Document Type : Original Paper
Authors
1 Department of Statistics, Higher Education Center of Eghlid, Eghlid, Islamic Republic of Iran
2 Department of Statistics, Faculty of Sciences, Shiraz University, Shiraz, Islamic Republic of Iran
Abstract
In this article, a new proper and favorite stress-strength parameter has been introduced. The maximum likelihood and uniformly minimum variance unbiased estimators of the purposed parameter have been derived for the Exponential distribution. Moreover, the nonparametric estimator of this parameter has also been obtained as well as some important properties of this estimator. A simulation study and the analysis of a real data set have been done for illustrative purposes.
Keywords
- Kotz S, Lumelskii Y, Pensky M. The stress-strength model and its generalization: theory and applications. World Scientific, Singapore. 2003.
- Ventura L, Racugno W. Recent advances on Bayesian inference for . Bayesian Anal. 2011;2(6):1-18.
- Rezaei S, Tahmasbi R, Mahmoodi M. Estimation of for generalized Pareto distribution. J Stat Plan Inference. 2010;140:480–494.
- Hassan AS, Nagy HF, Muhammed HZ, Saad MS. Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values. J. Taibah Univ. Sci. 2020;1(14):244-253.
- Almarashi AM, Algarni A, Nassar M. On estimation procedures of stress-strength reliability for Weibull distribution with application. PLoS ONE. 2020;15(8):e0237997.
- Mirjalili SM, Torabi H, Nadeb H, Bafekri SF. Stress-strength reliability of Exponential distribution based on type-I progressively hybrid censored samples. Statistical research and training center. 2016;13:89–105.
- Kazemi MR. Interval estimation of stress-strength reliability parameter for exponential-inverted exponential model: Frequentist and Bayesian approaches. J. stat. model. theory appl. In Press, 2020.
- Khalifeh A, Mahmoudi E, Chaturvedi A. Sequential fixed-accuracy confidence intervals for the stress–strength reliability parameter for the exponential distribution: two-stage sampling procedure. Comput. Stat. 2020;35:1553–1575.
- Krishnamoorthy K, Mathew T, Mukherjee S. Normal-Based Methods for a Gamma Distribution: Prediction and Tolerance Intervals and Stress-Strength Reliability. Technometrics. 2012;50:69-78.
- Huang K, Mi J, Wang Z. Inference about reliability parameter with gamma strength and stress. J. Stat. Plan. Inference. 2012;142(4):848-854.
- Chen P, Ye Z. Approximate Statistical Limits for a Gamma Distribution. J. Qual. Technol. 2017;49:64-77.
- Xia ZP, Yu JY, Cheng LD, Liu LF, Wang WM. Study on the Breaking Strength of Jute Fibers Using Modified Weibull Distribution. Compos. - A: Appl. Sci. Manuf. 2009;40:54-59.
- Saracoglu B, Kinaci I, Kundu D. On estimation of R = P(Y < X) for exponential distribution under progressive type-II censoring. J. Stat. Comput. Simul. 2012;82(5),729-744.
- Bhattacharyya GK, Johnson RA. Estimation of reliability in a multicomponent stress-strength model. J. Am. Stat. Assoc. 1974;69:966-970.
- Eryilmaz S. Multivariate stress-strength reliability model and its evaluation for coherent structures. J. Multivar. Anal. 2008;99:1878-1887.
- Pakdaman Z, Ahmadi J. Stress- Strength reliability for in exponential case. J. Turk. Stat. Assoc. 2013;3(6):92-102.
- Rao GS, Kantam RRL. Estimation of reliability in multicomponent stress-strength model: Log-logistic distribution. Electron. J. Appl. Statist. Anal. 2010;2(3):75-84.
- Dey S, Mazucheli J, Anis MZ. Estimation of reliability of multicomponent stress-strength for the generalized logistic distribution. Stat. Methodol. 2016;15:73-94.
)