Tube Design MPN Estimate

Fit a Poisson tube-positivity MPN by maximum likelihood using actual inoculum volumes, replacing a fixed three-tube lookup table.

Description

An MPN estimate infers concentration from positive and negative tube outcomes under a Poisson occupancy model.

An MPN estimate infers concentration from positive and negative tube outcomes under a Poisson occupancy model. Actual original-sample volume per tube determines the positivity probability, so a fixed lookup design is unnecessary.^{[1, 2]}

Fit a Poisson tube-positivity MPN by maximum likelihood using actual inoculum volumes, replacing a fixed three-tube lookup table.

When to use Tube Design MPN Estimate

Use this tool to fit a Poisson tube-positivity MPN by maximum likelihood using actual inoculum volumes, replacing a fixed three-tube lookup table.

Prepare the sample, count, growth or assay measurements requested by this tool. Confirm units, sampling periods and reporting bases; supply independently established comparison criteria where requested.

How to use Tube Design MPN Estimate and understand its results

Prepare the sample, count, growth or assay measurements requested by this tool. Confirm units, sampling periods and reporting bases; supply independently established comparison criteria where requested.
Enter volumesMl, positiveTubes, totalTubes using the field table and calculation rules, then run the tool.
Read mpnPerMl, mpnPer100Ml. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
volumesMl	Volumes ml	list of number	Required
positiveTubes	Positive tubes	list of number	Required
totalTubes	Total tubes	list of number	Required

Supply aligned nonempty lists of positive original-sample inoculum volumes in mL, positive integer total tubes and integer positive tubes no greater than totals. At most 128 groups are supported and the design must contain both positive and negative tubes overall. The helper brackets the likelihood-score root and bisects for 150 iterations, returning MPN/mL and 100 times that value as MPN/100 mL.

P(positive tube) = 1−exp(−concentration × volume)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
mpnPerMl	Mpn per ml	number
mpnPer100Ml	Mpn per 100 ml	number

json

{
  "input": {
    "volumesMl": [
      1,
      1,
      1
    ],
    "positiveTubes": [
      1,
      1,
      1
    ],
    "totalTubes": [
      2,
      2,
      2
    ]
  },
  "output": {
    "mpnPerMl": 0.6931471805599452,
    "mpnPer100Ml": 69.31471805599452
  }
}

Limitations and assumptions

Volumes must reflect dilution's original-sample equivalent. Independent tubes, random distribution and detectable growth from occupied tubes are assumptions; clumping or failed detection can invalidate them. All-positive/all-negative designs are errors here rather than finite estimates.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use MPN Profile Likelihood Bounds: Estimate MPN and profile-likelihood bounds from tube inoculum volumes and counts; caller supplies a likelihood-ratio critical value (about 3.84146 for asymptotic 95%). For a complementary task, use Water Coliform Sample Compliance: Audit water-sample coliform observations against a supplied per-sample allowance, retaining tested volumes; nondetection is not guaranteed sterility.

Further background: Most probable number from serial dilutions.

References

Tube Design MPN Estimate — tool.io
Most probable number from serial dilutions — U.S. Food and Drug Administration

Similar or alternative tools

MPN Profile Likelihood Bounds
Estimate MPN and profile-likelihood bounds from tube inoculum volumes and counts; caller supplies a likelihood-ratio critical value (about 3.84146 for asymptotic 95%).
Water Coliform Sample Compliance
Audit water-sample coliform observations against a supplied per-sample allowance, retaining tested volumes; nondetection is not guaranteed sterility.