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# Lot Tolerance Percent Defectives (LTPD) with Rectification Double Sampling Plan

Double sampling plans generally require less sampling than single sampling plans but are more complicated to use.

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, as is the AOQL plan, is normally used on batches, or lots prior, to shipping to a customer ensuring that the outgoing quality matches the specified level for customer acceptance. Several samples are taken randomly, and the number of defectives counted. If the number of defectives exceed a certain number for that sample size the batch is rejected, and 100 percent inspection carried out. Defective items are then removed and replaced with good items ensuring.

For this type of plan, you must specify the AQL and a LTPD. This 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 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 an assumed 3.5% of defectives there is an equal chance of accepting or rejecting the batch.

The sampling plan itself is displayed in a table.

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