Feller Correction Explained

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What is the Feller Correction?

When using a microbial air sampler, there is a statistical probability that one or more viable microorganisms enter the same hole in the sample head, and impact in the agar forming only one (1) colony forming unit, rather than two (2) colony forming units. In the particle counter world, this is referred to as "Coincidence Error." The probability theory that the Feller Correction equation is based was developed in 1968 by William Feller, and first introduced in 1989 byJanet Macherfor use in multi-jet microbial air impactors having between 200 to 400 holes. The equation provides a statistical adjustment to account for the probability of two or more microorganisms entering the same inlet.

The main premise is the larger the number of holes and smaller diameter of holes, the lower the probability of 1 or more microorganisms entering the inlet. Also, as can be seen above, the higher the CFU count, the larger the correction. In the pharmaceutical industry, after 250 CFU's the sample is classified as, "Too Numerous To Count" (TNTC). 

The Feller Correction for most microbial air samplers will generally not start making adjustments until 18 to 21 colony forming units are enumerated, depending on the manufacturer. Grade A and B clean areas generally have recommended CFU limits of LESS THAN 1 or 10 respectively. If CFU counts in these clean areas approach the Feller Correction limits, you obviously have a much larger problem than a Feller Correction.

Therefore, in the life science industry, the Feller Correction has somewhat limited impact on production.

Weaknesses of the Feller Correction

One of the main complaints, particularly among manufacturers of high efficiency samplers, is that the equation does not take into consideration inlet geometries, inlet or impaction velocity, design efficiency/inefficiency, physical collection efficiency, or biological collection efficiency. Also, contrary to the assertions made by some manufacturers, it cannot be applied to slit-to-agar impaction samplers, or non-impaction samplers.

Beware of marketing hype

The Feller Correction does not confirm the air sampler has superior physical and biological collection efficiencies. Indeed, designing a microbial air sampler is a balancing act, really a dance between physical collection efficiency, biological collection efficiency, and the Feller Correction. We know that among all manufacturers of microbial air samplers that there are vastly different physical and biological collection efficiencies. This is further evident in differing theoretical and experimental d50 values (Yao, 2006).  With low efficiency samplers, the experimental d50 particle size will be greater than their theoretical d50 value.  In certain cases, because of design errors among some manufacturers (not Climet) users will need to order petri dishes with a custom agar fill of upwards of 50ml to fulfill the new requirements of ISO 17141. 

Applied to Slit-to-Agar Sample Heads?

No. Macher's Feller Correction cannot be applied or adapted to slit-to-agar sample heads, which becomes very apparent if one reads Janet Macher's 1989 research article that introduces the use of a Feller Correction with multi-jet impactor microbial air samplers typically having 200-400 holes. 

Problem #1: Slit-to-Agar undercounts
In the article, Macher did a comparison study with a slit-to-agar sampler and a multi-jet impactor. It was concluded the slit-to-agar routinely undercounted compared to the multi-jet impactor unless the air concentration was above 1400 cfu/m3. According to the FDA, when the number of CFU per plate exceeds 250, it is recorded as Too Numerous to Count (TNTC) [Source].

Problem #2: Feller Correction Not Scientifically Supported
Regarding slit-to-agar,  there is at least one claim that, "Particles tend to run in straight lines and adhere to surfaces (agar plates) directly in their path." This is certainly true for settlement plates in a laminar flow area. However, if you understand how an active air microbial sampler works, this claim is completely unsupported by any academic or reliable scientific sources. To the contrary, for decades it has been a well-known fact that Microbe Carrying Particles (MCPs) have varying trajectories as they enter the inlet of the impaction sampler. Also, physical collection of active air samplers can vary with smaller MCPs (with less mass) having a lower probability of impaction into the agar surface and therefore being uncollected  [ Yao (2006), Stewart, et al. (1995), and Whyte et al. (2007) ]. Please, refer to the images above.

Indeed, the trajectory (or path) of a microbe carrying particle (MCP) is highly influenced by: (1) the size or mass of the MCP; (2) the inlet velocity and air stream; and (3) inlet geometries. Subsequently, the claim that a slit-to-agar sample head can be referenced as 1,650 holes takes a wonderful piece of imagination and runs contrary to all academic and scholarly sources.

Conclusion
On rare occasions, a customer has requested that Climet design a slit-to-agar sample head. To confirm. Climet will not design or support a slit-to-agar sample head due to inherent unreliability, propensity to undercount, and inability to accurately and scientifically calculate the Feller Correction. It is Climet's belief that a slit-to-agar sample head could be used in an IAQ (Indoor Air  Quality) investigation, but has no business  being utilized in a regulated life science clean area.