Dependence Rayleigh competing risks model with generalized censored data

doi:10.23919/JSEE.2020.000058

Journal of Systems Engineering and Electronics ›› 2020, Vol. 31 ›› Issue (4): 852-858.doi: 10.23919/JSEE.2020.000058

• Reliability • Previous Articles

Dependence Rayleigh competing risks model with generalized censored data

Liang WANG^1,^2,*(), Jin'ge MA³(), Yimin SHI⁴()

¹ School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
² School of Mathematics, Yunnan Normal University, Kunming 650500, China
³ School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
⁴ Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2019-07-05 Online:2020-08-25 Published:2020-08-25
Contact: Liang WANG E-mail:liang610112@163.com;807369960@qq.com;ymshi@nwpu.edu.cn
About author:WANG Liang was born in 1983. He received his B.S. degree in applied mathematics from Northwest University in 2006, and M.S. and Ph.D. degrees in applied mathematics from Northwestern Polytechnical University in 2009 and 2012, respectively. Now, he is a postdoctoral candidate at the School of Mathematics and Statistics in Xi'an Jiaotong University and works as an associated professor in Yunnan Normal University and Xidian University. His research interests include life testing and reliability theory. E-mail: liang610112@163.com|MA Jin'ge was born in 1995. She received her B.S. degree in statistics from Baoji University of Arts and Sciences in 2018. Now, she is a master candidate at the School of Mathematics and Statistics in Xidian University. Her research interests include system reliability analysis. E-mail: 807369960@qq.com|SHI Yimin was born in 1952. He received his B.S. degree from Northwest University in 1976, and M.S. degree from Northwestern Polytechnical University in 1987. Currently, he is a professor of Northwestern Polytechnical University. His research interests include applied probability and statistics, and reliability theory and application. E-mail: ymshi@nwpu.edu.cn
Supported by:
the China Postdoctoral Science Foundation(2019M650260);the National Natural Science Foundation of China(11501433);This work was supported by the China Postdoctoral Science Foundation (2019M650260), and the National Natural Science Foundation of China (11501433)

Abstract

Abstract:

The inference for the dependent competing risks model is studied and the dependent structure of failure causes is modeled by a Marshall-Olkin bivariate Rayleigh distribution. Under generalized progressive hybrid censoring (GPHC), maximum likelihood estimates are established and the confidence intervals are constructed based on the asymptotic theory. Bayesian estimates and the highest posterior density credible intervals are obtained by using Gibbs sampling. Simulation and a real life electrical appliances data set are used for practical illustration.

Key words: dependence competing risks, bivariate distribution, generalized progressive hybrid censoring (GPHC), likelihood estimation, Bayesian analysis

Liang WANG, Jin'ge MA, Yimin SHI. Dependence Rayleigh competing risks model with generalized censored data[J]. Journal of Systems Engineering and Electronics, 2020, 31(4): 852-858.

Figures/Tables 3

Table 1

Table 2

Table 3

References 27

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T	K	MLE			NIP			IP
T	K	$\lambda_1$	$\lambda_3$	$\mu$	$\lambda_1$	$\lambda_3$	$\mu$	$\lambda_1$	$\lambda_3$	$\mu$
0.9	25	1.053 9	1.052 7	0.246 8	0.550 7	0.542 5	0.058 5	0.511 5	0.508 5	0.052 4
	25	[1.839 0]	[1.837 5]	[0.519 7]	[0.512 7]	[0.497 1]	[0.018 4]	[0.434 2]	[0.447 8]	[0.012 0]
	30	0.985 6	0.973 4	0.136 9	0.435 8	0.431 3	0.049 6	0.421 8	0.395 2	0.045 8
	30	[1.658 0]	[1.679 1]	[0.332 5]	[0.370 9]	[0.383 0]	[0.010 7]	[0.293 2]	[0.298 8]	[0.009 4]
1.2	25	1.050 7	1.045 1	0.176 9	0.531 7	0.528 4	0.053 6	0.467 1	0.480 9	0.049 5
	25	[1.780 3]	[1.805 5]	[0.429 0]	[0.475 4]	[0.466 8]	[0.015 4]	[0.358 9]	[0.388 4]	[0.010 3]
	30	0.792 1	0.790 4	0.098 2	0.414 8	0.414 9	0.041 5	0.386 8	0.357 3	0.039 7
	30	[1.029 0]	[1.028 9]	[0.236 4]	[0.290 9]	[0.290 1]	[0.008 3]	[0.240 2]	[0.249 1]	[0.006 9]

T	K	ACI			NIP HPD			IP HPD
T	K	$\lambda_1$	$\lambda_3$	$\mu$	$\lambda_1$	$\lambda_3$	$\mu$	$\lambda_1$	$\lambda_3$	$\mu$
0.9	25	0.860 6	0.853 3	0.830 1	0.873 3	0.884 3	0.879 9	0.872 4	0.885 6	0.886 8
	25	[2.830 5]	[2.814 5]	[0.335 2]	[2.807 6]	[2.801 7]	[0.288 9]	[2.463 7]	[2.551 4]	[0.281 7]
	30	0.862 1	0.859 7	0.856 9	0.876 5	0.882 4	0.881 4	0.887 2	0.883 7	0.895 6
	30	[2.709 3]	[2.709 9]	[0.330 1]	[2.207 8]	[2.211 0]	[0.257 5]	[1.982 6]	[2.005 9]	[0.249 1]
1.2	25	0.865 9	0.872 5	0.833 5	0.872 9	0.886 1	0.881 6	0.887 1	0.869 9	0.901 0
	25	[2.419 6]	[2.380 8]	[0.340 4]	[2.515 9]	[2.479 5]	[0.247 9]	[2.415 9]	[2.418 5]	[0.240 9]
	30	0.870 7	0.882 6	0.835 4	0.877 7	0.884 3	0.897 1	0.889 1	0.891 4	0.912 2
	30	[2.310 5]	[2.347 1]	[0.340 0]	[2.188 6]	[2.166 8]	[0.251 6]	[2.021 3]	[2.052 4]	[0.233 6]

Estimate	$\lambda _1 $	$\lambda _2 $	$\lambda _3 $	$\mu $
MLE	0.007 1	0.012 9	0.004 7	2.105 8
Bayes	0.009 4	0.010 6	0.006 2	2.087 9
ACI	(0.002 4, 0.203 7)[0.201 3]	(0.008 9, 0.282 1)[0.273 2]	(0.001 1, 0.168 0)[0.166 9]	(1.437 8, 4.278 2)[2.840 4]
HPD	(0.003 2, 0.169 3)[0.166 1]	(0.009 4, 0.233 9)[0.224 5]	(0.002 8, 0.146 3)[0.143 5]	(1.213 9, 3.682 3)[2.468 4]

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Dependence Rayleigh competing risks model with generalized censored data

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