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Cascade and System Reliability for Exponential Distributions
... Singh (2013) [5] studied the system reliability of n-cascade system by stress following the normal distribution and strength following the exponential distribution. Reddy (2016) [6] present the estimation of R=P[X>Y] by considering the system cascade stress strength model. Mutkekar and Munoli (2016) [7] endeavored to provide the statistical inference for " (1+1) cascade system the exponential distribution" below joint action of the stress strength attenuation factors. ...
... Singh (2013) [5] studied the system reliability of n-cascade system by stress following the normal distribution and strength following the exponential distribution. Reddy (2016) [6] present the estimation of R=P[X>Y] by considering the system cascade stress strength model. Mutkekar and Munoli (2016) [7] endeavored to provide the statistical inference for " (1+1) cascade system the exponential distribution" below joint action of the stress strength attenuation factors. ...
... ):MSE and MAPE the values for experiment (4)Table(7):MSE and MAPE the values for experiment(6) ...
Abstract. In this paper derived the mathematical formulas of the Reliability for Special (2+1) cascade model, expression
for model reliability are found when strength and stress distributions are generalized inverse Rayleigh random variables.
The estimation for the reliability function (R) of model is done by Sixth different methods (ML, Mo, LS, WLS, Rg and Pr)
and make the compare between them in simulation study with the program made by (MATLAB 2016) using two statistical
criteria MSE and MAPE , where it found that best estimator between the six estimators is ML.
Keywords: Cascade model, Attenuation factor, Scale parameter, Reliability, Strength-Stress.
... Singh (2013) [5] studied the system reliability of n-cascade system by stress following the normal distribution and strength following the exponential distribution. Reddy (2016) [6] present the estimation of R=P[X>Y] by considering the system cascade stress strength model. Mutkekar and Munoli (2016) [7] endeavored to provide the statistical inference for " (1+1) cascade system the exponential distribution" below joint action of the stress strength attenuation factors. ...
... Singh (2013) [5] studied the system reliability of n-cascade system by stress following the normal distribution and strength following the exponential distribution. Reddy (2016) [6] present the estimation of R=P[X>Y] by considering the system cascade stress strength model. Mutkekar and Munoli (2016) [7] endeavored to provide the statistical inference for " (1+1) cascade system the exponential distribution" below joint action of the stress strength attenuation factors. ...
... ):MSE and MAPE the values for experiment (4)Table(7):MSE and MAPE the values for experiment(6) ...
In this paper derived the mathematical formulas of the Reliability for Special (2+1) cascade model, expression for model reliability are found when strength and stress distributions are generalized inverse Rayleigh random variables. The estimation for the reliability function (R) of model is done by Sixth different methods (ML, Mo, LS, WLS, Rg and Pr) and make the compare between them in simulation study with the program made by (MATLAB 2016) using two statistical criteria MSE and MAPE, where it found that best estimator between the six estimators is ML.
... distribution to find reliability. Reddy (2016) (6) presented estimation of R = (X > Y) by considering the cascade stress-strength model. Devi, Umamaheswari and Swathi (2016) (7) studied general expression for reliability by n cascade system is derivative when stress and strength follow the lindley distribution and numerical values R (1) , R (2) , R (3) and R 3 have been computed for the some specific values of parameters. ...
... distribution to find reliability. Reddy (2016) (6) presented estimation of R = (X > Y) by considering the cascade stress-strength model. Devi, Umamaheswari and Swathi (2016) (7) studied general expression for reliability by n cascade system is derivative when stress and strength follow the lindley distribution and numerical values R (1) , R (2) , R (3) and R 3 have been computed for the some specific values of parameters. ...
This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.
... When a system unit fails, it is replaced by a standby unit and the stress changed times the previous stress [1]. In a previous study, Karam 3 4 ) units, in which three units 1 , 2 3 are work and the unit 4 is a standby unit. ...
In this paper presents the R reliability mathematical formula of the (3 + 1) Exponential cascade model. The reliability of the model is expressed by exponential random variables, which are stress and strength distributions. The reliability model was estimated by three dissimilar methods (ML, Pr and LS) and simulation was performed using MATLAB 2016 program to compare the results of the reliability model estimates using the MSE criterion, the results indicated that the best estimator among the three estimators was ML.
... [35,36] studied deteriorating/imperfect production process which randomly shifts to "out of control state". Similarly, imperfection production models have been considered by [37][38][39][40][41][42]. ...
... In real time situations, scientists and engineers come across various practical difficulties in using both differential and integral equations as mathematical model for time dependent problems [1][2][3][4]. Many solutions to these problems do exist but with complicated steps it is further difficult to extend their ideas to higher dimensional problems. ...
In this paper presents the R reliability mathematical formula of (3+1) Weibull Cascade model. The reliability of the model is expressed by Weibull random variables, which are stress and strength distributions. The reliability model was estimated by six dissimilar methods (ML, Mo, LS, WLS, Rg and Pr) and simulation was performed using MATLAB 2012 program to compare the results of the reliability model estimates using the MSE criterion, the results indicated that the best estimator among the six estimators was ML.
In this paper, we are mainly concerned with estimating cascade reliability model (2+1) based on inverted exponential distribution and comparing among the estimation methods that are used . The maximum likelihood estimator and uniformly minimum variance unbiased estimators are used to get of the strengths and the stress ;k=1,2,3 respectively then, by using the unbiased estimators, we propose Preliminary test single stage shrinkage (PTSSS) estimator when a prior knowledge is available for the scale parameter as initial value due past experiences . The Mean Squared Error [MSE] for the proposed estimator is derived to compare among the methods. Numerical results about conduct of the considered estimator are discussed including the study of mentioned expressions. The numerical results are exhibited and put it in tables.
In the present work, it is assumed that the n-components are arranged in the hierarchial order. The n-cascade system surviving with loss of m components by k number of attacks is studied; the general equation for the reliability is obtained for the above said system; and the system reliability is computed numerically for 6-cascade system for 2-number of attacks.
In this paper we study the reliability of an N-cascade system whose stress and strength follow normal and exponential distributions, respectively. In this system we can observe that reliability increases for lower values of strength parameter (lambda) and stress parameter (mu). Marginal reliability rate also increases at higher values of lambda. Hence we conclude that the addition of components by a cascade system gives a significant improvement.
An n-Cascade system is defined as a special type of standby system with n components. A component fails if the stress on it is not less than its strength. When a component in cascade fails, the next in standby is activated and will take on the stress. However, the stress on this component will be a multiple k times the stress that acted on its predecessor. The system fails if due to an initial stress, each of the components in succession fails. The stress is random and the component strengths are independent and identically distributed variates, with specified probability functions; k is constant. Expressions for system reliability are obtained when the stress and strength distributions are exponential. Reliability values for a 2-cascade system with Gamma and Normal stress and strength distributions are computed, some of which are presented graphically.
In this paper an expression for the reliability of an n-cascade system is allowed when the strengths of the components follows an exponential distribution and the imminent stress is impinged on the first component with a gamma distribution. Also the stress on the successive components are acted by deterministic but unequal factors. The results are observed for the cases when the parameter p takes higher values, one can infer that the systems with larger parameters value and lesser attenuation factors are more reliable.
Case Study of Cascade Reliability with Weibull Distribution
- Shyam Sundar
T.Shyam Sundar, Case Study of Cascade Reliability with Weibull Distribution, International Journal
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The Reliability of a Cascade System with Normal Stress and Strength Distribution
- A C N Raghavachar
- B Kesava Rao
- S N N Pandit
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Reliability of Cascade System withNormal
- T S Uma Maheswari
- A Rekha
- E Rao
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T.S.Uma Maheswari, A.Rekha, E.Anjan Rao
and A.R.Char, Reliability of Cascade System
withNormal Stress and Exponential Strength,
Microelectronics Reliability, Vol. 33, No. 7, 1993,
pp. 929-936,
http://dx.doi.org/10.1016/0026-2714(93)90289-B.