Interval estimation for -out-of- load-sharing systems

Load-sharing systems are commonly seen in industry; e.g., water pumps in a cooling system. In a load-sharing system, the stress level on each surviving component increases as components fail. The load-sharing nature of the component failure process creates difficulties in statistical inference for the system. This article develops two interval procedures for failure data from load-sharing systems. We assume that the component lifetime under each stress level follows an exponential distribution, a common distribution in reliability engineering. A log-linear link function is used to model the relationship between the stress levels and component lifetimes. In the two proposed interval procedures, we construct confidence intervals for the model parameters by using pivotal quantities and generalized pivotal quantities. Interval estimation for important reliability characteristics including the mean lifetime and the reliability of the load-sharing system is also discussed. A simulation study shows that the confidence intervals produced from the proposed procedures are more accurate compared with traditional approximate interval procedures, such as the large sample normal approximation and the bootstrap. A numerical example is used to demonstrate the performance of the proposed procedures.