# Sample estimation of reliability of stress-strength models The function provides sample estimates of reliability of stress-strength models, where stress and strength are modeled as independent r.v., whose distribution form is known except for the values of its parameters, assumed all unknown ```r estSSR(x, y, family="normal", twoside=TRUE, type="RG", alpha=0.05, B=2000) ``` ## Arguments - `x`: a random sample from r.v. X modeling strength - `y`: a random sample from r.v. Y modeling stress - `family`: the distribution of both X and Y - `twoside`: if TRUE, the function computes two-side confidence intervals; otherwise, one-side (a lower bound) - `type`: type of confidence interval (CI) to be built. For the normal family, "RG" stands for Reiser-Guttman, "AN" for large sample (asymptotically normal), "LOGIT" or "ARCSIN" for logit or arcsin variance stabilizing tranformations, "B" for percentile bootstrap, "GK" for Guo-Krishnamoorthy (one-sided only). - `alpha`: the complement to one of the nominal confidence level - `B`: number of bootstrap replicates (for type "B") ## Details For more details, please have a look at the references listed below ## Returns A list comprising - **ML_est**: the sample value of the maximum likelihood estimator; for normal r.v. $\hat{R}=\Phi[(\bar{x}-\bar{y})/\sqrt{\hat{\sigma}_x^2+\hat{\sigma}_y^2}]$, where $\bar{x}$ and $\bar{y}$ are the sample means, and $\hat{\sigma}_x^2$, $\hat{\sigma}_y^2$ the biased maximum likelihood variance estimators - **Downton_est**: (for normal r.v.) the sample value of one of the approximated UMVU estimators proposed by Downton $\hat{R}'=\Phi[(\bar{x}-\bar{y})/\sqrt{s_x^2+s_y^2}]$ - **CI**: the confidence interval - **confidence_level**: the nominal confidence level $1-\alpha$ ## References Barbiero A (2011) Confidence Intervals for Reliability of Stress-Strength Models in the Normal Case, Comm Stat Sim Comp 40(6):907-925 Downton F. (1973) The Estimation of Pr (Y < X) in the Normal Case, Technometrics , 15(3):551-558 Kotz S, Lumelskii Y, Pensky M (2003) The stress-strength model and its generalizations: theory and applications. World Scientific, Singapore Guo H, Krishnamoorthy K (2004) New approximate inferential methods for the reliability parameter in a stress-strength model: The normal case. Commun Stat Theory Methods 33:1715-1731 Mukherjee SP, Maiti SS (1998) Stress-strength reliability in the Weibull case. Frontiers In Reliability 4:231-248. WorldScientific, Singapore Reiser BJ, Guttman I (1986) Statistical inference for P(Y

estSSR function