: Theory, Methods, and Applications, Springer Science & Business Media, 2000.
14. [7] N. Balakrishnan and R. Aggarwala, Progressive Censoring: Theory, Methods, and Applications, Springer Science & Business Media, 2000.
15. [8] N. Balakrishnan and R.A. Sandhu, A simple simulation algorithm for generating progressive type II censored sample, Amer. Statist. 49 (2), 229-230, 1994.
16. [8] N. Balakrishnan and R.A. Sandhu, A simple simulation algorithm for generating progressive type II censored sample, Amer. Statist. 49 (2), 229-230, 1994.
17. [9] U. Balasooriya, S.L. Saw and V. Gadag, Progressively censored reliability sampling plans for the Weibull distribution, Technometrics 42 (2), 160-167, 2000.
18. [9] U. Balasooriya, S.L. Saw and V. Gadag, Progressively censored reliability sampling plans for the Weibull distribution, Technometrics 42 (2), 160-167, 2000.
19. [10] A. Biswas, S. Chakraborty and M. Mukherjee, On estimation of stress–strength reliability with log-Lindley distribution, J. Stat. Comput. Simul. 91 (1), 128-150, 2021.
20. [10] A. Biswas, S. Chakraborty and M. Mukherjee, On estimation of stress–strength reliability with log-Lindley distribution, J. Stat. Comput. Simul. 91 (1), 128-150, 2021.
21. [11] A.C. Cohen, Progressively censored samples in the life testing, Technometrics 5 (3), 327-339, 1963.
22. [11] A.C. Cohen, Progressively censored samples in the life testing, Technometrics 5 (3), 327-339, 1963.
23. [12] B.B. de Andrade, A.R. do Nascimento and P.N. Rathie PN, Parametric and nonparametric inference for the reliability of copula-based stress-strength models, Qual. Reliab. Eng. Int. 36 (7), 2249-2267, 2020.
24. [12] B.B. de Andrade, A.R. do Nascimento and P.N. Rathie PN, Parametric and nonparametric inference for the reliability of copula-based stress-strength models, Qual. Reliab. Eng. Int. 36 (7), 2249-2267, 2020.
25. [13] E. Demir and B. Saraçoğlu, Maximum likelihood estimation for the parameters of the generalized Gompertz distribution under progressive type-II right censored samples, Journal of Selcuk University Natural and Applied Science 4 (1), 41-48, 2015.
26. [13] E. Demir and B. Saraçoğlu, Maximum likelihood estimation for the parameters of the generalized Gompertz distribution under progressive type-II right censored samples, Journal of Selcuk University Natural and Applied Science 4 (1), 41-48, 2015.
27. [14] B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans, Society for Industrial and Applied Mathematics, 1982.
28. [14] B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans, Society for Industrial and Applied Mathematics, 1982.
29. [15] A. El-Gohary, A. Alshamrani and A.N. Al-Otaibi, The generalized Gompertz distribution, Appl. Math. Model. 37 (1-2), 13-24, 2013.
30. [15] A. El-Gohary, A. Alshamrani and A.N. Al-Otaibi, The generalized Gompertz distribution, Appl. Math. Model. 37 (1-2), 13-24, 2013.
31. [16] D.I. Gibbons and L.C. Vance, Estimators for the 2-parameter Weibull distribution with progressively censored samples, IEEE Trans. Rel. 32 (1), 95-99, 1983.
32. [16] D.I. Gibbons and L.C. Vance, Estimators for the 2-parameter Weibull distribution with progressively censored samples, IEEE Trans. Rel. 32 (1), 95-99, 1983.
33. [17] A.S. Hassan, A. Al-Omari and H.F. Nagy, Stress–strength reliability for the generalized inverted exponential distribution using MRSS, Iran. J. Sci. Technol. Trans. A: Sci. 45 (2), 641-659, 2021.
34. [17] A.S. Hassan, A. Al-Omari and H.F. Nagy, Stress–strength reliability for the generalized inverted exponential distribution using MRSS, Iran. J. Sci. Technol. Trans. A: Sci. 45 (2), 641-659, 2021.
35. [18] M.K. Jha, S. Dey, R.M. Alotaibi and Y.M. Tripathi, Reliability estimation of a multicomponent stress-strength model for unit Gompertz distribution under progressive type II censoring, Qual. Reliab. Eng. Int. 36 (3), 965-987, 2020.
36. [18] M.K. Jha, S. Dey, R.M. Alotaibi and Y.M. Tripathi, Reliability estimation of a multicomponent stress-strength model for unit Gompertz distribution under progressive type II censoring, Qual. Reliab. Eng. Int. 36 (3), 965-987, 2020.
37. [19] C. Jiang, X. Liu, X. Wang, X. Wang and S. Su, Interval dynamic reliability analysis of mechanical components under multistage load based on strength degradation, Qual. Reliab. Eng. Int. 37 (2), 567-582, 2021.
38. [19] C. Jiang, X. Liu, X. Wang, X. Wang and S. Su, Interval dynamic reliability analysis of mechanical components under multistage load based on strength degradation, Qual. Reliab. Eng. Int. 37 (2), 567-582, 2021.
39. [20] J.K. Jose, Estimation of stress-strength reliability using discrete phase type distribution, Comm. Statist. Theory Methods 51 (2), 368-386, 2022.
40. [20] J.K. Jose, Estimation of stress-strength reliability using discrete phase type distribution, Comm. Statist. Theory Methods 51 (2), 368-386, 2022.
41. [21] M. Jovanović, Estimation of P(X
42. [21] M. Jovanović, Estimation of P(X
43. [22] C. Kuş and M.F. Kaya, Estimation for the parameters of the Pareto distribution under progressive censoring, Comm. Statist. Theory Methods 36 (7), 1359-1365, 2007.
44. [22] C. Kuş and M.F. Kaya, Estimation for the parameters of the Pareto distribution under progressive censoring, Comm. Statist. Theory Methods 36 (7), 1359-1365, 2007.
45. [23] C.T. Lin and S.J. Ke, Estimation of P(Y
46. [23] C.T. Lin and S.J. Ke, Estimation of P(Y
47. [24] D.V. Lindley, Fiducial distributions and Bayes theorem, J. R. Stat. Soc. Ser. B. Stat. Methodol. 20 (1), 102–107, 1958.
48. [24] D.V. Lindley, Fiducial distributions and Bayes theorem, J. R. Stat. Soc. Ser. B. Stat. Methodol. 20 (1), 102–107, 1958.
49. [25] D.V. Lindley, Approximate Bayesian methods, Trabajos de Estadística y de Investigación Operative 31, 223-245, 1980.
50. [25] D.V. Lindley, Approximate Bayesian methods, Trabajos de Estadística y de Investigación Operative 31, 223-245, 1980.
51. [26] Y.L. Lio and T.R. Tsai, Estimation of P(X
52. [26] Y.L. Lio and T.R. Tsai, Estimation of P(X
53. [27] M.A.W. Mahmoud, N.M. Kilany and L.H. El-Refai, Inference of the lifetime performance index with power Rayleigh distribution based on progressive first-failure– censored data, Qual. Reliab. Eng. Int. 36 (5), 1528-1536, 2020.
54. [27] M.A.W. Mahmoud, N.M. Kilany and L.H. El-Refai, Inference of the lifetime performance index with power Rayleigh distribution based on progressive first-failure– censored data, Qual. Reliab. Eng. Int. 36 (5), 1528-1536, 2020.
55. [28] N.R. Mann, Best linear invariant estimation for Weibull parameter under progressive censoring, Technometrics 13 (3), 521-534, 1971.
56. [28] N.R. Mann, Best linear invariant estimation for Weibull parameter under progressive censoring, Technometrics 13 (3), 521-534, 1971.
57. [29] H.K.T. Ng, P.S. Chan and N. Balakrishnan, Estimation of parameters from progressively censored data using EM algorithm, Comput. Stat. Data Anal. 39 (4), 371-386, 2002.
58. [29] H.K.T. Ng, P.S. Chan and N. Balakrishnan, Estimation of parameters from progressively censored data using EM algorithm, Comput. Stat. Data Anal. 39 (4), 371-386, 2002.
59. [30] H.K.T. Ng, P.S. Chan and N. Balakrishnan, Optimal progressive censoring plans for the Weibull distribution, Technometrics 46 (4), 470-481, 2004.
60. [30] H.K.T. Ng, P.S. Chan and N. Balakrishnan, Optimal progressive censoring plans for the Weibull distribution, Technometrics 46 (4), 470-481, 2004.
61. [31] M. Obradović, M. Jovanović, B. Milosević and V. Jevremović, Estimation of P(X
62. [31] M. Obradović, M. Jovanović, B. Milosević and V. Jevremović, Estimation of P(X
63. [32] R. Pakyari and N. Balakrishnan, A general purpose approximate goodness-of-fit test for progressively type-II censored data, IEEE Trans. Rel. 61 (1), 238-244, 2012.
64. [32] R. Pakyari and N. Balakrishnan, A general purpose approximate goodness-of-fit test for progressively type-II censored data, IEEE Trans. Rel. 61 (1), 238-244, 2012.
65. [33] K.P. Patil and H.V. Kulkarni, On the interval estimation of stress–strength reliability for exponentiated scale family of distributions, Qual. Reliab. Eng. Int. 33 (7), 1447- 1453, 2017.
66. [33] K.P. Patil and H.V. Kulkarni, On the interval estimation of stress–strength reliability for exponentiated scale family of distributions, Qual. Reliab. Eng. Int. 33 (7), 1447- 1453, 2017.
67. [34] M.R. Piña-Monarrez, Weibull stress distribution for static mechanical stress and its stress/strength analysis, Qual. Reliab. Eng. Int. 34 (2), 229-244, 2018.
68. [34] M.R. Piña-Monarrez, Weibull stress distribution for static mechanical stress and its stress/strength analysis, Qual. Reliab. Eng. Int. 34 (2), 229-244, 2018.
69. [35] B. Saraçoğlu, İ. Kınacı and D. Kundu, On estimation of P(Y
70. [35] B. Saraçoğlu, İ. Kınacı and D. Kundu, On estimation of P(Y
71. [36] A.A. Soliman, Estimation of parameters of life from progressively censored data using Burr-XII model, IEEE Trans. Rel. 54 (1), 34-42, 2005.
72. [36] A.A. Soliman, Estimation of parameters of life from progressively censored data using Burr-XII model, IEEE Trans. Rel. 54 (1), 34-42, 2005.
73. [37] R. Valiollahi, A. Asgharzadeh and M.Z. Raqab, Estimation of P(Y
74. [37] R. Valiollahi, A. Asgharzadeh and M.Z. Raqab, Estimation of P(Y
75. [38] R. Viveros and N. Balakrishnan, Interval estimation of parameters of life from progressively censored data, Technometrics 36 (1), 84-91, 1994.
76. [38] R. Viveros and N. Balakrishnan, Interval estimation of parameters of life from progressively censored data, Technometrics 36 (1), 84-91, 1994.
77. [39] S.J. Wu, Estimations of the parameters of the Weibull distribution with progressively censored data, J. Jpn. Stat. Soc. Jpn. Issue 32 (2), 155-163, 2002.
78. [39] S.J. Wu, Estimations of the parameters of the Weibull distribution with progressively censored data, J. Jpn. Stat. Soc. Jpn. Issue 32 (2), 155-163, 2002.
79. [40] S.J. Wu and C. Kuş, On estimation based on progressive first-failure-censored sampling, Comput. Stat. Data Anal. 53 (10), 3659-3670, 2009.
80. [40] S.J. Wu and C. Kuş, On estimation based on progressive first-failure-censored sampling, Comput. Stat. Data Anal. 53 (10), 3659-3670, 2009.
81. [41] Z. Xiong and W. Gui, Classical and Bayesian inference of an exponentiated halflogistic distribution under adaptive type II progressive censoring, Entropy 23 (12), 1558, 2021.
82. [41] Z. Xiong and W. Gui, Classical and Bayesian inference of an exponentiated halflogistic distribution under adaptive type II progressive censoring, Entropy 23 (12), 1558, 2021.
83. [42] H.K. Yuen, S.K. Tse, Parameters estimation for Weibull distributed lifetime under progressive censoring with random removals, J. Stat. Comput. Simul. 55 (1-2), 57-71, 1996.
84. [42] H.K. Yuen, S.K. Tse, Parameters estimation for Weibull distributed lifetime under progressive censoring with random removals, J. Stat. Comput. Simul. 55 (1-2), 57-71, 1996.