Control Charts – Strange Situation

SS,
My gut tells me that the samples of 10 individual values are on pieces of paper somewhere. Go ask them how they collected the data, and where the put the pieces of paper they recorded them on. Then your problem is solved.
Regards,
Dr. Scott

SS,
With a subgroup size of n=10 then I would suggest using an I-mR chart to test stability. Second, with that large a subgroup, the distribution of the means should be normal. If you observe unstable or non-normal data based on these means, please get back to me for next steps.
As far as future data collection goes, just tell your folks not to lose the n=10 points they are making the mean from. And don’t believe what they say, they have that data, or have had it, written down (or on their PCs) somewhere. I have faced this very issue before, and know it to be fact!
Regards,
Dr. Scott
 

Hi SSIn order to estimate process capability you will need estimates of the mean and standard deviation of the INDIVIDUAL values of the variable of interest, assuming that the process is operating in a stable and predictable manner and that the variable of interest is normally distributed. The X chart of the means of the samples 10 will give you an indication of whether or not you have stability and predictability. Let’s suppose that you do. The mean and standard deviation used to give the limits on your chart will provide you with estimates of the mean and standard deviation not of the individual measures but of the MEANS of samples of 10 measurements. The mean of the distribution of means is the same as that as that of the distribution of individual measurements BUT the standard deviation of the distribution of means is the standard deviation of individual measurements divided by the square root of 10 (the standard error of the sample mean). Thus to get an estimate of the standard deviation needed for your capability calculations you have to multiply the estimate from your chart by the square root of 10.I simulated 50 samples of size 10 from the normal distribtion with mean 53 and standard deviation 4 in Minitab. I then computed the 50 sample means and plotted an Individuals (X) chart of these means. The centre line was at 53.237 so this is an estimate of mu which is actually 53. The limits were at 49.636 and 56.836 with difference 7.2 corresponding to six standard deviations (the gap between the three sigma limits). Hence an estimate of the standard deviation of the means is one sixth of this i.e. 1.2. Multiplying by the square root of 10 (3.162)gives 3.79 as an estimate of sigma which is actually 4.Without individual measurements you cannot check for normality. Past experience or the experience of others in your industry might give some indication.I am not sure what Dr Scott means when he/she refers to “capability of the means”. If you are assessing capability using a column of INDIVIDUAL values obtained as a series of samples of n = 10 then subgroup size 10 should be specified. However if you only have a column of MEANS for the samples of n = 10 then you would get a completely erroneous outcome from running a capability analysis via Minitab on that column. I hope this ramble is of some use to you!Bower Chiel

Dr Scott,Now he is averaging his averages. What is his criteria for choosing 10 as a subgroup size? The 10 averages that will be subgrouped have nothing to do with the original 10 individual values that were averaged.

SS,
Heck if I know at this point. My basic advice is one that Bower Chiel also suggested; get the individual data. SS says he has asked, but can’t get the individual data. I cannot tell you how many times I have heard this before.
Once, I stood up and ended a top executive meeting after being told that one set of data was available only monthly. I in as polite a way as could manage at the time asked each of the executives to follow me out to the production line of interest. Once there, I kindly introduced myself to the lead operator of shift 2, made a bit of small talk (cause I am always truly interested in what the line operators have to say), and then asked him if he knew where the monthly averages we were getting came from.
His response was, “Oh sure”. He took me to a large cabinet that had the data he collected from the line each hour. Each sheet was pink (turns out the data was not only collected each hour, but was in triplicate). I asked what he did with the other two sheets (the yellow and the white). He said he took it to that lady in the office over there. So off we went to talk to the lady in that office over there.
I asked her what she did with the sheets she received. She said she entered the hourly data into the PC on her desk, and then stored the data sheet in a file (similar to the cabinet on the line). I asked what she did with the third sheet. She responded that she just tossed it in the trash since nobody asked for or needed it. The PC was programmed to take the data, average it, and give the division VP a monthly average of the results, along with many other averages from the various production lines (the same person that said that was all that was available).
There are many more interesting and humorous parts to this story, but space is short here. The bottom line is, you can’t just ask. Follow the data trail yourself until you find what you need.
Regards,
Dr. Scott
 

Dr Scott,
I had a situation once where a data acquisition unit collected measurements off a continuous-flow process.  Every 50 or so measurements, it calculated and stored the average and standard deviation of the 50 and then emptied the buffer.  (It used the avg and stdev to decide whether the process needed to be stopped.)  The DAU could have been reprogrammed to store individual data (even if it was sampled), but this would have taken more effort than they were willing to commit.  So sometimes, the data trail leads to this!  It wasn’t an SS project so I didn’t pursue it any further, but I kept thinking, what a waste of good data!  What were they thinking? 

BC,
Our server emptied the “buffer” as well after the monthly calculations. But fortunately I was lucky that the line operator kept the original papers (measures) until the file cabinet was full. Then he would just grab a couple of handfuls off the bottom of the stack (the oldest) and make space for the new ones.
So we were able to get the individual data for a few months of hourly data. Lucky me.
Regards,
Dr. Scott