Approximate Prediction Interval for Component Life Based on System Failure Data

Here we consider a two-component system where the components are identical but do not work independently within the system. Assuming the joint distribution of component lives to be Bivariate Exponential (BVED), system (series, parallel or stand-by) life distribution comes out to be a proper mixture of x²-distributions. We approximate the system life distribution as a chi-square with a multiplier that depends on system configuration. Prediction intervals for a single future observation (on component life) are constructed on the basis of system life observations. Further, we have taken Gamma and Rectangular priors for the parameters of the BVED and have approximated the unconditional distribution of system life as Beta with suitable parameters. Taking logarithmic transformation, we get Bayesian prediction intervals.