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

Quality Manager

Operating Characteristic Curve(OCC, for large lots)


The OC analysis of sample plans helps to provide the desired consumer and producer risk. Consumer risk is the risk of accepting low quality lots, also called Type I risk (alpha). Producer risk is the risk of rejecting good quality lots, also called Type II risk (beta). The OCC plots the probability of acceptance for different levels of quality, and the objective is to be able to accept lots according to the desired acceptance quality level (AQL) 95% of the time.

The picture below shows an OC analysis 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 OCC behaves in compliance with the rules governing the Binomial probability distribution function. It requires large samples and assumes a low probability of occurrence for nonconformities, it works with attribute measures, and it assumes only 2 possible outcomes, such as good-bad, on-off, etc. A chart of the Binomial distribution is shown in the material concerning P-charts in this help file.

Input data The input data for the OCC does not require a worksheet range selection. Instead the user must enter the following values in the tool window:
  • Sample size is the number of items in a lot.
  • Low, is the lower bound of the x-axis (horizontal), cell A10 in the first table of section Output Results in this help chapter.
  • High, is the upper bound of the x-axis, cell A29 in the first table of section Output Results in this help chapter.
  • Number of classes, e.g., rows 10-29 in the first table of section Output Results in this help chapter.
  • 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


Output from the OCC is made up of two charts and two tables in accordance with the user's selection in the third window.

The table below shows the Acceptance curve, which is the probability of accepting a lot according to different levels of error (columns from zero to four). We read, for instance, 64% in cell D14. This means that if 4% (cell A14) of items in the lot are defective there is a probability equal to 64% that the lot will be accepted as a good one according to our hypothesis in cell D9 that only 2 items are defective. The information in the table is summarized in the chart Probability of Acceptance.

Total Quality Management Control Charts Excel Add-In Software

Total Quality Management Control Charts Excel Add-In Software


Excel formula for Acceptance
=BINOMIAL(B9;[sample size];A10)

The table below shows the probability of rejecting an acceptable lot, which is 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-BINOMIAL(I9;[sample size];H10)
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