Principle (Throughput Vs Processing Time/Std Dev): Throughput is decreasing in the mean and standard deviation of the individual process time of the stations.
In an unpaced line a cycle is completed only when all the machines in the line finish processing their job. Thus the cycle time of the line is given by the maximum of the individual processing time of the stations. The throughput of a synchronous line is given by the ratio of the line availability to the cycle time of the line. Thus, as the mean of the individual processing time increases so does the maximum of them and thus the cycle time increase too. Consequently with the increase in the cycle time, the throughput decreases. Similarly, as the standard deviation increases so does the likelyhood that some of the line will take more time to finish processing and hence the cycle time increases and the throughput decreases.
Example
Consider a line with five stations, with each station having lognormal distribution with identical parameters. Moreover assume that all the stations are reliable, that is, the availability is 1.
Effect of Mean
The following figure illustrates the simulated throughput for such a
line when the mean is changed from 2.5 minutes at each station to 7.5 minutes
at each station. The standard deviation is fixed at 1.0 min.
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We see a decrease in throughput as expected, and for this particular
distribution the change is more or less linear.
Effect of Standard Deviation
For the same line as above, the following figure shows the effect on
throughput when the standard deviation of the line is changed from 0 minutes
to 17 minutes, while the mean is kept constant at 5.0 minute. The decrease
in throughput is non-linear in this case, with lower change when the standard
deviation is low, with the effect progressively increasing as the standard
deviation increases.
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