How do I Calculate and Interpret Stability Index?

[#1]

I am using the Process Capability platform and see in several places a "Stability Index" is calculated.  But I cannot find in the help documentation a definition for how Stability Index is calculated.  Can anyone help?

[#2 · Accepted solution]

The Process Screening Report - Stability Index 

[#3]

Just be sure to understand how Overall and Within Sigma are calculated.  

Stability Index = (Overall Sigma / Within Sigma)

Stability Ratio = (Overall Sigma / Within Sigma)^2

Overall Sigma is straightforward and assumes the data belongs to one big subgroup.  The sigma is calculated in relation to the grand mean of the data. The sum of squared distances from each observation to the grand mean.  Divided by the total number of observations.  

Within Sigma is not so straightforward and depends on the principles of rational sampling and rational subgrouping.   It can be calculated many different ways and that depends on the subgrouping.  Does it it make sense to subgroup the data in this way and if so why? 

If we subgroup "unlike things" together, then we will confuse within subgroup variation with between subgroup variation - we don't want this because then chart limits don't help us detect a meaningful signal.  So we have to think about things like: processing history (sequence of manufacture) and whether or not parts come from the same oven(s) or are made within the same hour(s).

[#4 · Accepted solution]

Here is a cut and paste from a search of the help pages for "stability index calculation"

Stability Index

A measure of stability of the process. A stable process has a stability index near one. Higher values indicate less stability. The stability index is defined as follows:

(Overall Sigma / Within Sigma)

If a three way control chart is selected in the launch, the stability index is defined as follows:

(Overall Sigma / Between-and-Within Sigma)

[#5]

hello team,

any idea of criteria for instability index? 

Istab close to 1 is not realistic because if within sigma is globally the Machine variation, there remain 4 other Ms (Man, Method, Material, Mother nature) that contribute to overall sigma

If we consider that the variances of each M are similar, a rule of thumb be can be Instability index < 2.23 (square root of 5) for a stable process

Can you please challenge this criteria

Regards,

François

[#6]

I do not have a criterion for this index.

The ratio is defined by the overall variation (standard deviation for entire sample, no subgroups) and the average variation within subgroups (average standard deviation with bias correction). The index, therefore, depends on the definition of the rational subgroup used in a given control chart construction. How does machine or other factors define the rational subgroup and the overall sample?

[#7]

@francois_berger I echo @Mark_Bailey's commentary. 

Here is some more info that might help.

There doesn't seem to be a strong consensus in the literature around a threshold criterion on the stability index ("close to 1" is mentioned in the literature but that's a rough rule of thumb). From practitioner point of view, I think we should use logic to explain and defend the threshold chosen for our analysis (ideally based on some predefined "risk level" or documented risk assessment). 

Per our support documentation: In the The Process Screening Report, we say that "A stable process has a stability index near one. Higher values indicate less stability."  In  Process Performance Plot we say: "A stability index that exceeds 1.25 indicates that the process is unstable." 

In this paper [1], Sall writes: "With hundreds or thousands of processes, it is good to make a report with the processes sorted so that the ones of greatest concern are at the top.” Sort by Stability Ratio" [or Stability Index (SI), which is just the square root of the Stability Ratio; see section of the paper entitled Process Stability Measures]. 

In this paper [2], the authors make a compelling argument that the SI should be used as a screening check on "process state" rather than a measure of "stability."  They also detail their own procedure for using SI in the discussions section (pp. 12-14). 

References: 

[1] Sall, J. "Scaling-up Process Characterization." Quality Engineering 30, no. 1 (2018): 62–78. https://doi.org/10.1080/08982112.2017.1361539.

[2] Wang, J., & Wang, Y. (2023). Investigation of the real meaning of the stability index and its empirical analysis. Processes, 11(10), 2958. https://doi.org/10.3390/pr11102958

[#8]

Thank you!

[#9]

Stability Index of >1 could be an indicator of potential special cause variation in the process. I recommend testing the observations for stability violation before conducting capability study.