Efficiency prediction (minimum versus average)

  • I
  • Thread starter roam
  • Start date
  • #1
1,266
11

Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
29,082
5,350
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?
 
  • #3
mathman
Science Advisor
7,771
419
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.
 

Related Threads on Efficiency prediction (minimum versus average)

  • Last Post
Replies
8
Views
5K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
4
Views
530
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
16K
  • Last Post
Replies
3
Views
596
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
2
Views
4K
Top