Variables Sampling Plan - Fraction Defectives - Standard Deviation Known

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.

This type of sampling plan protects against the receipt, or release of lots with excessive defectives. Defectives are items where measurements fall outside specification limits. For example moisture content may be specified for a delivery of a raw material. If the percentage of moisture that falls outside specification limits is excessive the lot will be rejected. The proportion falling outside specification limits is called fraction defective. The percentage is called percent defectives, which is 100 times the fraction defectives.

There are two types of sampling plans provided for fraction defectives plans. One is for standard deviation known and the other standard deviation unknown. (However, if the standard deviation is unknown, more reliable results will be achieved by using the Sd known plans, achieved by estimating the standard deviation through large enough preliminary sampling and monitoring for changes through control charts. (If a change in Sd is detected the sampling plan needs to be revised.)

Because percent defectives is easier to understand for some people, the BIS.Net App uses percent defectives.

This plan requires for you to specify the lower and upper specification limits, the AQL and LTPD, including the producer’s and consumer’s risks and known standard deviation.

AQL is called the Acceptable Quality Level. Some may understandably object to the term Acceptable Quality Level. There should be no such a thing as Acceptable Quality Level some will argue. The only Acceptable Quality Level some say is zero percent defectives according to critics of this concept. However, in the real world many processes cannot consistently produce products without defectives. Each process, it may be argued produces an inherent percentage of defectives, which must be accepted as a ‘fact of life’, until engineering efforts lower the average percent of defectives. Once the inherent process percent of defectives is known, it becomes the AQL.

The Producer’s risk is the probability of rejecting a lot with defectives equal to the AQL. This produce will wish for this probability to be low.

The LTPD is the maximum percent defectives that you are willing to tolerate. Of course, the ideal is 0, but a realistic level is needed, or you will most likely reject every lot. You must also specify the maximum consumers risk associated with the LTPD. The consumer risk is the risk carried by whoever receives the product. It is the percent probability of ACCEPTING lots that are at the LTPD.

The AQL is defined by your process and hence is not something that can be negotiated with your customer. However, your customer may decide to use an alternative supplier if your AQL is considered too high. What needs to be negotiated is the Consumers risk, which is the risk for the customer. Similarly, the LTPD needs to be negotiated with the customer. Defining the AQL, Producer’s risk, the LTPD and Consumer’s risk will determine the sampling plan’s sample size and hence the need for negotiation.

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 purpose of the OC Curve is to assess the probabilities of acceptance and rejection at all levels of percentage defectives

Shewhart chart demonstrating the issues with spc theory

For this sample plan a sample size of 63 is taken and if the average is less than 0.9 or greater than 9.1 the lot is rejected.

This sampling plan is NOT robust to non-normality.

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