How to Do Stability Study on a Measurement System

    Measurement system analysis includes five types of studies: bias, linearity, stability, repeatability and reproducibility. Among all of them, stability study is relevant easy and requires not too much concept in statistics. One can do it with some basic knowledge in SPC.

    Now let’s take a look at the detailed steps for stability study:

1. Pick a sample

    The first step is to pick a sample which will be measured and monitored. The sample is not necessary to be a calibrated standard with known value. It can just be any sample, and its value can also be unknown. But of course, same as any other analysis, this sample must have little within sample variation.

2. Collect the measurement data and establish the control chart with control limits

    Control charts, with established control limits, are needed for stability study. This can be done same as the conventional SPC (You may refer to this article about how to establish the control limits). The difference is, for process control, multiple samples are collected and one datum is read from each sample to form one subgroup, while for stability study, multiple readings are obtained from the same sample, as picked in Step 1, to form one subgroup.

    So how many readings should be obtained for each subgroup and how many subgroups should be collected before the control limits can be established? In P.86 of the 4th edition of AIAG’s MSA manual, 5 measurements are done in each shift, and totally 100 measurements are done to establish the control limits, i.e. 20 subgroups with a subgroup size of 5. But the 2nd edition of AIAG’s SPC manual suggests collecting at least 25 subgroups with at least 100 data points before establishing the control limits (P.57). My personal opinion is to stick with the rules in the SPC manual.

    An example of the control charts established is shown in the graph below. AIAG's MSA manual suggests using Xbar-R or Xbar-s control charts.

Figure 1 Control charts with control limits for stability study, cited from 4th edition of AIAG's MSA manual.

3. Analyze the control charts and determine the stability of the measurement system

    After establishing the control charts and control limits, one can then analyze the control charts and see whether any data point indicates a special cause. Same criteria for identifying the special cause in SPC, as shown below, can be used here.

Figure 2 Criteria for Identifying Special Cause, Cited from 2nd Edition of AIAG's SPC manual

    If no data point indicates a special cause in the control charts, then one can concludes that the stability of the measurement system is good. Otherwise, special cause exists in the measurement system and one needs to identify it and take actions to remove it to improve the stability.

4. Keep on monitoring 

    The stability study of the measurement system is completed up to Step 3. But if you’re careful, you don’t have to stop here. You can just keep collecting readings from the picked sample, with the defined subgroup size and sampling frequency, and plot the measured results in the control charts. By doing so, you are continuously monitoring the stability of the measurement system and actions can be taken whenever a special cause is detected. A continuous monitoring on the measurement system is certainly better than once a year study.