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I have a set of data now where if I were generate a IMR Chart the process looks in control however if I were to generate a X-R Chart the process looks out of control. The data was originally collected using n=1. The sampling plan was later changed to n=2. So there are two different sampling plan involved in the data set now. Should I use I-MR chart or X-R Chart?
The reason that you see this happen is due to central limit theorem as in the Xbar chart you are actually ploting the distribution of sample means.
This means that the control limits will be tighter and this makes the chart more sensitive. You will find that the control limits differ by a factor of the Sqrt of the sample size (n).
In most cases the Xbar chart is used over the I chart as it generally gives an earlier indication of the process going out of control.
Hope this helps
Watch out for the small sample size with Xbar and R charts. Studies have shown that you generally require a sample size of at least 4 (n=4) to be robust against the normality assumption. Without normality you could end up making false inferences.
Also, with a smaller sample size, your beta error is significantly hindered. With a sample size of 5, the probability of detecting a 2 sigma shift on the first subsequent sample is 92.92 %. If your sample size is only 2, then the probability goes down significantly to ~40%. Watch out!
My advice, don’t use xbar and R charts for your data if n=2!
As far as I-MR charts, the ability to detect small shifts is very poor. If you’re interested in detecting small shifts in your process, take a look at EWMA charts (estimated weighted moving average). These charts are also insensitive to non-normal data. EWMA is also better than the CUSUM method for detecting large shifts.
Hope this helps!??!
The first question to answer is: what is the basis for the rational subgrouping scheme? Once that is understood, the choice of charts will be much more straightforward.
To add to Jonathan’s advice about rational subgrouping….
Let me give examples of rational subgrouping. 1. If you are measuring a quality measurement across a material, then you are getting multiple measurements so you have a rational subgroup and you should use Xbar R charts. Do not confuse rational subgrouping with multiple measurements on the same position of the material you are measuring. These multiple measurements are just trying to reduce measurement variation (see Gage R&R discussions) and so an I-MR chart would be appropriate. Many high tech measurements (e.g. particle size, contaminant level) actually measure multiple times to average results to improve the instruments’ precision (degree of variability) 2. If you are just measuring some periodic time frame, e.g. once per hour, then the use of I-MR charts are best (again assuming you don’t have multiple measurements across the length, width, top vs bottom, etc.).
I have worked with some people that insist you can do Xbar R charts on single points and just subgroup two consecutive measurements. They are trying to get an idea of consistency between batches and concentrate on the R charts. I’m not a big fan of this approach since the MR charts and Individual charts give similar analysis.
Firstly, I think we should verify is there any target spec for the characteristic? If yes, so you better use the target and deviation control chart, that works well in individual or subgrup cases. In the central tendency chart, you place the target as the center line; and in the dispersion chart, you use deviation from target rather than range or even standard deviation. May I help you with sending your data to me?
Most important is what question do you want to answer ? What kind of data do you have ?
Possibly you have variable data. IMR chart provdes the short term variation & trend. If you have different subgroups , then always go for X Bar R or S chart . They are essentially more powerful. For example say I have data of cycle time for invoice processing. I – MR chart will give me only overall picture but it will be difficult for me to understand where do I prioritize my focus . With sub groups ( like region , man who is processing , group , business unit etc) I ‘ll be able to find out within & between variation of different subgroups & that will help me to prioritize my focus.
You may like to share the data & the question you want to answer .
Is it possible to make contact with you regarding your comments about IMR and X Bar charts…this sounded very helpful for something I’m working on so would be helpful to have quick discussion if you dont mind
Thank you for making contact with my dear son Alek after almost five years. Unfortunately, Alek had a nervous breakdown while waiting for someone to respond to his post. He is currently comotose at the Mental Health Institute for Six Sigma Practioners in Phoenix. I’m sure he would love to have you visit. Contact me for further information. Bless you child.
Dearest Mother of poor Alek,
I was so sorry to hear of Alek’s ailment due to time passed post reply syndrome. It is an awful awful thing. I can empathise in many ways ever since I was diagnosed with congential word blindness at an early age leading – as you now know – to limited reading comprehension and surface dyslexia. Pls send my best to Alek (if I have read ur post correctly, that is)..
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