# Shifting the Paradigm: Acceptable Quality Level Sampling Can Be Deceptive

April 1, 2011

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This is my first of many blogs for

*Quality*magazine. Because of this, it seems appropriate to first establish the tone of what I plan to cover in blog series.

In business, there are many pink elephant-in-the-room issues, which are not typically discussed. These unchallenged practices or policies often lead to behaviors that result in very unhealthy unintended consequences. In this blog, I will confront many of these traditional methodologies and then describe what could be done to overcome these issues.

The first pink elephant I will confront is Acceptable Quality Level (AQL). The content of this blog was taken from sections 21. 10 and 21.11 of Integrated Enterprise Excellence Volume III, Improvement Project Execution: A Management and Black Belt Guide for Going Beyond Lean Six Sigma and the Balanced Scorecard.

With AQL sampling plans, a lot is inspected to determine if it should be accepted or rejected. Sampling plans are typically determined from tables as a function of an AQL criterion and other characteristics of the lot. Pass/fail decisions for an AQL evaluated lot are based only on the lot’s performance, not on previous product performance from the process. AQL sampling plans do not give a picture of how a process is performing.

AQL sampling plans are inefficient and can be very costly, especially when high levels of quality are needed. Often, organizations think that they will achieve better quality with AQL sampling plans than is possible. The trend is that organizations are moving away from AQL sampling plans; however, many organizations are slow to make the transition. The following describes the concepts and shortcomings of AQL sampling plans.

When setting up an AQL sampling plan, much care needs to be exercised in choosing samples. Samples must be a random sample from the lot. This can be difficult to accomplish. Neither sampling nor 100% inspection guarantees that every defect will be found. Studies have shown that 100% inspection is at most 80% effective.

There are two kinds of sampling risks:

Good lots can be rejected, or

Bad lots can be accepted.

The operating characteristic (OC) curve for sampling plans quantifies these risks. Figure 1 shows an ideal operating curve. Because we cannot achieve an ideal OC curve, we describe OC curves using the following terms:

**Acceptable Quality Level (AQL)**AQL is typically considered to be the worst quality level that is still considered satisfactory. It is the maximum percent defective that for purposes of sampling inspection can be considered satisfactory as a process average. The probability of accepting an AQL lot should be high. A probability of 0.95 translates to an a risk of 0.05.

**Rejectable Quality Level (RQL)**

This is considered to be unsatisfactory quality level. This is sometimes called lot tolerance percent defective (LTPD). This consumer’s risk has been standardized in some tables as 0.1. The probability of accepting an RQL lot should be low.

**Indifference Quality Level (IQL)**Quality level is somewhere between AQL and RQL. This is frequently defined as quality level having probability of acceptance of 0.5 for a sampling plan.

An OC curve describes the probability of acceptance for various values of incoming quality. Pa is the probability that the number of defectives in the sample is equal to or less than the acceptance number for the sampling plan. The hypergeometric, binomial, and Poisson distributions describe the probability of acceptance for various situations.

The Poisson distribution is the easiest to use when calculating probabilities. The Poisson distribution can often be used as an approximation for the other distributions. The probability of exactly x defects [P(x)] in n samples is illustrated in the equation to the left.

Figure 2 shows an AQL operating characteristic curve for an AQL level of 0.9%. Someone who is not familiar with the operating characteristic curves of AQL would probably think that passage of this AQL 0.9% test would indicate goodness. Well this is not exactly true because from this operating curve (OC) it can be seen that the failure rate would have to be actually about 2.5% to have a 50%/50% chance of rejection.

AQL sampling often leads to activities that are associated with attempts to test quality into a product. AQL sampling can reject lots that are a result of common-cause process variability. When a process output is examined as AQL lots and a lot is rejected because of common-cause variability, customer quality does not improve.

In lieu of using AQL sampling plans to periodically inspect the output of a process, more useful information can be obtained by using control charts first to identify special-cause issues. Process capability/performance studies can then be used to quantify the common cause of the process. If a process is not capable, something needs to be done differently to the process to make it more capable.

My next blog will provide an example that quantifies the degree of uncertainty that one can have with AQL testing.

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