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Lot Tolerance Percent Defects (LTPD) without Rectification Sampling Plan

The BIS.Net Team BIS.Net Team

This sampling plan must not be confused with Lot Tolerance Percent Defective sampling plans. Instead of taking a sample of n items and counting the number of defectives, a sample of n items is taken, and the number of defects counted. Rectification plans are not applicable for defects sampling plans.

The most common application is for testing incoming goods, but outgoing goods can also be tested as final protection.

Understanding this type of plan requires understanding some basic concepts.

Lots or batches (used interchangeably below) for Attributes Sampling Plans consist of discrete items.

A sampling plan consists of a sample size and acceptance value. A lot is rejected if the number of defects in the total of samples taken exceeds the acceptance value.

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 defects. However, in the real world many processes cannot consistently produce products without defects. Each process, it may be argued produces an inherent number of defects, which must be accepted as a ‘fact of life’, until engineering efforts lower the defect rate.

The BIS.Net Acceptance Sampling App defines AQL as the average number of defects per 100 items which is inherent to the process until engineering changes reduce it.

High AQL must not be confused with high quality. It means that the average number of defects per 100 items produced by an in-control process is high and hence of inferior quality, not high quality.

LTPD is the maximum average number of defects per 100 items that can be tolerated. Of course, the ideal is 0, but a realistic level is needed, or the sampling plan will most likely reject every lot.

For this type of plan, you must specify the AQL and an associated producer’s risk and a LTPD(defects) and its associated consumer’s risk. The producer’s risk is the risk to whoever produces the product. It is the percent probability of REJECTING the lot at the AQL. To design your sampling plan, you need to specify this risk with a reasonable value.

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.

If the plan is used to screen incoming goods, then the AQL should be provided by the supplier. The producer’s risk should be decided by the producer. The LTPD is decided by the recipient i.e. the consumer as should the consumers risk. In practice both parties should agree on the AQL, LTPD, Producer’s and Consumer’s Risks

BIS.Net Acceptance Sampling uses Machine Power to obtain exact probabilities of acceptance, based on the Poisson distribution to find the optimum sampling plan.

The output includes an OC curve as shown below, which can be used to determine the probability that a lot will be accepted or rejected at a hypothetical quality level. For example, at the assumed 4.5 defects per 100 units there is an equal chance of accepting or rejecting the batch.

Shewhart chart demonstrating the issues with spc theory

The sampling plan itself is displayed in a table. The sample size and acceptance value define the plan. The Producer’s risks and Consumer’s risks are the actual risks for the sampling plan. Due to the discreteness of the sampling plan the exact values will not always equal the specified plan.

Shewhart chart demonstrating the issues with spc theory
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