Statistical inference of Marshall-Olkin bivariate Weibull distribution with three shocks based on progressive interval censored data

ABSTRACT

There are several failure modes may cause system failed in reliability and survival analysis. It is usually assumed that the causes of failure modes are independent each other, though this assumption does not always hold. Dependent competing risks modes from Marshall-Olkin bivariate Weibull distribution under Type-I progressive interval censoring scheme are considered in this paper. We derive the maximum likelihood function, the maximum likelihood estimates, the 95% Bootstrap confidence intervals and the 95% coverage percentages of the parameters when shape parameter is known, and EM algorithm is applied when shape parameter is unknown. The Monte-Carlo simulation is given to illustrate the theoretical analysis and the effects of parameters estimates under different sample sizes. Finally, a data set has been analyzed for illustrative purposes.

KEYWORDS:

• Dependent competing risks
• Marshall-Olkin bivariate Weibull (MOBW) distribution
• progressive interval censoring
• EM algorithm
• Bootstrap confidence intervals (CIs)

Acknowledgments

This work is supported by the National Natural Science Foundation of China (71571144, 71401134, 71171164, 11701406), the Natural Science Basic Research Program of Shaanxi Province (2015JM1003), The Program of International Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province (2016KW-033).

Additional information

Funding

National Natural Science Foundation of China [71571144, 71401134, 71171164, 11701406]; Natural Science Basic Research Program of Shaanxi Province [2015JM1003]; Program of International Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province [2016KW-033].