Stress – Strength Reliability Estimation

In the stress-strength modeling, R=P(Y <X) is a measure of component reliability
when it is subjected to random stress Y and has strength X. For a particular
situation, consider Y as the pressure of a chamber generated by ignition of a solid
propellant and X as the strength of the chamber, then R represents the probability of
successful firing of the engine. In this context, R can be considered as a measure of
system performance and it is naturally arise in electrical and electronic systems. It
may be mentioned that R is of greater interest than just reliability since it provides a
general measure of the difference between two populations through their respective
random variables and has applications in many areas. For example, if X is the
response for a control group, and Y refers to a treatment group, R is a measure of
the effect of the treatment. Also, it may be mentioned that R equals the area under
the receiver operating characteristic (ROC) curve for diagnostic test or biomarkers
with continuous outcome The ROC curve is widely used, in biological, medical and
health service research, to evaluate the ability of diagnostic tests or bio-markers to
distinguish between two groups of subjects, usually non-diseased and diseased
subjects. For more application of R, see Kotz et al. (2003).