Variables Sampling Plan for Lot Average

The BIS.Net Team BIS.Net Team

Variables acceptance sampling plans are used when quality characteristics are measured on a continuous scale. Variables sampling plans tend to be more efficient than Attributes Sampling plans with a much lower sample size.

A variables sampling plan for the lot average (or batch) protects against the receipt, or release of lots whose lot average must not exceed or fall below an unacceptable level. Other types of variables sampling plans are about fraction defectives. Sampling plans for lot averages are relevant when lots are later mixed for processing, whereby lot variability is removed through mixing. Fraction defectives is not relevant due to the mixing process. For example, the cocoa butter fat levels of a batch of cocoa-beans may need to fall within specified levels. Reasonable variability is of little concern as the beans will be mixed during conching.

This plan requires for you to specify acceptable and unacceptable levels for the average, including producers and consumers risks and known standard deviation. The unacceptable level is the worst that can be tolerated. Single or double limits are supported. Our research, supported by simulations, has shown that the theory for unknown standard deviations is dubious and hence Standard Deviation unknown plans are not provided. Instead, reliable results will be achieved by using the Standard Deviation known plans, by first estimating the standard deviation through large enough preliminary sampling and monitoring for changes through control charts. If a change in Standard Deviation is detected the sampling plan needs to be revised.

The sampling plan is operated by taking the required sample size and accepting the computed average falls within action limits and rejected if the computed average falls outside the computed action limit.

The BIS.Net Acceptance Sampling Plan App provides an OC CURVE and the Sampling Plan for its output, such as shown below.

Shewhart chart demonstrating the issues with spc theory

The vertical green lines are the lower and upper acceptable levels. The redlines the unacceptable levels. These cut off points are used only to determine the sampling plan. Just as with specifications product is not suddenly bad once the specification limit is exceeded. The purpose of the OC Curve is to assess the probabilities of acceptance and rejection at all levels of the lot average, not just at the defined acceptable and non-acceptable levels. For example when the Lot average is 11.26 there is an equal chance of accepting or rejecting the lot. If this is unsatisfactory the sample size may need to be increased by defining stricter criteria

Shewhart chart demonstrating the issues with spc theory

For this sample plan a sample size of 3 is taken and if the average is less than 3.75 or greater than 11.26 the lot is rejected.

This sampling plan is robust to non-normality if sample size is greater than 30, however experience has shown that lower sample sizes perform adequately.

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