Mean kinetic temperature: what it measures, and where it misleads

Mean kinetic temperature is the figure a stability or storage protocol asks for when an average is not good enough. It answers one question: did the product experience more thermal stress than the condition it was supposed to be stored at?

It is also a figure that is easy to calculate wrongly, and easier still to calculate correctly from a record that is incomplete. This article covers what MKT measures, why it behaves the way it does, and what to check before you trust one.

Why an average is the wrong answer

Chemical degradation does not respond to temperature in a straight line. It speeds up roughly exponentially as temperature rises, which is the relationship the Arrhenius equation describes. An hour at 30 °C does more damage than an hour at 20 °C undoes. So a history that swings above and below 25 °C is harder on a product than a steady 25 °C, even when the two have exactly the same average.

Mean kinetic temperature captures that. It is the single constant temperature that would have had the same cumulative effect as the actual, varying history. Two consequences follow:

• MKT is always at or above the arithmetic mean. They are equal only when the temperature never varied.
• The more the temperature varied, the further MKT sits above the mean.

A worked example makes the size of the effect concrete. A product spends half its time at 20 °C and half at 30 °C. The average is 25.00 °C. The mean kinetic temperature is 26.26 °C. The warm half counts for more than the cool half gives back, and an average would have hidden more than a degree of real thermal stress.

How it is calculated

ProcessView+ uses the Haynes formulation of the Arrhenius relation:

MKT = (ΔH/R) ÷ −ln( (1/n) × Σ exp( −(ΔH/R) ÷ Tᵢ ) )

• Tᵢ is each reading, converted to kelvin.
• n is the number of readings.
• ΔH is the activation energy. The conventional value is 83.144 kJ/mol.
• R is the gas constant, 8.3144 J/(mol·K), which makes ΔH/R exactly 10 000 K. That round number is why 83.144 is the conventional figure.

Three details in that formula are where calculations go wrong.

It must be done in kelvin. The exponential only works on absolute temperature. A spreadsheet that feeds Celsius into the formula produces a number that looks plausible and is wrong.

The unit must be known, not assumed. A Celsius run read as Fahrenheit, or the reverse, gives a confident, reasonable-looking, wrong answer. ProcessView+ reads the unit each channel recorded, and if a session never recorded one it gives no figure rather than guess.

The activation energy is a convention, not a law. 83.144 kJ/mol is the value used when a product’s own activation energy is not known. If your protocol specifies a different value for your product, a figure calculated with the conventional one answers a slightly different question.

Which readings are included

MKT is meaningful over everything the product experienced, so ProcessView+ includes every logged reading of the channel over the whole run, including ramps. A figure calculated only over the soak describes the chamber’s best behaviour and leaves out the part where a product is most likely to see a temperature it should not.

Some protocols define the period differently, for example only the storage period between two pull points. If yours does, check that the figure you are reading covers the same period.

MKT is per channel, and only for temperatures

A stability chamber records temperature and humidity. MKT only means something for a temperature, so it is calculated for each channel separately, and a humidity channel says what it is instead of showing a number: (no MKT — parameter 2 ‘Humidity’ records %RH, not a temperature). That is the correct answer, not an error. A report that shows an MKT for a humidity channel has done arithmetic on the wrong kind of number.

The failure that looks like success: a partial record

MKT is calculated from readings, and a record can be missing some without anything looking wrong. A logging interruption leaves a hole, the calculation runs on the readings that exist, and out comes a figure with no sign that part of the history is absent. If the missing stretch was the warm one, the figure is low, and nothing tells you.

ProcessView+ checks for this. It takes the logging interval the session recorded, and any gap between readings longer than 1.5 times that interval counts as missing the readings the schedule expected in it. When readings are missing, the figure is still calculated, and always shown with its coverage:

25.11 °C (partial — 98.7% coverage, 4 rows missing across 1 gap)

Coverage is rounded down, so a record is only ever shown as 100.0% when it is complete.

A boundary worth knowing. That check finds holes in the log. It does not catch readings that were written on schedule while communication with the controller had failed, which repeat the last value rather than leaving a gap. MKT counts those readings as logged. ProcessView+ marks them separately, as sample coverage, and states it beside the verdict on the QA report. When you read an MKT, read the sample coverage next to it.

What MKT does not tell you

• It does not show short excursions. A two-hour spike to 40 °C in a month at 25 °C moves the MKT by about a tenth of a degree. The product may still have been out of its storage condition in a way your protocol cares about. Time in tolerance and the excursion record answer that; MKT does not.
• It says nothing about humidity. A chamber can hold a perfect MKT and lose its humidity for days.
• It is not a verdict. MKT describes the thermal history. Whether that history is acceptable is a judgment against your specification.
• Two readings are the minimum the arithmetic needs, not a recommendation. Whether a given number of readings over a given period is enough for your protocol is not something the software decides.

Five checks for any MKT figure

1. Was it calculated in kelvin? If it came from a spreadsheet, check the formula.
2. Is the unit of each channel known? A figure from a channel with no recorded unit is a guess.
3. Does it cover the right period? Whole run, storage period, or soak only.
4. Is the record complete? Look for a coverage figure. No coverage figure is not the same as 100%.
5. Were the readings actually observed? Check sample coverage for communication outages.

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ProcessView+ calculates MKT per channel for every run, shows it on the QA report cover with its coverage when the record is partial, and includes it in the signed audit record when electronic signatures are enabled. The free trial’s Stability Demo produces an MKT on a real report, on a built-in controller simulator. Demonstration runs are simulated and are not test results.