On system reliability in stress-strength setup. (English) Zbl 1186.62123
Summary: We study the stress-strength reliability for a general coherent system. An exact expression as well as bounds and approximations for the system reliability are presented. We also illustrate the estimation procedure for exponential stress-strength distributions.
References:
| [1] | Arnold, B. C.; Balakrishnan, N.; Nagaraja, H. N., Records (1998), Wiley: Wiley New York · Zbl 0914.60007 |
| [2] | Bairamov, I.; Arnold, B. C., On the residual lifelengths of the remaining components in an \(n - k + 1\) out of \(n\) system, Statistics & Probability Letters, 78, 945-952 (2008) · Zbl 1141.62081 |
| [3] | Baklizi, A., Estimation of \(P r \{X < Y \}\) using record values in the one and two parameter exponential distributions, Communications in Statistics: Theory and Methods, 37, 692-698 (2008) · Zbl 1309.62161 |
| [4] | Baklizi, A., Likelihood and Bayesian estimation of \(P r \{X < Y \}\) using lower record values from the generalized exponential distribution, Computational Statistics & Data Analysis, 52, 3468-3473 (2008) · Zbl 1452.62722 |
| [5] | Bhattacharyya, G. K.; Johnson, R. A., Estimation of reliability in a multicomponent stress-strength model, Journal of the American Statistical Association, 69, 966-970 (1974) · Zbl 0298.62026 |
| [6] | Block, H. W.; Costigan, T.; Sampson, A. R., Second order Bonferroni-type, product-type and setwise probability inequalities, (Stochastic Orders and Decision Under Risk. Stochastic Orders and Decision Under Risk, IMS Lecture Notes-Monograph Series (1991)) · Zbl 0760.60015 |
| [7] | Eryılmaz, S., A new perspective to stress-strength models, Annals of the Institute of Statistical Mathematics (2008) |
| [8] | Eryılmaz, S., Consecutive \(k\)-out-of-\(n\): \(G\) system in stress-strength setup, Communications in Statistics: Simulation and Computation, 37, 579-589 (2008) · Zbl 1159.90345 |
| [9] | Eryılmaz, S., Multivariate stress-strength reliability model and its evaluation for coherent structures, Journal of Multivariate Analysis, 99, 1878-1887 (2008) · Zbl 1169.62350 |
| [10] | Eryılmaz, S., Reliability properties of consecutive \(k\)-out-of-\(n\) systems of arbitrarily dependent components, Reliability Engineering and System Safety, 94, 350-356 (2009) |
| [11] | George, E. O.; Bowman, D., A full likelihood procedure for analyzing exchangeable binary data, Biometrics, 51, 512-523 (1995) · Zbl 0832.62092 |
| [12] | Hanagal, D., Estimation of system reliability in multicomponent series stress-strength models, Jounal of Indian Statistical Association, 41, 1-7 (2003) |
| [13] | Kotz, S.; Lumelskii, Y.; Pensky, M., The Stress-Stength Model and its Generalizations (2003), World Scientific: World Scientific Singapore · Zbl 1017.62100 |
| [14] | Krishnamoorthy, K.; Mukherjee, S.; Guo, H., Inference on reliability in two-parameter exponential stress-strength model, Metrika, 65, 261-273 (2007) · Zbl 1433.62061 |
| [15] | Kundu, D.; Raqab, M. Z., Estimation of \(R = P \{Y < X \}\) for three-parameter Weibull distribution, Statistics & Probability Letters, 79, 1839-1846 (2009) · Zbl 1169.62012 |
| [16] | Kuo, W.; Zuo, M. J., Optimal Reliability Modeling, Principles and Applications (2003), John Wiley & Sons: John Wiley & Sons New York |
| [17] | Rao, C. R., Linear Statistical Inference and Its Applications (1973), John Wiley & Sons · Zbl 0169.21302 |
| [18] | Raqab, M. Z., Evaluations of the mean residual lifetime of an \(m\)-out-of-\(n\) system, Statistics & Probability Letters (2009) |
| [19] | Rezaei, S.; Tahmasbi, R.; Mahmoodi, M., Estimation of \(P \{Y < X \}\) for generalized Pareto distribution, Journal of Statistical Planning and Inference, 140, 480-494 (2010) · Zbl 1177.62024 |
| [20] | Saracoglu, B.; Kaya, M. F., Maximum likelihood estimation and confidence intervals of system reliability for Gomperts distribution in stress-strength models, Selcuk Journal of Applied Mathematics, 8, 25-36 (2007) · Zbl 1142.62086 |
| [21] | Villen-Altamirano, J., RESTART simulation of non-Markov consecutive \(k\)-out-of-\(n\) repairable systems, Reliability Engineering and System Safety, 95, 247-254 (2010) |
| [22] | Zhang, Z.; Yang, Y., Ordered properties on the residual life and inactivity time of \((n - k + 1)\)-out-of-\(n\) systems under double monitoring, Statistics & Probability Letters (2010) · Zbl 1185.62179 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
