A reader asks
“I want practice to SPC method to know whether my production process is in control, in case of all data available is from batch to batch, is it rational to construct the sub-group based on batch to batch data? What conclusion can I get from batch to batch? Any suggestion? Thank you very much.”
The answer is, maybe. I’d need a more complete description of your process so I can figure out what you mean. For example, I don’t know if your process is chemical, mechanical, or electrical. I don’t know if batches are arbitrarily created by filling a container from a larger container. Et cetera.
The guiding principle is called rational subgrouping. Your control limits should compare long-term variability to limits based on short-term variability. The underlying premise is that in a stable process there won’t be any long-term variability unless something substantial changed in the process, i.e., a special cause. Usually this would mean basing your control limits on within-batch variation and plotting batch-to-batch results against these limits. However, for some processes this doesn’t work because there’s too little variation within a batch compared to between batches. For example, in a homogenous chemical solution the within batch variation may be miniscule. The solution in these cases is to use individuals control charts and base control limits on moving ranges from subgroups formed by consecutive observations. And if your data are autocorrelated (i.e., observations taken at close to the same time are correlated), then the sampling interval of the individuals chart will need to be adjusted.
Take a look at your process and see if this works for you.
PS: You may also wish to look at the article by John David Kendrick.