The function you provided for calculating the average waiting time for an order appears to have some issues. Let's correct it and then I'll explain the corrected function.

The correct function for average waiting time for an order can be represented as:

[ \text{Average Waiting Time} = \frac{\text{Annual Average Number of Orders} \times \text{Manufacturing Time Per Order}}{2 \times (\text{Annual Machine Capacity} - (\text{Annual Average Number of Orders} \times \text{Manufacturing Time Per Order}))} ]

This function is derived from queuing theory and takes into account the average number of orders, the manufacturing time per order, and the machine capacity. It aims to estimate the average amount of time a new order will have to wait before it can be processed by the machine.

The numerator of the equation represents the average time an order is in the system, given by the average of orders times the time it takes to manufacture one order. The denominator represents the excess capacity or idle time of the machine. Dividing the former by the latter gives the average waiting time for an order.

This function is structured this way to provide an estimate of the average waiting time for an order based on the interplay of these key variables in a manufacturing or processing system. It allows for an understanding of how these factors affect the time an order spends in the system before being processed.