Control chart selection of multiple batches review

#1
Hi All,

I recently face an annual quality review for all the batches we manufactured for each plastic component. For each batch, the sampling plan is 1pc every 8 hours.
In regularly, we will look into I-MR chart for each batch to see is there any out of trend, ppk and etc. The reason why choosing I-MR chart is that the subgroup of our sample plan is 1. In the annual review we want to see the process capability across multiple batches, which we will review the Ppk and trends of control chart.

The question here is that, should I use Xbar-R chart or Xbar-S chart instead of I-MR chart? The reason behind this is that I assume the condition is the same per batch.
Or it is still recommended to use I-MR chart to look into every sampling measurement across batches?

Thank you!
 
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Steve Prevette

Deming Disciple
Staff member
Super Moderator
#2
Personally, I prefer the I-MR chart for what you are doing. True, the Xbar-R or Xbar-S may be technically better, especially for trending the standard deviation, but are much harder to explain to managers, and also invoke a time delay of gathering the 4 or 5 sequential results into the Xbar.

By the way, Dr. Wheeler (author of lots of SPC books) advocates the I-mR. As an example, see Microsoft Word - The Chart For Individual Values.doc (scrummaster.dk).
 
#3
@Steve Prevette Thanks for your reply! After I read Dr.Wheeler's article in your reply, I can understand what should we need to pay attention when using I-mR chart. I also have another question to ask about:

If the subgroup size is larger than 1 (e.g. 3 samples / 4 hr), is I-mR chart still suitable for this sampling plan to represent process capability? I read some resource and material that recommend to choose Xbar-R when subgroup is between 2-9. In my opinion, I would expect mR chart lose its function when subgroup is large than 1.
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#4
Process capability can still be calculated from the I-mR chart. The mR chart provides the estimate of the standard deviation (2.66 times the average moving range is three standard deviations, so 2.66 divided by 3 times the average moving range is the standard deviation estimate). In fact, you can find the 2.66/3 number on the Xbar-R tables. I would not hesitate to use the I-mR for process capability.

If you do decide to go to xbar-R (with traditionally the subgroup size is 4 or 5 unless you have a "rational subgrouping" reason to do otherwise) you simply use the Range chart there to get the standard deviation for the capability calculations. You customer or other regulatory reasons my call for Xbar-R where you may choose to go there. But in effect, an I-mR is indeed using the same underlying theory as the Xbar-R.
 

John Predmore

Trusted Information Resource
#5
Instead of starting with your math, I would start by asking about your sampling plan. How did you decide on 1 piece every 8 hours? I gather that 8 hours is probably a work shift. But a lot can change in 8-hours! In the ImR article @Steve Prevette linked is the caveat: "the fact that we are going to compute limits using successive differences means that successive values must be logically comparable. That is, under the conditions expected to prevail when the process is operated predictably, successive values should differ only by what amounts to routine variation."

Part of the wisdom of X-bar charts is the idea of rational subgroups. You said you manufacture plastic components, but you didn't offer any details about your sources of variation. I will assume injection molding, because I have some experience in that department. If you have a multi-cavity mold (let's say 4 cavities for illustration), it may make sense to measure and chart the average of 4 parts from a single shot and call that a subgroup in an X-bar chart. What you know about the 4 pieces molded in a single shot is they all come from a homogeneous sample of material, molded under the same pressure and environmental conditions. Cavity 1 might be consistently bigger than cavity 4 in every shot, but by calling 4 pieces from a single shot a subgroup, cavity-to-cavity variation will be captured in subgroup ranges. If instead you measure individual parts from a 4-cavity mold (chosen at random) for an ImR chart, then cavity-to-cavity variation will be lumped in with shot-to-shot variability, which inflates your standard deviation over time, which reduces your process capability.

Maybe you use single-cavity molds, so my previous example doesn't apply to you. If you have 4 machines with single-cavity molds, and you sample randomly from the combined output of the 4 machines, that arrangement can have a similar effect. Machine-to-machine variation will be lumped in with variability over time, which makes your process appear less capable. It would be better to sample and chart the 4 machines separately for a more accurate picture of process capability, with the added benefit to identify any one machine which behaves differently from the others. But if you sample from the 4 machines at the same time and call that a subgroup for the purpose of a single X-bar chart, machine-to-machine variation will be captured in the within-subgroup variation and not appear in the subgroup-to-subgroup variability, like it will with an ImR chart.

So there are reasons why some people choose X-bar/R charts. It depends on your manufacturing process and your purpose for charting. It is always wise to think about and seek to understand your sources of variation.
 
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