Control charts with irregular time on x-axis

[#1]

I am watching the STIPS course on quality methods as I want to start making control charts, and I noticed that they said the x-axis should be regular time intervals. I want to use control charts to monitor the controls in a test method, but we do not run this method on regular time intervals. Instead, we run the test whenever sample is available. And it would be costly/impractical to run the test at regular intervals at this time. 

I am wondering what consequences, if any, we'll experience if the data fed into the control chart is collected at irregular time intervals. 

Thanks for your help!

[#2]

It helps to understand what control charts do.  

1. Range charts answer the question: Is the variation captured within subgroup (due to the x's changing within subgroup) consistent/stable?  If so, then you may compare the sources of variation within subgroup to the sources of variation captured between subgroup two determine which sources have greater leverage.  If not you should seek to understand why (this variation may indeed be special cause variation for at least the time period of the control charts).

2. The X-bar (or Y-bar since you are likely plotting Y's) answers the question: Is the variation captured between subgroups (due to the x's changing between subgroup) more than that predicted by the within subgroup variation (this is displayed as control limits on the X-bar chart).  If so, there is more variation between subgroup than within.  The between sources is where the leverage is and where you should focus to reduce variation in the system.  If not, the leverage lies with the within sources of variation.

Since the test method isn't constantly operating (and therefore the between subgroup sources are not changing when you aren't testing, it would be OK to just chart the data when you get it.  Make sure you have identified what sources are captured where on the charts when interpreting the charts.

[#3]

My answer is another way to look at the important points made by @statman. There are many cases in which regular sampling in time is impractical or impossible, but the charts still work as intended. You have a test method (process). You have a stable material (control sample). The control chart will tell you the inherent process variation and what to expect from the assay of the control. I think the fundamental principle is the definition of the rational sub-group in your case. The sub-group should be established such that inherent process variation dominates the variance because the probability of a special cause is negligible. The time between the sug-group sampling should maximize the opportunity for a special cause. So the setup for the replicates at each time point should emphasize common cause variation and exclude special cause variation as much as possible. The time between runs does not have to be regular, but what are the special causes that concern you? Calibration drift, reagent lot changes, changing disposables, mishandling or improper storage of reagents or controls, and so on come to mind.

It is easy to collect data and set up a chart. It is a fundamental tool. A helpful chart requires effort and consideration to be beneficial and trusted.