Reliability analysis of systems drawn from heterogeneous production lines is a fundamental problem in statistical reliability theory. Motivated by time-terminated life-testing experiments, this study considers the estimation of the stress–strength reliability parameter \( R = P(X < Y) \) , where the stress variable \(X\) and the strength variable \(Y\) are assumed to follow independent but non-identically distributed Lindley distributions. The observed data are modeled under a joint Type-I censoring scheme, in which the number of failures observed prior to a pre-fixed termination time is random. Both classical and Bayesian inferential procedures are developed for the estimation of \(R\) . In the classical framework, maximum likelihood estimators and large-sample confidence intervals are derived. In the Bayesian framework, posterior inference is carried out using importance sampling and Gibbs sampling with Metropolis–Hastings algorithm. The finite-sample properties of the proposed estimators are examined through extensive Monte Carlo simulation studies and illustrated using a real data set.
