Estimation of a Parallel Stress-strength Model Based on the Inverse Kumaraswamy Distribution
Main Article Content
Abstract
The reliability of the stress-strength model attracted many statisticians for several years owing to its applicability in different and diverse parts such as engineering, quality control, and economics. In this paper, the system reliability estimation in the stress-strength model containing Kth parallel components will be offered by four types of shrinkage methods: constant Shrinkage Estimation Method, Shrinkage Function Estimator, Modified Thompson Type Shrinkage Estimator, Squared Shrinkage Estimator. The Monte Carlo simulation study is compared among proposed estimators using the mean squared error. The result analyses of the shrinkage estimation methods showed that the shrinkage functions estimator was the best since it has a minor mean squared error than the other methods followed by the additional shrinkage estimator. The stress and strength belong to the In
verse Kumaraswamy distribution
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
licenseTermsHow to Cite
Publication Dates
References
Hameed, B. A.; Salman, A. N.; Kalaf, B. A. On Estimation of P (Y< X) in Case Inverse Kumaraswamy Distribution. Ibn AL-Haitham Journal For Pure and Applied Sciences, 2020, 33(1), 108-118
Raheem, S. H., Kalaf, B. A.; Salman, A. N. Comparison of Some of Estimation methods of Stress-Strength Model: R= P (Y< X< Z). Baghdad Science Journal, 2021, 18(2 (Suppl.)), 1103-1103.
Gupta, R.D. ; Gupta, R.C. Estimation for pr (x > y) in the Multivariate Normal case. Statistic, 1990, 21, 91–97.
Hanagal, D.D. Estimation of system reliability under bivariate Pareto distribution, Parishankyan Samikkha, 1996, 3, 3-18.
Hangal, D.D. On The Estimation of System Reliability in Stress-Strength models, Economic Quality Control, 1998, 13, 17-22.
Sezer, D.; Kinaci, I. Estimation of a stress-strength parameter of a parallel system for Exponential Distribution Based on Masked Data, Journal of Selçuk University Natural and Applied Science, 2013, 2( 3), 60-68.
Karam, N. S. System Reliability Estimations of Models Using Exponentiated Exponential Distribution, Iraq Journal of Science, 2013, 54(3), 828-835.
Cheng, C. Reliability of Parallel Stress-Strength Model, Journal of Mathematical Research with Applications, 2018, 38, 4, 427-440.
Kumaraswamy, P. A Generalized Probability Density Function for Double- Bounded Random Processes, Journal of Hydrology, 1980, 46( 1-2), 79-88.
Jones, M. C. Kumaraswamy’s Distribution: A Beta-Type Distribution with Some Tractability Advantages, Statistical Methodology. 2009, 6, 1, 70-81.
AL-Fattah, A. M.,; EL-Helbawy, A. A. ; AL-Dayian, G.R. Inverted Kumaraswamy Distribution: Properties and Estimation, Pakistan Journal of Statistics, 2017, 33(1), 37-61.
Fatima, K.; Jan, U., ; Ahmad, S. P. Statistical properties and applications of the exponentiated inverse Kumaraswamy distribution, Journal of Reliability and Statistical Studies, 2018, 11(1), 93-102.
Iqbal, Z.;Tahir, M. M.; Riaz, N.; Ali, S. A.; Ahmad, M. Generalized inverted Kumaraswamy distribution: properties and application", Open Journal of Statistics, 2017, 7(04), 645-662.
Karam, N. S.; Ali, H. M. Estimation of Two component Parallel System Reliability Stress-Strength Using Lomax distribution. Magistra, 2014 ,26(88), 78.
Kalaf, B. A.; Raheem, S. H.; Salman, A. N. Estimation of the reliability system in model of stress-strength according to distribution of inverse Rayleigh. Periodicals of Engineering and Natural Sciences (PEN), 2021, 9(2), 524-533.
Ibrahim, A.; Kalaf, B. A. Estimation of the survival function based on the log-logistic distribution. International Journal of Nonlinear Analysis and Applications, 2022, 13(1), 127-141.
Thompson, J.R. Some shrinkage Techniques for Estimating the mean. J. Amer. Statist. Assoc. 1968, 63, 113-122.
Al-Hemyari, Z. A.; Khurshid. A.; Al-Joberi. A.N. On Thompson Type Estimators for the Mean of Normal Distribution, revista investigation operational J. 2009, 30( 2),109-116.
Jebur, I. G.; Kalaf, B. A.; Salman, A. N. An efficient shrinkage estimator for generalized inverse Rayleigh distribution based on bounded and series stress-strength models. In Journal of Physics: Conference Series . IOP Publishing. 2021, May, 1897, 1, 012054.
AN, A. J.; Rahiem, S. H.; Kalaf, B. A. Estimate the Scale Parameter of Exponential Distribution Via Modified Two Stage Shrinkage Technique. Journal of College of Education, 2010 (6).