Pharma glass defects – Part 46. Analysis of related defects

Hello everyone – welcome to Part 46 of an ongoing series devoted to visual defects that may occur in pharma glass vials.  I occasionally touch on the topic of related defects – see my prior post on the Malformed and Unfinished Finish defect types.  An understanding of related defects is important because they are a potential source of confusion during the initial identification of a defect.  For example, consider an example in which a lot of glass vials is being evaluated as part of the incoming inspection process at a fill-finish site.  One of the samples pulled as part of the inspection process is reported to have an Adhered Glass defect – let’s assume it’s located on the interior surface of the vial, thereby making it a Major A defect.  However, we later learn that a determination was never made to see if the reported defect was removable.  If the defect had been found to be readily removable, we would presumably be dealing with Loose Glass, a defect which is instead classified as Minor. 

Why is this important?  Recall that the Acceptable Quality Level (AQL) is an important concept in determining whether an incoming lot of material is accepted or rejected by the customer.  The AQL, generally expressed as a percentage or a ratio, is a measure of the worst quality level for a given attribute that is still considered to be acceptable.  For example, an AQL value of 0.65 for a given defect category means that a batch of product is acceptable provided that no more than 0.65% of the sampled batch is found to have that defect.  The value of the AQL will be dependent on the severity classification of a given defect type – i.e., the AQL values will generally decrease in the order Minor > Major B > Major A > Critical to reflect the relative importance of the defect (see Footnote 1).  Going back then to our prior example of Loose Glass versus Adhered Glass, the misclassification of a Minor defect as a Major A defect can be enough to cause a lot of material to be improperly rejected due to the difference in AQL values associated with the Minor and Major A categories.

I could create a table that compiles all of the related defects for converted tubular glass vials in PDA TR 43, but I’m not sure if that’s particularly helpful.  Instead, I wanted to take a crack at creating a visualization that I hope is more intuitive and user friendly.  Figure 1 is one version of a network graph that can be used to illustrate connections between related defects (see Footnote 2).  Each defect is represented by a blue-colored circular node.  The size of the node has been scaled to represent the number of connections (indicated by a black line) shared by a given defect relative to all other defects.  A defect that appears without a blue-colored node is unrelated to any other defect and, by extension, is not touched by a black line.  The nodes are arranged in alphabetical order starting at Adhered Glass (located at the 9 o’clock position on the circle) and going counter-clockwise to end at Wavy Top.

Using this network graph approach, it’s relatively easy to see that the Contamination defect has the largest number of related defect types.  However, the number of nodes in the graph may make it difficult to truly see how many connections are typical among the defects.  Figure 2 is a basic histogram showing the frequency of defects having a given number of connections to other related defect types.  Note that there are 8 defects that have no other related defects (see Footnote 3) and it is most common to only have a single related defect type.  It turns out that the average number of connections is therefore only ~1.1.

This is all sounds relatively straightforward, but I think it’s worth making a few additional points.  First, there are some apparent inconsistencies within the specification of related defects that may be leading to an underestimate of the number of connections among related defects.  For example, PDA TR 43 states that the Crack defect is related to the Check and the Broken General defect types.  However, neither the Check or Broken General entries for related defects include cross references back to the Crack defect.  Second, it would be incorrect to assume that related defects are the only potential options for misclassification of a defect.  I’ve encountered cases in which Tooling Marks were misclassified as Cracks or Checks, neither of which are formally listed as related defects in PDA TR 43.  It’s the same story for Scratches and Checks.  Finally, none of this discussion speaks to the probability of misclassification.   What’s more likely – confusing a Pressure Mark for a Tooling Mark?, a Knot for a Stone?, etc.  I don’t have a good answer here – anyone who has specific experiences is welcome to chime in.  I think it’s generally more likely to see debate  And so while I think Figure 1 is a generally useful and interesting way to consider related defects, it should by no means be regarded as an all-encompassing tool that captures all possible opportunities for misclassification.

Questions or comments? – please leave them below or contact me directly.

Footnotes

1.       The AQL value for a Critical defect deserves extra attention.  In some cases, observing a single instance of a Critical defect is sufficient to trigger the rejection of a batch of glass vials, implying that the AQL is 0.0%.  However, incoming inspection is generally based on sampling from a larger batch of manufactured material.  Finding no instance of a Critical defect in the smaller sample set does not guarantee that no Critical defect will be found in the larger population, and so specifying an AQL of 0.0% is not statistically valid.  Instead, we would indicate “None allowed”.

2.       If you’re curious, Figure 1 was created in Python using the Networkx module.  I started with what is called an “adjacency matrix”, meaning a square binary matrix that describes the absence or presence of a connection between defects using 0 or 1, respectively.  This adjacency matrix gets fed into Networkx to create the network graph using the “shell layout” for arranging the nodes and drawing the appropriate connections.  Finally, the Matplotlib module was used to construct the actual visualization.  There are some alternate layout schemes that might make it a little easier to identify highly connected node, but you also lose the alphabetical ordering that I think makes Figure 1 more user friendly.

3.       The 8 defects that have no other related defects per PDA TR 43 are Airline, Concave Bottom, Flared Bottom, Flared Shoulder, Leaner, Malformed Shoulder, Reboil, and Sunken Neck.