Statistical Quality Control

In a double sampling plan, the maximum number of samples taken is two. This means that during the inspection process, the inspector will take a first sample and evaluate it. If the first sample fails to meet the required criteria, a second sample will be taken to make a final decision on the acceptance or rejection of the entire lot. This approach allows for a more efficient and cost-effective inspection process while still ensuring the quality of the products.

A triple sampling plan is not a sampling plan because it is not a recognized or commonly used method of sampling. Single, double, and sequential sampling plans are all well-established and widely used techniques in sampling. However, triple sampling plan is not commonly used or recognized, making it the correct answer.

Producer's risk refers to the risk that a producer or supplier of goods or services faces when a lot is rejected even though the quality is actually good. It is also known as Type I error or alpha risk. This means that the producer may incur costs or penalties due to the rejection of a lot, even if the quality of the products is acceptable.

Consumer's risk refers to the risk that a consumer or buyer may accept a lot or batch of products even if the quality is not really good. This means that there is a finite probability of accepting a lot that does not meet the required quality standards. This risk is borne by the consumer or buyer, as they may end up with a subpar product despite accepting the lot.

The consumer's risk refers to the likelihood that the consumer will accept a bad lot. This means that there is a chance that the consumer will receive and agree to purchase a batch of products that do not meet their expectations or standards. This could result in the consumer being dissatisfied with the quality or performance of the goods they receive.

All the statements provided are true regarding single sampling plans. In single sampling plans, the lot under test will be rejected if the total defective items in the sample exceed an acceptance number "C". Additionally, all items of a random sample of size "n" must be defined and tested. If a sample is rejected, it results in either 100% sampling or the return of the lot to the producer. Therefore, all the statements mentioned are correct.

If the number of defects in a double sampling plan falls between the two cut off numbers C1 and C2, it means that the initial sample did not provide a clear indication of the quality of the lot. In this case, taking another sample would be necessary in order to obtain a more accurate assessment of the lot's quality.

The producer's risk refers to the probability that the consumer will reject a good lot. This means that there is a chance that the consumer may not accept a lot of products that are actually of good quality.

A single sampling plan is a decision rule that determines whether to accept or reject a lot based on the results of one random sample. This means that only one sample is taken from the lot, and based on its results, a decision is made. This is in contrast to sequential sampling plans, where multiple samples are taken and decisions are made based on the cumulative results. Random sampling plan refers to the method of selecting the sample, while double sampling plan involves taking two samples and making a decision based on their combined results.

The average outgoing quality limit (AOQL) refers to the maximum value of the average outgoing quality across all possible values of the proportion defective. This means that it represents the highest average quality level that can be expected for a given proportion of defective items. AOQL is used as a benchmark to ensure that the outgoing quality of a product or process does not exceed a certain acceptable limit.