In this study, the mth raw moments of sample extremes of order statistics from discrete uniform distribution are obtained. The results of sample extremes of order statistics of random variable for the independent and identically discrete uniform distribution are given. Numerical values are shown in table form
This article deals with numerical investigation of reliability of pump systems from thermal power plants. The reliability is examined by using intensity function for a system composed of n-linearly ordered pumps. The time between failures of pumps is taken as experimental. Firstly, appropriate model for the data is determined. Estimates of parameters are obtained with maximum likelihood method and intensity function models are written. Finally, reliability of consecutive 3-out-of-5:F systems are calculated for certain time periods by using the obtained intensity functions.
The system signature calculated independently from the distribution of the lifetime of the units in the analysis of technical systems enables us to have important information about the reliability of the system. System signature is a probability vector obtained from possible sequences of units according to the moments of deterioration. The reliability of the system can be easily obtained if the distribution of the lifetime of the units is known and if the distributions can be listed as open among themselves. However, when the distributions cannot be listed as open among themselves, it is a very important finding that the system reliability is calculated with the help of system signature by generating the order statistics. It is also possible to calculate the odds ratios of the units when the lifetime of the units is certain. In this study, odds ratio could be calculated by calculating the probability of fail the system of each unit by considering the possible situations of the system, as in the system signature, regardless of the distribution of lifetime of the units. In addition, the technical system is represented by a matrix by establishing a relation between the system fail probabilities of the units obtained in the study and the system signature. However, examples of some technical systems given in the study.
This paper deals with a two-parameter new mix distribution called as RL (Rayleigh-Logarithmic) distribution with increasing failure rate. Firstly, probability density function, distribution function, r th moment, survival and hazard functions of this two-parameter RL distribution are examined. Then, estimation of parameters by using standard statistical techniques such as maximum likelihood method and entropy are given for the new mix model. In the application part, a real data set is receipted and when RL distribution compared with other distributions, this RL distribution is shown be a good competitor.
In this paper, the system signature of the system is creating by using the long-term method and then the transition matrices of each step are calculated. In this way, it is possible to have information about the reliability of the system after each unit becomes failure. Also, in this study, three systems are presented as examples.
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