Acceptance Sampling
Reduce Your Inspection Costs
Regardless of your industry, you have to monitor quality to avoid heavy losses in time, money, and good will. While there are a number of methods, including control charts, available to protect you and your customers from poor quality, these methods aren’t always possible or appropriate. In such cases you might think that you have to inspect every part that you receive or ship to ensure quality, but 100% inspection is impractical, as well as expensive and time consuming.
Minitab's acceptance sampling is a practical, affordable alternative to costly 100% inspection. It offers an efficient way to assess the quality of an entire lot of product and to decide whether to accept or reject it.
What is an Acceptance Sampling Plan?
An acceptance sampling plan tells you how many units to sample from a lot or shipment and how many defects you can allow in that sample. If you discover more than the allowed number of defects in the sample, you simply reject the entire lot.
When you create an acceptance sampling plan in Minitab, you specify the worst quality that you’ll accept on a regular basis (referred to as AQL) and the quality level that you'll reject (referred to as RQL). With AQL and RQL values, Minitab calculates the sampling requirements that match the risks that you’re willing to take.
Set your standards too low, and you risk wasting money on a lot of poor quality. Set your standards too high, and you could alienate your suppliers by rejecting acceptable lots.
Creating a simple attributes acceptance sampling plan
Suppose you work for a grocery store that receives a shipment of 540 fresh-cut flowers every week. You want to develop a sampling plan to make decisions regarding the lot without having to inspect all of the flowers. Because some defects are inevitable, you and your supplier decide on quality levels and risks that allow some defects while maintaining profitability for both of you.
You decide that the worst quality you are willing to accept on a regular basis is 2% defective (AQL) and the quality that you want to reject most of the time is 8% defective (RQL). - In Acceptable quality level (AQL), enter 2.
- In Rejectable quality level (RQL or LTPD), enter 8.
- In Lot size, enter 540 and click OK.
The producer's risk is the risk you will reject a good lot, while the consumer's risk is the risk you will accept a poor lot. |  |
Sample PlanYour sampling plan is simple. Randomly sample 98 flowers from your shipment. If you find 4 or fewer defective flowers, accept the entire lot of flowers. Otherwise, reject the entire lot of flowers. |  |
OC CurveThe Operating Characteristic Curve (OC Curve) is additional output that shows you the probability that you will accept lots with various levels of quality.
With this sampling plan, you will accept lots that average 2% defective (AQL) about 95% of the time, and lots that average 8% (RQL) only 10% of the time. |  |
Comparing plans to find the best one
The sampling plan that Minitab automatically suggests is a good starting point, but sometimes people involved in the sampling procedure want you to adjust the sample size and acceptance number. In cases like these you can easily generate multiple plans at the same time and compare OC Curves to find the best plan.
In this example, Minitab compares the original sample plan to three new scenarios:
- More convenient sample size: The inspectors find it most convenient to inspect 10 flowers from each of the nine boxes in the shipment. They want you to change the sample size from 98 to 90.
- Smaller sample size: Looking to save time, your supervisor suggests taking a much smaller sample. He wants you to reduce the sample size from 98 to 50.
- Larger acceptance number: Your supplier is nervous that his shipments will be unfairly rejected. He wants you to raise the acceptance number and accept at least 10 defective flowers before returning an entire lot.
Enter the sample size for each plan that you want to compare, and then enter the acceptance number for each plan in the same order. - Choose Stat > Quality Tools > Acceptance Sampling by Attributes.
- Choose Compare User Defined Sampling Plans.
- In Sample sizes, enter 98 90 50 98.
- In Acceptance numbers, enter 4 4 4 10 and click OK.
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Minitab produces this graph that compares your original plan to the three scenarios.
The black line represents your original sample plan with sample size of 98 (n) and acceptance number of 4 (c). The red line represents a relatively small departure from the original plan, showing a negligible reduction in the producer’s risk and a slight increase in the consumer’s risk. You are willing to change your sample size to a more convenient one to keep your inspectors happy. |  |
The green and blue lines represent more significant changes to the sampling plan which result in more risk than you are willing to accept. Share this curve with your boss and point out that the resulting consumer risk is much too high for you to consider reducing your sample size to 50. Show your supplier that the resulting consumer risk is much too high for you to consider raising your acceptance number to 10. Perhaps you will evaluate other acceptance numbers between 4 and 10. |  |
Putting it to use
Minitab's acceptance sampling plans alone will not magically improve or control your processes. Instead, they offer a handy tool to reduce your inspection costs by providing statistically valid procedures to accept/reject incoming material or final product. They also allow you to easily create and compare various plans to communicate with your team members.