Reliability of supply between production lines

We compare four strategies for ensuring a reliable just-in-time supply from a seat production line, which is prone to machine failure, to a car assembly line, which is assumed to operate at a constant speed over single shifts. The strategies are as follows: holding buffer stock; duplication of the least reliable machine; duplication of the production line as a stand-by; and running two production lines concurrently. Times between machine failures are assumed to have independent exponential distributions. A general distribution of repair times is allowed for by using phase-type representations. We show the stationary distribution for these models, and compare stationary distributions with average times within levels over shifts conditional on all machines working at the start of a shift. We compute moments of sojourn times within an arbitrary subset of states, which are relevant when cost is a non-linear function of downtime. We use first passage time results to obtain probabilities of line failure within a shift, and use these results to compare the four strategies.D. A. Green and A. V. Metcalf