mytest > help > Part 2. MM4XL Tools > 1. Strategic Tools > Quality Manager > 4. Acceptance Sampling > Hypergeometric Operating Characteristic Curve (HOCC, for small lots)

Quality Manager

Hypergeometric Operating Characteristic Curve (HOCC, for small lots)


The HOCC is used instead of the OCC when the number of lots is small. In the literature it is sometimes recommended that you use the OCC when the sample size exceeds 10% of the lot size. Other authors suggest using the HOCC for samples smaller than 20% of the lot size.

The picture below shows an HOCC drawn with MM4XL's Quality Manager tool. The result can, of course, be printed in a worksheet.

Total Quality Management Control Charts Excel Add-In Software


The HOCC behaves in compliance with the rules governing the Hypergeometric probability distribution function. It can work with small samples, it requires attribute measures, and it assumes only 2 possible outcomes, such as good-bad, on-off, etc. The following is a chart of the Hypergeometric distribution.

Total Quality Management Control Charts Excel Add-In Software


Input data

The input data for the HOCC does not require a worksheet range selection. Instead the user must enter the following values in the tool window:
  • Lot size is the number of items in a lot.
  • Low, is the lower bound of the x-axis (horizontal), cell C39 in the first table of section Output Results in this chapter.
  • High, is the upper bound of the x-axis, cell C61 in the first table of section Output Results in this help chapter.
  • Increment, is the number of defectives in a lot, range C39:C61 in the first table of section Output Results in this help chapter. The value must be smaller than that of the Lot size.
  • Number of columns. These are the lines in the charts. The first column (line) is equal to the probability of finding zero defectives in the lot; the second column is equal to 1 defective in the lot and so on. The number of columns should be lower than the sample size plus one, because there cannot be more defectives than the total items in the sample.


Output results


The HOCC curve works the same way as the OCC, with the difference that the first column of the tables refers to the number of defective items rather than to the percentage. One table and one chart refer to the probability of acceptance of samples.

Total Quality Management Control Charts Excel Add-In Software

Total Quality Management Control Charts Excel Add-In Software


Excel formula for Acceptance
=HYPERGEO(D39;[sample size];C39;[lot size])

The table below shows the probability of rejecting an acceptable lot, found by subtracting the probability of acceptance (see the table above) from one. The information in the table is summarized in the chart Probability of Rejection.

Total Quality Management Control Charts Excel Add-In Software

Total Quality Management Control Charts Excel Add-In Software


Excel formula for Rejection
=1-HYPERGEO(D39;[sample size];C39;[lot size])
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