Estimation of the reliability for repairable system after maintenance actions is usually based on mathematical models, which can be classified as parametric and non-parametric models where the parametric model is required a prior specified life time distribution while Non-parametric model is that relaxes of the assumption of the life time distribution. Nonparametric life time models are including proportional hazard model and proportional odd model. In this paper we develop repairable reliability model concentrate on generalized repairable model that indicate the mixture of proportional hazard model and proportional odd model. A proportional hazard-proportional odds (PH-PO) model for the purpose of to improve the repairable reliability to obtain accurate estimates of reliability for repairable industrial boiler system at normal operating conditions depending on transformation parameter for reliability prediction for repairable system that represent Beji industrial boiler in power plant. The results show the odd model better than hazard model for repairable system after preventive maintenance depends on time to repair where transformation parameter (c) equal 0.0525094 it is closer to odds model than hazard model. In addition, reliability industrial boiler in case without temperature effect is better than reliability with temperature effect by using exponential model where we note that the reliability at 500 it is worse state where degrade more than (400,450) .
One way of obtaining information about reliability of units is to accelerate their life by testing at higher levels of stress (such as increasing elevated temperatures or voltages). Predicting the lifetime of a unit at normal operating conditions based on data collected at accelerated conditions is a common objective of these tests. Different models of accelerated life testing are used for such extrapolations. Two statistical based models are widely used: parametric models which require a prior specified lifetime distribution, and nonparametric models that relax of the assumption of the life time distribution. The proportional odds model is a nonparametric model in accelerated life testing based on the odds function and show that it gives a more accurate reliability estimates than proportional hazard model. This paper will concentrate on the models of proportional odds nonparametric accelerated life test for reliability prediction.