Allocation of extra components to ki-out-of-mi subsystems using the NPI method

The allocation of components to systems remains a challenge due to the components success and failure rate which is unpredictable to design engineers. Optimal algorithms often assume a restricted class for the allocation and yet still require a high-degree polynomial time complexity. Heuristic methods may be time-efficient but they do not guarantee optimality of the allocation. This paper introduces a new and efficient model of a system consisting of k_i-out-of-m_i subsystems for allocation of extra components. This model is more general than the traditional k-out-of-n one. This system which consists of subsystem i (i = 1, 2, ..., x) is working if at least k_i(out of m_i) components are working. All subsystems are independent and the components within subsystem i (i = 1, 2, ..., x) are exchangeable. Components exchangeable with those of each subsystem have been tested. For subsystem i, n_i components have been tested for faults and none were discovered in s_i of these n_i components. We assume zero-failure testing, that is, we are assuming that none of the components tested is faulty so s_i = n_i, i = 1, 2, ..., x. We are using lower and upper probability that a system consisting of x independent k_i-out-of-m_i subsystems works. This allocation problem dealt with in this paper can be categorised as either to which subsystem the expected number of extra components should be allocated subject to achieving maximum reliability (Lower probability) of the system consisting subsystems, so s_i = n_i, i = 1, 2, ..., x. The resulting component allocation problems are too complicated to be solved by traditional approaches; therefore, the nonparametric predictive inference (NPI) method is used to solve them. These results show that NPI is a powerful tool for solving these kinds of problems which are helpful for design engineers to make optimal decisi- ons. The paper also includes suggestions for further research.