Main Article Content

Hassna H. Kadem
Nada S. Karam


The electronic devices, equipment and complex machines used in many fields such as telecommunications, medicine, astronautics and others are all subject to malfunctions, which cause material and moral losses, waste of time and other damages. Hence the importance of reliability issue in our working life by evaluating the performance and efficiency of these systems and Measuring the reliability of any device will be the basis for the development of most of these devices . Then In this paper will  discussed the Estimation of Reliability Rn for cascade system when the stress and strength are Inverse Rayleigh distributed random variables. under-voltage rating. The cascade system is a redundant component system, which is a redundant component with under-voltage rating and independently distributed power, in which the redundant component replaces the faulty component.. Cascade system is a special case of Stress- Strength models system. Also we discussed the Estimation of Marginal Reliabilities R1, R2 and R3 for Cascade system by three estimation methods (Max. likelihood, Weighted Least Square, Least Square) and Compare between the estimators  of  R4.

© 2018 JASET, International Scholars and Researchers Association


Download data is not yet available.


Metrics Loading ...

Article Details

How to Cite
Kadem HH, Karam NS. Cascade stress-strength system Reliability Estimation of Inverse Rayleigh Distribution. jaset [Internet]. 2020 Oct. 1 [cited 2022 Dec. 1];3(2):9-19. Available from:


-Khan Adil H. and Jan T R., " Estimation of Multi Component Systems Reliability in Stress- Strength Models” University of Kashmir, Srinagar, India (2014). DOI:

- Ahmed H.Kh, " The Reliability for special (2+1) Cascade Model " M.SC. Thesis, AL-Mustansiriya University (2019).

- Ali H.M " Comparison of some methods to estimate some of stress – strength Lomax models" M.SC. Thesis, AL-Mustansiriya University (2013).

- Doloi C., Borah M. and Sriwastav G., " Cascade system with random attenuation factor”, IAPQR Transactions 35(2), 81–90 (2010).

- Doloi C. and Borah M.," Cascade System with Mixture of Distributions, International Journal of Statistics and Systems”, Vol.7,(1):11-24 (2012).

- Gogoi J. and Borah M, " Estimation of reliability for multi component systems using exponential, gamma and lindley stress-strength distributions", Journal of Reliability and Statistical Studies, Vol. 5, Issue 1, 33-41(2012).

- Hassna H.K, “Reliability of Cascade Stress- Strength System" M.SC. Thesis, AL- Mustansiriya University (2018).

- Karam N.S." One, Two and Multi-Component Gompertz Stress- strength Reliability Estimation”, Mathematical Theory and Modeling, vol.6, No.3, ISSN:(2224-5804) (2016).

- Raghavachar. A.C.N,Kesava Rao.B,and Pattabhi Ramacharyulu N.C “Survival function under stress Attenuation in cascade reliability” OPSEARCH ; Volume 20,Issue 4:190- 207(1983).

- Raghda kh. A.," Inverse Rayleigh Distribution: Properties and Different methods of Estimation" M.SC. Thesis, AL-Mustansiriya University (2017).

- Patowary A N, Hazarika J and Sriwastav G L (2012) " Estimation of Reliability in Interference Models Using Monte Carlo Simulation ", Reliability: Theory & Applications, Vol.1, 78-84.

- Ramk H G., " Stress- Strength Reliability Estimation for Component Under a Fixed Number of Stresses", M.Sc. Thesis, Al- Mustansiriya University (2016).

- Salah H. Abid, " The fréchet stress- strength model " International Journal of Applied Mathematical Research-2014. 3(3) 207-213 DOI:

- Shawky, A.I., and Badr, M.M., 2012."Estimations and Prediction from the Inverse Rayleigh Model Based on Lower Record Statistics", Life Science Journal, 9(1):985-990.

- Singh, A.K., Dalpatadu, R.and Tsang, A., 1996. "On Estimation of Parameters of the Pareto Distribution", Actuarial research clearing house, vol.1, 407-409.

- Sriwastav, G.L. and Kakati, M.C. "A Stress- Strength Model with Redundancy ", IAPQR Trans., 6, No.1, 21-27(1981).