Determining temperature variance and sampling rate

#1
Hi All,
I am hoping you can help me with a work problem. If i am missing any information, please let me know and i can provide it. Apologies if my statistical language below is not entirely correct.
Context
I am an engineer working at a quarry which is in a geothermal environment. We need to understand the temperature of each blast hole to determine what explosive product to put in a hole prior to blasting, however it is quite expensive to sample every hole (it requires a thermocouple to be installed and left in each hole). Each blast has approximately 200 holes.
Problem
1. We want to understand what would be the minimum number of blasts (given a 200 hole average for each blast) would we need to collect samples in each hole to gain a statistically significant sample size to be confident (95 and 99%) of the variance in temperature between individual holes
2. How many blasts/samples would we need to determine if we could reduce the sampling rate and by how much (i.e. sample only every 2nd/3rd/4th hole) and be confident we would be within a certain temperature range (e.g. +-5°C) for the holes that weren't measured.

Thanks in advance.
 

katxt

Active Member
#2
Can we make things a little clearer please.
minimum number of blasts (given a 200 hole average for each blast) would we need to collect samples in each hole to gain a statistically significant sample size to be confident (95 and 99%) of the variance in temperature between individual holes
What would the answer to question 1 look like? It seems that you want something like "after sampling 10 (say) blast sites of 200 holes, we can be 95% sure that 95% of temperatures will lie between 86 and 94 degrees." Is this what you are after? If not, perhaps you could make up an example of the sort of thing you are hoping for.
 
#3
Hi Katxt, thanks for your response.
Yes you are close. Modified question below.

Q: After sampling a certain number of blast sites of 200 holes, we can be 95% certain that the temperatures between adjacent holes in a blast pattern do not vary by more than 5°C (say).

This will allow us to make a decision to reduce the sampling rate to every second hole or every third hole etc (depending on the variance) and be confident that the holes that was not sampled will be within a similar temperature range (e.g. ±5°C) as the holes that were measured.
So its not so much about the temperature variance across an entire blast pattern (which might vary by 15-20°C or more), but rather between adjacent holes.

I have attached a ppt with three slides to show current sampling practice (slide 1), sampling every second hole (slide 2) and sampling every 3rd hole (slide 3) as an example.. I hope this helps.
 

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katxt

Active Member
#4
OK, I see it now.
It looks as if you are working in a heavy duty environment with explosions and hot stuff all over, so here is my main piece of advice. If there is any risk that getting it wrong could lead to loss of life, mutilation, financial ruin, damage to equipment or reputation, or legal action, then you need to get the services of a professional statistician with Professional Indemnity Insurance, rather than take the advice of some random guy off the internet. Look for a specialist in geo-statistics, not just a general statistician from your local university. Ask them to explain "kriging" in simple terms.
Having said that, here is some advice from a random guy off the internet.
Q: After sampling a certain number of blast sites of 200 holes, we can be 95% certain that the temperatures between adjacent holes in a blast pattern do not vary by more than 5°C (say).
We cannot be 95% sure that all of the pairs of adjacent holes differ by 5°C or less. However, we can say things like "We are 95% sure that 99% of the pairs will differ by 5°C or less." You choose the percentages to suit the risks you are prepared to take and the data gives you the 5°C. This is called a tolerance interval.
So, what you can do is take a collection of differences from adjacent holes. Use first measure - second measure to get a normal distribution. Decide what percentages you want. Go to https://statpages.info/tolintvl.html From there you can experiment with how much data you will need and how tight you can get the limits. In general, the more data you have, the lower the limit.
As for the collecting, you need to sample from adjacent holes, so page 3 is probably inappropriate. Page 2 has a regular pattern which statisticians generally don't like, in case they accidentally match up with patterns underground. I suggest picking pairs more at random.
(Are those real measurements?)
Cheers, kat