Principle (Length of Line): For a line where all the processing times are identical at all the stations, the throughput is decreasing in the number of the stations in the line.
The cycle time of unpaced line is given by the maximum time taken by any station in the line. The average cycle time of the line is the overall mean of the maximum of the processing times Therefore, any addition of station following a non-deterministic processing time, introduces an additional chance that a station will take more time to finish its job in any cycle. Hence, the average cycle time increases too and hence the decrease in throughput.
Example
Consider a line where all stations are identical with each station's
processing time following a lognormal distribution with mean 5 minutes
and standard deviation of 1 minute. Further, all the stations are reliable
and hence the availability of the line is 1. The figure below shows the
effect of the throughput of the line as we keep on adding such stations
to the line. We see that the throughput decreases non-linearly with the
addition of stations. Notice that the effect diminishes as we keep on adding
stations.
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