Efficiency prediction (minimum versus average)

[roam]

I am trying to determine the efficiency of a light source for treating plants. When using the light source, there is an equal probability of encountering two different plant species.

The light source has a certain electro-optical efficiency $\eta_{\text{eo}}$. And each plant type has a different receptiveness (i.e. absorbance) to the light $\eta_{\text{a}}$. So, the total efficiency of the process will be the product of the two efficiencies:

$$\eta_{\text{total}}=\eta_{\text{eo}}.\eta_{\text{a}} \tag{1}$$

Some research papers that I have read predict the efficiency of such a system to be the minimum of the two efficiencies:

$$\eta_{\text{total}}=\min\left(\eta_{\text{eo}}\eta_{\text{a}_{1}},\ \eta_{\text{eo}}\eta_{\text{a}_{2}}\right). \tag{2}$$

where the subscripts denote the plant type. However, the authors did not provide any statistical justifications for that.

So, what could be the reasoning for this? Is it not better to use the average value instead? i.e.,

$$\eta_{\text{total}}=\eta_{\text{eo}}.\left(\frac{\eta_{\text{a}_{1}}+\eta_{\text{a}_{2}}}{2}\right).$$

Any explanations would be greatly appreciated.

 

[Dale]

Some research papers that I have read predict the efficiency of such a system to be the minimum of the two efficiencies:

Can you link to the papers?

 

[mathman]

It appears to me that the authors want to stress the effect on both plants, so the minimum gives a measure of the effect on both.