摘要 :
Here we have considered an n-standby system with one and more than one repair facility (ies) for interference (or stress-strength) models. The system is working under impacts of stresses. Each impact is called a cycle. When a comp...
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Here we have considered an n-standby system with one and more than one repair facility (ies) for interference (or stress-strength) models. The system is working under impacts of stresses. Each impact is called a cycle. When a component fails it goes for repair; the repair policy is first-come-first-serve (FCFS). The failure times of components, system and repair times all are measured in cycles. The reliability of the system at the iVth cycle is evaluated in different cases. When stress-strength distributions both are either exponential or gamma or normal the reliability of the system is numerically evaluated for given n, N and for some particular values of the parameters involved and are tabulated. The numerical values of the system reliability are on the expected line.
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The interference theory, which is the subject matter of this paper, has acquired an important place in reliability study of the systems. In it the system's strength and stress working on it are taken into consideration for evaluat...
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The interference theory, which is the subject matter of this paper, has acquired an important place in reliability study of the systems. In it the system's strength and stress working on it are taken into consideration for evaluation of its reliability. Two aspects of reliability problems are considered here viz. evaluation of system reliability from mathematical model of the system and inference of reliability. Under the former we have discussed some important interference or stress-strength (S-S) models along with the expression of reliability in each case. The models considered here are: for single component systems, when S-S are independent/correlated, when they have mixture of distributions, when more than one stress is working on a component i.e. a component may fail in different ways, when parameters of the distributions are random variables and for multi-components systems, the chain model, cold, warm and cascade redundancy with perfect and imperfect switches and when S-S are stochastic processes. In addition we have discussed some time dependent S-S models where along with S-S time is also taken into consideration and some maintenance (in particular repair) problems. For inference in interference models we have discussed parametric (classical and Bayesian), as well as non-parametric studies. The studies involving Monte-Carlo simulation for estimation of reliability and other characteristics are also presented. We have highlighted some studies of reliability growth models also.
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In the context of interference models of reliability theory, the cascade system is a particular type of standby system where the stress faced by the new component taking the place of a failed component is attenuated by a factor K,...
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In the context of interference models of reliability theory, the cascade system is a particular type of standby system where the stress faced by the new component taking the place of a failed component is attenuated by a factor K, where K may be a constant, parameter or even a random variable; K is called an attenuation factor. To estimate reliability or its other characteristic of cascade system by analytical method is very difficult due complicated reliability expressions. Further, the real life data are hard to come. In this paper, an attempt has been made to estimate the reliability $$\hat{R}$$ R ^ of a cascade system when stress–strength (S–S) follow either exponential, normal or gamma distribution by using Monte-Carlo Simulation (MCS). We have checked normal approximation of estimated reliability samples ( $$\hat{R}$$ R ^ ) by normal probability plot (NPP) and fitted normal distribution to those estimated reliability samples for which NPP shows good normal approximation. We have also performed Kolmogorov–Smirnov (K–S) one sample and $$\chi^{2}$$ χ 2 -test for goodness of fit. For test of significance between estimated reliability $$\hat{R}$$ R ^ and true reliability R for some given values of parameters of distributions, t test and z-test are performed.
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Due to non-stationary behavior of ihe hydroclimatic data and since there appears much more missing values, researchers generally adopt non-parametric (NP) methods, viz., Mann-Kendall and Sen's slope estimator in the study of trend...
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Due to non-stationary behavior of ihe hydroclimatic data and since there appears much more missing values, researchers generally adopt non-parametric (NP) methods, viz., Mann-Kendall and Sen's slope estimator in the study of trend. Keeping these points in mind, this study attempts to investigate the nature of the trends in some hydroclimatic variables on the Dibrugarh region of Assam, using stated non-parametric methods. The study utilizes monthly total rainfall and fnonthly average of minimum and maximum temperature over last 50 years (1966-2015). The analysis reveals decreasing trend in annual rainfall, whereas an increasing trend has been observed in maximum and minimum temperature for the last fifty years as a whole. On the other hand, from thedecadal analysis, particularly for the decade 2006-2015, for the months of May ami August, it is observed that the rainfall increases significantly, perhaps due to this, the minimum temperature decreases significantly for those two months. However, the trend in rainfall of pre-monsoon season increases as compared to the other three seasons throughout the years.
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Accident is one of the burning problems for pre-mature end to human lives. Road accident in India is an increasing trouble and has raised one of the country's major problems. This paper outlines development of a conventional time ...
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Accident is one of the burning problems for pre-mature end to human lives. Road accident in India is an increasing trouble and has raised one of the country's major problems. This paper outlines development of a conventional time series model viz. Autoregressive Integrated Moving Average (ARIMA) model for the annual total number of deaths due to accident (natural and unnatural) in India covering the period 1967 to 2015 and to forecast the number of annual accidental deaths likely to occur in future.We investigated and found that ARIMA (2,2,1) model is suitable for the given data set.
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The Auto Regressive Moving Average (ARIMA) model deals with only one single time series and did not allow the inclusion of other information in the model and forecasts. One way to solve this predicament is to use regression with A...
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The Auto Regressive Moving Average (ARIMA) model deals with only one single time series and did not allow the inclusion of other information in the model and forecasts. One way to solve this predicament is to use regression with ARIMA errors and provides all the advantages of regression with the powerful time series features of an ARIMA model. This study aims to develop a simple linear regression model with ARIMA errors to yearly production of wheat in India for the period of 1960-2016, where explanatory variable represents time. It is observed that our fitted model is more accurate to our data than ARIMA model.
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