Mathematical characterization of human reliability for multi-task system operations

The article provides a mathematical reliability methodology for estimating the contribution of the human operator in a human-machine system. The methodology is applicable to high value, high risk human-machine operations where failures can be catastrophic and costly such as rendezvous and docking of a space craft at the International Space Station, critical control activities in a nuclear power plant, etc. The methodology consists of a mathematical probabilistic conceptual approach for the analytical characterization of human reliability for multi-task system operation. From a system perspective, reliability for a system includes three different reliability elements: (1) hardware reliability, (2) software reliability, and (3) human reliability. Therefore, the reliability of a system is just as constrained by the reliability of the human operator as it is by the reliability of the hardware and software. The elements of the bathtub curve for human reliability are constructed analogous to comparable elements of the bathtub curve for hardware reliability. This human error rate bathtub curve concept enables the formulation of a useful, workable mathematical modeling process for human reliability (R.E. Giuntini and W.R. Wessels, 1997). The results consist of a fully developed method that can be applied to quantify human reliability in a human-machine system. A detailed mathematical process of each of the three error rate phases: (1) learning error rate phase, (2) stabilized error rate phase, and (3) fatigue error rate phase is presented in terms of the Weibull probability distribution to characterize the human reliability process.