Controlling automation level in robot production. Perfect and stochastic schemes

We propose a mathematical formalism with which we compare three organization schemes for discrete production: manual, with robots produced outside a facility, and with robots produced on the same facility (self-replication). For each of the three schemes, we consider production conditions that presume perfect production (the probability of correctly performing a technological operation equals 1) and stochastic production (all technological operations during production are correctly performed with probability less than one). We solve the problem of finding the optimal level of automation for this production that would minimize human intervention in the production process for various schemes of production. We show that including a feedback with respect to the ready product (self-replication) may lead to an additional decrease in production cost.