Bernoulli production lines with quality-quantity coupling machines: monotonicity properties and bottlenecks

Serial production lines with machines having their quality parameters monotonically decreasing as a function of their efficiencies are analyzed. The Bernoulli reliability and quality models are assumed. It is shown that in such systems the production rate of good parts is a non-monotonic function with respect to machine efficiencies. Thus, bottlenecks may be eliminated by either increasing or decreasing machine efficiency, depending on the operating point.