Reliability Stress-Strength Models for Dependent Observations with Applications in Clinical Trials

We consider the applications of stress-strength models in studies involving clinical trials. When studying the effects and side effects of certain procedures (treatments), it is often the case that observations are correlated due to subject effect, repeated measurements and observing many characteristics simultaneously. We develop maximum likelihood estimator (MLE) and uniform minimum variance unbiased estimator (UMVUE) of the reliability which in clinical trial studies could be considered as the chances of increased side effects due to a particular procedure compared to another. The results developed apply to both univariate and multivariate situations. Also, for the univariate situations we develop simple to use lower confidence bounds for the reliability. Further, we consider the cases when both stress and strength constitute time dependent processes. We define the future reliability and obtain methods of constructing lower confidence bounds for this reliability. Finally, we conduct simulation studies to evaluate all the procedures developed and also to compare the MLE and the UMVUE.