Reliability inference of stress–strength model for the truncated proportional hazard rate distribution under progressively Type-II censored samples

•The stress–strength reliability is analyzed by the truncated PHR distribution.•The pivotal quantity estimation is deduced for stress–strength reliability.•Boot-p technique is used to obtain the confidence interval of stress–strength reliability.•The modified generalized confidence interval is adopted to estimate the stress–strength reliability.•Accuracy of the proposed methodology is tested by simulation and real datasets.