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, such as control charts, that can help 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, and costs too much time and money.
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 can accept.
Set your standards too low, and you could waste 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 that 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 a decision about the lot without inspecting all of the flowers. Because some defects are inevitable, you and your supplier decide on quality levels and risks that allow some defects but maintain profitability for both of you.
You decide that the worst quality you can accept on a regular basis is 2% defective (AQL) and the quality that you want to reject on a regular basis 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.
- Click OK.
The producer’s risk is the risk that you will reject a good lot, and the consumer’s risk is the risk that you will accept a poor lot
Your 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.
The Operating Characteristic Curve (OC Curve) 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 you need 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: 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 concerned that his shipments will be unfairly rejected. He wants you to raise the acceptance number and accept at least 10 defective flowers before you reject 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.
- Click OK.
Minitab produces this graph which 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 and shows a negligible reduction in the producer’s risk and a slight increase in the consumer’s risk. You decide 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 can accept.
Share this curve with your boss and point out that the resulting consumer risk is much too high to reduce your sample size to 50.
Show your supplier that the resulting consumer risk is much too high to raise your acceptance number to 10. Perhaps you will evaluate other acceptance numbers between 4 and 10.
Putting acceptance sampling to use
Minitab’s acceptance sampling plans alone do 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.