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Tolerance regions with segmented fermentation processes

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Abstract

Many microbial fermentation processes exhibit different phases (e.g. adaption phase, main growth phase, main production phase). The process variables e.g. the biomass vary randomly about their mean. The experimentalist is interested to know the break points of the different phases, and a tolerance region, i.e. a range of possible values of the process variable that can be considered as normal. This paper deals with statistical methods for determining break points and tolerance regions.

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Abbreviations

a i :

intercept in phasei

b i :

specific growth rate in phasei

e t :

deviation of a measurement in timet

tEX :

expectation of variableX

r :

number of phases of fermentation

T i :

break point of phaseit

t ij :

time of measurementj in phasei

t n−2.1−α/2 :

quantile oft distribution

Y(t) :

logarithm of measurement at timet

1 −α :

cover probability of tolerance region

1 −β :

part covered by the tolerance region

σ 2 :

variance ofe t

φ(·) :

standard normal distribution

\(\chi _{n_i - 2, 1 - \alpha }^2\) :

quantile of chisquare distribution

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Authors and Affiliations

  1. Hans-Knöll-Institut für Naturstoff-Forschung, Beutenbergstr. 11, 07745, Jena, Germany

    M. Horn, W. Rausch, M. Peißker & D. Riesenberg

Authors
  1. M. Horn
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  2. W. Rausch
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  3. M. Peißker
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  4. D. Riesenberg
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Horn, M., Rausch, W., Peißker, M. et al. Tolerance regions with segmented fermentation processes. Bioprocess Engineering 9, 259–262 (1993). https://doi.org/10.1007/BF01061531

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  • DOI: https://doi.org/10.1007/BF01061531

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