Lot Tolerance Percent Defectives (LTPD) with Rectification Single Sampling Plan

The BIS.Net Team BIS.Net Team

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 high quality.

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 defectives in the sample size 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 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.

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.

Average Outgoing Quality is the average percentage of defectives in lots which is released to the customer. Like the above, a high AOQ does not mean high quality but inferior quality.

With a rectification sampling plan the average AOQ is lower than the average percent of defectives prior to sampling. The reason is that some batches will be rejected, and hundred percent inspected and then rectified. The zero defectives in the rectified batches lowers the average percent of defectives in all released outgoing lots.

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 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 both the LTPD and Consumer’s risk will determine the sampling plan’s sample size and hence the need for negotiation.

The algorithm used by BIS.Net Analyst will obtain the sample size and acceptance value which minimizes the total number of items to be inspected (taking into account those when 100% inspection is required) when the lot has defectives at the AQL level, whilst ensuring the consumer risk is less, or equal to the one specified for the specified LTPD.

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 3.5% of defectives 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 risk is the risk of falsely rejecting the batch at the AQL. The Consumer’s risk is the actual risk obtained as compared to the specified risk. Due to the discreteness of the sampling plan the exact values will not always equal the specified plan. These exact values are displayed in the table.

The expected items inspected is the average number of items inspected when lots are at the AQL. This includes items inspected for lots rejected which are then 100 percent inspected.

Shewhart chart demonstrating the issues with spc theory
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