The distribution of the passage time in a two‐station reliable production line: an exact analytic solution

Examines the distribution of the time spent by particular jobs in a two‐station reliable production line with a single machine at each station and FIFO queuing discipline. The processing times are assumed to follow the exponential distribution with different means. Develops an analytic model to determine the Laplace‐Stieltjes transform (LST) of the distribution function of the passage time in the system. Inversion of the LST gives the required distribution. Gives a counter‐example to demonstrate the method and its limitations.