But the variance in the delivery time is caused by the demand variance.
True, but the variance in demand is just one of the system inputs.
The variance, trend, or average of one of the critical factors of the other inputs will be conspiring to give an unacceptable variance in the output of the system.
The higher the variation of the inputs, the higher is the requirement for the skill or capability to stop an unacceptable variance occurring in the output
Variance of any critical input factor
May lead to
Variance of an apparently unrelated output critical factor