The lower specification limit (LSL) is the minimum allowed value for the product or service. This limit does not indicate how the process is performing but how you want it to perform.
The upper specification limit (USL) is the maximum allowed value for the product or service. This limit does not indicate how the process is performing but how you want it to perform.
You must specify at least one specification limit for a variables acceptance sampling plan.
Use the LSL and USL to define customer requirements and to evaluate whether your process produces items that meet the requirements.
Minitab compares your process data to the specification limits to determine whether to accept or reject an entire lot of product.
The historical standard deviation is the known standard deviation of your process. Use a historical standard deviation when you have collected enough data over time to state with confidence what the process standard deviation is. If the process is stable and in control, then you can use a historical standard deviation instead of a calculated standard deviation.
The lot size is the population that you collect your samples from when you decide whether to accept or reject the entire lot.
Often, the lot size is chosen to be convenient for shipping and handling for both the supplier and consumers. For example, a convenient lot size might be an entire shipment. Because sampling plans assume homogeneity of parts in a lot, the units that comprise a lot should be produced under the same process conditions. Also, larger lots are generally more economical to inspect than a series of smaller lots.
The consumer and supplier should agree to the highest defective rate that is acceptable (AQL). The consumer and supplier should also agree to the highest defective rate that the consumer will tolerate in an individual lot (RQL).
To protect the producer, the risk of rejecting a lot that has acceptable quality must be low. To protect the consumer, the risk of accepting a lot that has poor quality must be low.
In acceptance sampling, the sample size is the number of items that are randomly chosen from a single lot for inspection.
The critical distance is the value that Minitab uses to compare with the sample mean and specification limits to determine whether to accept or reject a lot.
For example, suppose you sample lots of plastic pipes. Your sample plan calls for randomly sampling 104 of the 2500 pipes in a shipment. The lower specification for wall thickness is 0.09 inches. Minitab determines the critical distance to be 3.55750.
Minitab calculates the maximum standard deviation (MSD) when you provide both LSL and USL and do not provide a historical standard deviation.
If the Z-values are greater than the critical distance, and if the standard deviation is less than the maximum standard deviation, then accept the entire lot. Otherwise, reject it.
If the Z-values are greater than the critical distance, and if the standard deviation is less than the maximum standard deviation, then accept the entire lot. Otherwise, reject it.
The probability of accepting lots at the AQL should be close to 1 – α. The probability of accepting lots at the RQL should be close to β. The probability of rejecting is simply 1 – the probability of accepting.
The average outgoing quality level represents the relationship between the quality of the incoming material and the quality of the outgoing material, assuming that rejected lots will be 100% inspected and all defective items will be replaced or reworked.
You must specify the lot size in order to calculate the AOQ and AOQL.
In this example, when the average incoming quality level is 100 defectives per million, the average outgoing quality is 91.1 defectives per million. When the average incoming quality level is 300 defectives per million, the average outgoing quality is 28.6 defectives per million. The incoming quality is worse than the outgoing quality because rejected lots will be 100% inspected and will have all nonconforming units replaced or reworked.
You must specify the lot size in order to calculate the ATI.
The operating characteristic (OC) curve shows the ability of an acceptance sampling plan to distinguish between good and bad quality lots. The OC curve plots the probability of accepting lots that have different incoming quality levels for each sampling plan.
In this example, if the actual defectives per million is 100, you have a 0.950 probability of accepting this lot based on the sample and a 0.050 probability of rejecting it. If the actual defectives per million is 300, you have a 0.100 probability of accepting this lot and a 0.900 probability of rejecting it.
The average outgoing quality (AOQ) curve shows the relationship between the quality of the incoming material and the quality of the outgoing material, assuming that rejected lots will be 100% inspected and defective items will be replaced or reworked and inspected again (rectifying inspection).
In this example, when the average incoming quality level is 100 defectives per million, the average outgoing quality is 91.1 defectives per million. When the average incoming quality level is 300 defectives per million, the average outgoing quality is 28.6 defectives per million. The incoming quality is worse than the outgoing quality because rejected lots will be 100% inspected and will have all nonconforming units replaced or reworked.
The worst average outgoing defective level (AOQL) of 104.6 defectives per million occurs when the incoming quality level is 140.0 defectives per million.
The average total inspection (ATI) curve shows the relationship between the quality of the incoming material and the number of items that need to be inspected, assuming that rejected lots will be 100% inspected and defective items will be replaced or reworked and inspected again (rectifying inspection).
The acceptance region plot is used for illustrating sample requirements. When the upper and lower specifications are known, and the standard deviation is unknown, the acceptance region plot lets you see the region of sample means and sample standard deviations for which you will accept a lot.
As the sample standard deviation increases and approaches the maximum, the mean needs to be on target for you to accept a shipment. If the process variation is tight and the standard deviation is small, the mean can vary between the specification limits.