Lot Tolerance Percent Defectives (LTPD) without Rectification Double Sampling Plan

The BIS.Net Team BIS.Net Team

Double sampling plans generally require less sampling than single sampling plans but are more complicated to use. For AOQL and LTPD with rectification sampling plans the expected number of items inspected can be considerably less. For LTPD without rectification sampling plans the saving in number of items inspected is very small because there is no rectification involved. Often sample size for the first sample is considerably larger than the second sample which may cause confusion. The sampling plan is only recommended when the cost of sampling is very high.

For a double sampling plans you take a first sample consisting of n items and each item is checked to see if it is defective. The number of defective items is then counted and compared with the first sample acceptance value for the sampling plan. If the number of defectives is less or equal to the first sample acceptance value the batch is rejected. If it exceeds the SECOND sample acceptance value the batch is rejected. If the number of defectives of the first sample are more than the first sample acceptance value and less or equal to the resample value the batch is resampled. If the total number of defectives of BOTH samples exceeds the second sample acceptance value the batch is rejected and accepted otherwise.

This type of sampling plan can be used on batches, or lots prior to shipping to a customer when rectification is not possible. For example, when testing cans of soft drink for composition, rectification is not possible because every can would have to be opened to test the composition and decide which cans needs replacing. More often the plan is used to screen incoming goods. Rejected batches are returned to the supplier.

Understanding this type of plan requires understanding some basic concepts.

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

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. 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.

High AQL must not be confused with high quality. It means that the average percent of acceptable level of defectives in a batch is high and hence of inferior quality, not high.

LTPD is the maximum percent defectives 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 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. If the LOT has percent defectives better or equal to the AQL it makes no sense to reject such a lot because the process cannot do better. But, because a limited number of samples are taken there will be a risk of rejecting a lot with defectives equal to the specified AQL. This risk is the producer’s risk. 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

Obtaining the sampling plan was historically achieved by using Poisson charts and binomial probability approximations to calculate probabilities of acceptance needed for the optimization. Today using machine power, approximations are no longer needed. BISNET Acceptance Sampling uses Machine Power to obtain exact probabilities of acceptance and 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 an assumed 3.2% of defectives there is an equal chance of accepting or rejecting the batch.

The sampling plan itself is displayed in a table which is used as explained above.

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