Process Control

#1
Hi,

Could anyone help me with a statistical process control problem i have?

I am measuring a process which gives a measured value range from 0 to infinite, although in practice values are mostly 0 with a few outliers typically reaching a max value of 10.

The measured values are never below 0 so i have a heavily skewed distribution with 0 being the most common value, typically the standard deviation will be about 0.4 with a mean of 0.2. I'll have 40-80 samples per month.

For my process to remain in control i need to show that 90% of my measurements have a value of less than 1 with a 95% confidence. What is the best way of doing this? I'd like to understand how to work this out.

Any help would be most appreciated.

thanks

Steve
 

hlsmith

Omega Contributor
#2
Can you tell us more about these measurements? Are they independent or related to each other? Once we understand these data we can then discuss their distribution.
 

rogojel

TS Contributor
#3
hi,
just a quick and stupid idea: you could transform your data into a Passed/Failed (i.e below 1 Passed, over 1 Failed) and use a simple 1 sample proportion test. That would give you exactly the information you want.
regards
rogojel
 
#4
All the measurements are independent. The values are actually n x 10^6, so a value of 1 represents 1,000,000 if that makes a difference.
 
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#5
hi,
just a quick and stupid idea: you could transform your data into a Passed/Failed (i.e below 1 Passed, over 1 Failed) and use a simple 1 sample proportion test. That would give you exactly the information you want.
regards
rogojel
I had a similar thought last night to transform into pass/fail but wasn't sure how i'd get the confidence limit out! Looking through the 1 sample proportion test now!

An example of my data in summary is:

81 samples
mean : 0.23
standard deviation : 0.83

Number passed: 77
Number Failed : 4
(where fail is measured value >1)
 

Miner

TS Contributor
#6
Are the zeroes true zeroes, or do you have a limit of detection (level below which the measurement device cannot detect something even when present)?
 

rogojel

TS Contributor
#7
hi,
with these data I get a percentage out of bounds p=4,9% with the 95% confidence boundaries of 1,3% -12,1% so the "real" out of bounds percentage is somewhere between 1,3% and 12% which is a pretty good agreement with what you need. Actually you do not even need to use the 1 sample p-test, just estimate the population parameter. If memory serves, you can use a p-chart to control the percentages.

regards
rogojel
 
#8
I am measuring a process which gives a measured value range from 0 to infinite, although in practice values are mostly 0 with a few outliers typically reaching a max value of 10.

The measured values are never below 0 so i have a heavily skewed distribution with 0 being the most common value, typically the standard deviation will be about 0.4 with a mean of 0.2. I'll have 40-80 samples per month.

For my process to remain in control i need to show that 90% of my measurements have a value of less than 1 with a 95% confidence.

What is the best way of doing this? I'd like to understand how to work this out.
I am always disturbed when someone asks for "the best way". One can often find reasonable ways and good ways, but what is the "best way"? In theoretical statistics it is sometimes possible to derive something that is optimal, under well formulated conditions. But what is possible in practice?

For my process to remain in control i need to show that 90% of my measurements have a value of less than 1 with a 95% confidence.
Is it that you want a confidence interval for the (empirically observed) 90% percentile and that you want the confidence level to be 95%?

Maybe this link can help. Start with the median and then do the interval for the 90% percentile.

Then there is also this link.

Many links can be found by searching for "quantile confidence interval" or "percentile confidence interval".

I don't understand this problem. Maybe I return.