9758

Estimation of Time to Excessive Microbial Count

Many microbial count records in foods and water resemble a random time series. The distribution of the entries allows you to estimate the frequency of future counts exceeding a level deemed undesirable or dangerous. This Demonstration lets you generate Monte Carlo simulations of such counts using the lognormal, normal, log-Laplace, or Laplace distribution function as a model, with hypothetical or experimentally determined parameters, and record the times at which a specified threshold has been exceeded. You can use the distribution and histogram of these times to assess how soon an excessive count might be encountered if conditions remain unchanged.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Snapshots 1, 2, 3: simulated fluctuating microbial counts having a Laplace, normal, or log-Laplace distribution, with the chosen parameters and a histogram of the times to exceed the specified upper threshold
Microbial count records encountered in foods and water frequently resemble a randomly fluctuating time series with the entries having a characteristic underlying distribution. Provided that the entries are independent and have no trend or periodicity, their distribution allows you to estimate the probability, or future frequency, of encountering a count exceeding an undesirable threshold [1–3].
When the counts are taken at fixed intervals, their distribution also allows you to estimate the most probable first time of such an occurrence. This Demonstration generates Monte Carlo simulations of random microbial count series using the lognormal, normal, log-Laplace, or Laplace distributions as the fluctuation model [2, 3]. If the threshold is exceeded, the run terminates. The program keeps every run, which you can view individually with the chosen threshold superimposed. The program also creates and displays a histogram of the times at which the chosen threshold has been exceeded and shows their calculated mean, standard deviation, and skewness.
The counts' distribution function is selected with a setter bar and you can vary its parameters, whether they are hypothetical or obtained from experimental data. You can also change the threshold level, the run to plot, the runs' length, the number of runs to be generated, and the seed, in case you want to generate reproducible count records.
If at a particular setting all the runs start with a count already exceeding the threshold, the plots are replaced by a message in red alerting you to this. A message is displayed in blue when none of the generated counts exceeds the threshold in any of the runs.
References
[1] M. Peleg and J. Horowitz, "On Estimating the Probability of Aperiodic Outbursts of Microbial Populations from Their Fluctuating Counts," Bulletin of Mathematical Biology, 62(1), 2000 pp. 17–35. link.springer.com/content/pdf/10.1006%2 Fbulm .1999.0112.
[2] M. G. Corradini, M. D. Normand, A. Nussinovitch, J. Horowitz, and M. Peleg, "Estimating the Frequency of High Microbial Counts in Commercial Food Products Using Various Distribution Functions," Journal of Food Protection, 64(5), 2001 pp. 674–681. www.ncbi.nlm.nih.gov/pubmed/11347999.
[3] M. Peleg, Advanced Quantitative Microbiology for Food and Biosystems: Models for Predicting Growth and Inactivation, Boca Raton, FL: CRC Press, 2006.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+