http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Narayanaswamy Balakrishnan,Ghobad Barmalzan,Abedin Haidari 한국통계학회 2018 Journal of the Korean Statistical Society Vol.47 No.1
Adding parameters to a known distribution is a useful way of constructing flexible families of distributions. Marshall and Olkin (1997) introduced a general method of adding a shape parameter to a family of distributions. In this paper, based on the Marshall– Olkin extension of a specified distribution, we introduce two new models, referred to as modified proportional hazard rates (MPHR) and modified proportional reversed hazard rates (MPRHR) models, which include as special cases the well-known proportional hazard rates and proportional reversed hazard rates models, respectively. Next, when two sets of random variables follow either the MPHR or the MPRHR model, we establish some stochastic comparisons between the corresponding order statistics based on majorization theory. The results established here extend some well-known results in the literature.
Bo Sun,Narayanaswamy Balakrishnan,Fei Chen,Bin-Bin Xu,Zhaojun Yang,Yiming Liu 대한기계학회 2020 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.34 No.4
The servo turret is a complex electromechanical hydraulic component that is the most likely to fail in a numerical control lathe. Reliability evaluation is used to make statistical inferences about the reliability characteristics of products according to all the information related to product reliability. Failure data is the basis of reliability evaluation; however, it is very difficult to collect many accurate failure data for reliability evaluation. In this paper, the reliability of servo turret is evaluated based on failure data that contains accurate failure data and interval censored data. First, a mixture Weibull distribution is chosen for fitting the reliability model. Then, expectation-maximization algorithm is used for estimating the parameters of the distribution which contains hidden variable, and the confidence interval of parameters is constructed using the delta method. In the simulation, different percentages of accurate data and interval data are used and compared with data containing only accurate data. The accuracy of this method is evaluated by mean square error. Finally, the method is applied to the failure data of servo turret and the parameters of mixture Weibull distribution are determined. For possibly simplifying the mixed Weibull distribution, the hypothesis of shape or scale parameters being equal is tested. The hazard property and mean time between failure are then estimated and associated 95 % confidence intervals are obtained.
A robust class of multivariate fatigue distributions based on normal mean-variance mixture model
Sasaei Mahsa,Pourmousa Reza,Balakrishnan Narayanaswamy,Jamalizadeh Ahad 한국통계학회 2021 Journal of the Korean Statistical Society Vol.50 No.1
The Birnbaum–Saunders (BS) distribution, introduced in 1969, is a popular univariate fatigue life distribution which has been widely used to model right-skewed lifetime and reliability data. In this paper, a new class of generalized multivariate BS distributions is proposed based on mean-variance mixture models to accommodate strongly skewed and heavy tailed multivariate lifetime data. Some special cases of this class as well as their properties are then discussed. We present a hierarchical representation which facilitates an efficient EM-type algorithm for the computation of maximum likelihood estimates. Empirical results from a simulation study and real data analyses show that this class of distributions outperforms many existing extensions of the BS distribution in modeling lifetime data.