Real time study of a k-out-of-n system: n identical elements with increasing failure rates

Reliability models based on Markov chain (Except in queueing systems) have extensive applications in electrical and electronic devices. Here, we consider a k-out-of-n:G system with n parallel and identical elements with increasing failure rates (failure rates are Weibull distributed) and nonrepairable elements. The failure rate of remaining elements increases when some elements fail. The system works until at least k elements work. The system of equations are established and the exact equations are sought for the parameters like MTTF (mean time to first failure) and the probability of system working at the time t. A numerical example is solved to demonstrate the procedure clarifying the theoretical development.