Dear Experts,
If I want to develop a X bar chart , and the subgroup size is 6 , how can I deal with the missing values in the subgroups , for example , in subgroup three I have 2 out of six missing values.
Thanks.

Dear Experts,
If I want to develop a X bar chart , and the subgroup size is 6 , how can I deal with the missing values in the subgroups , for example , in subgroup three I have 2 out of six missing values.
Thanks.


Do you have a statistical software(minitab, JMP?). It is capable of doing that.
If you are using excel, the only way i know is using the "if" function to select the x-bar constant to be appllied for the LCL/UCL calculation,. This will give you a changing control limit, depending on the subgroup size.

={if(count("range")=6, x-bar constant,(if(count("range")=5,x-bar constant,if(...}

Why are there missing values? If there is not some sort of systemic reason for the missing values, and they are basically missing on a random basis, you could try plotting the xbar-R charts just on the basis of sequentail 6 results and see what it is telling you. I'd be careful with this, since the subgroupings would not necessarily be "rational".

Or, yes, you could set up a chart where the number of samples in each subset is variable, as suggested in the previous post.

In addition to the good advice from Reynald, I would ask why the subgroup has parts missing.

Did someone just forget to collect the samples? In that case, it is not much problem.

Did the process fail and only 4 parts were produced? Did two of the six parts sampled not function and were removed from the sample? In cases like this, the statistical basis for the chart is in question, since the sample is not random.


Tim F

P.S. Hey Steve, looks like we both had about the same though at the same time! :-)

Dear Experts,
The reason behind the missing values is that, we are monitoring the actual time of the in-patient initial assessment, some times physicians does not right the time in the assessment sheet.
Thanks.

Dear Experts,
The reason behind the missing values is that, we are monitoring the actual time of the in-patient initial assessment, some times physicians does not right the time in the assessment sheet.
Thanks.
I'd say that you should then work on that as a data quality problem. But meanwhile, I'd treat those as invalid data and throw them out, and form the subgroups from the remaining valid data.

Dear Experts,
I have developed an Xbar&R chart; the X-bar chart gave me one point out of the UCL (point # 5) while the R-chart gave me 3 points out of UCL , points # (7 , 10 , and 21).
Point # 5 contain 3 missing out of 6 , point # 10 contain 4 missing out of 6 , and 11 is the same , 4 missing out of 6.
I have thrown the missing values.
My question is, is it normal to see one point in the X-bar chart and another points in the R-chart , like the above case?
And, because we had points out side the UCL, so can we say that the process out of control, or we have to check the four points before any judgment.
Many thanks.

My question is, is it normal to see one point in the X-bar chart and another points in the R-chart , like the above case?
And, because we had points out side the UCL, so can we say that the process out of control, or we have to check the four points before any judgment.
Many thanks.

Yes, you can see a signal on the R-chart, and not on the x-bar and vice versa. A signal on the R-chart is usually an individual item being way out. An x-bar change is usually a change to many items.

One note - until the R-chart is in control (which it is not at this time), you should not put much faith in the xbar chart. This is because the average range from the R-chart becomes the criteria for the control limit on the xbar chart.

Yes, I would say you should consider your process "out of control". Yes, you should go ahead and research the four points in question to determine if there is one reason all four are out of control, or if there are individual causes.

Why have you chosen n=6 as your subgroup size? If you use n=5 as the subgroup size, it is easy to find x-bar. Just double the sum of X and move the decimal one place to the left. When n=5, the ((sum of X) X 2)/10 = (sum of X)/5. There is no need even to have a calculator Concievably, someone that can only add and subtract could make a control chart.:2cents:

Yes, you can see a signal on the R-chart, and not on the x-bar and vice versa. A signal on the R-chart is usually an individual item being way out. An x-bar change is usually a change to many items.

One note - until the R-chart is in control (which it is not at this time), you should not put much faith in the xbar chart. This is because the average range from the R-chart becomes the criteria for the control limit on the xbar chart.

Yes, I would say you should consider your process "out of control". Yes, you should go ahead and research the four points in question to determine if there is one reason all four are out of control, or if there are individual causes.
Dear Mr. Steve,
Thanks for the information.
Suppose no reason for the four points, what should be done in the case, do I have to remove these points and redevelop the charts?
Thanks.

Dear Mr. Steve,
Thanks for the information.
Suppose no reason for the four points, what should be done in the case, do I have to remove these points and redevelop the charts?
Thanks.


There are two schools of thought on that. If you really, really, really can't come up with what was special about those four points, the followers of Dr. Wheeler would likely say leave them in the calculations. Following this advice, I still wouldn't put much reliance on the xbar chart until you get a good run (25 sets) on the rbar chart that are stable.

I lean more towards the idea that SPC is for prediction. I'd try throwing out the 4 points and seeing if that gives you a remaining set of at least 25 points that are stable both on R and xbar, and give a better prediction of future performance. If so, I'd go with that as the prediction of future performance, though would still be wary until I got 25 clean points without having to throw any out.

Dear Mr. Steve,
Actually the process contain only 21 sets, not 25 sets.
I have taken what you prefer, and I have thrown the four points, but again the X-bar has been showing 2 points above the UCL, and one below the LCL.
The R-chat comes up with one point above the UCL.
Thanks.

Dear Mr. Steve,
Actually the process contain only 21 sets, not 25 sets.
I have taken what you prefer, and I have thrown the four points, but again the X-bar has been showing 2 points above the UCL, and one below the LCL.
The R-chat comes up with one point above the UCL.
Thanks.

This can happen - as you remove outliers, new points become outliers. Definitely confirmation that the process is out of control. At this point, I'd continue to research the original four points and perhaps this new one from the R-chart, and concentrate on the R-chart and getting the variability under control. Until the R-chart gets under control, do not put much emphasis on the xbar.