How Many Samples Do You Need to Be Confident Your Product Is Good?

How Many Samples Do You Need to Be Confident Your Product Is Good?

By Discovery Lean Six Sigma

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How Many Samples Do You Need to Be Confident Your Product Is Good?

How many samples do you need to be “95% confident that at least 95%—or even 99%—of your product is good?

The answer depends on the type of response variable you are using, categorical or continuous. The type of response will dictate whether you 'll use:

  1. Attribute Sampling: Determine the sample size for a categorical response that classifies each unit as Good or Bad (or, perhaps, In-spec or Out-of-spec).
  2. Variables Sampling: Determine the sample size for a continuous measurement that follows a Normal distribution.

The attribute sampling approach is valid regardless of the underlying distribution of the data. The variables sampling approach has a strict normality assumption, but requires fewer samples.

In this blog post, I'll focus on the attribute approach.

Attribute Sampling

A simple formula gives you the sample size required to make a 95% confidence statement about the probability an item will be in-spec when your sample of size n has zero defects.

, where the reliability is the probability of an in-spec item.

For a reliability of 0.95 or 95%,

For a reliability of 0.99 or 99%,  

Of course, if you don't feel like calculating this manually, you can use the Stat > Basic Statistics > 1 Proportion dialog box in Minitab to see the reliability levels for different sample sizes.  


1-proportion test

1-proportion output

These two sampling plans are really just C=0 Acceptance Sampling plans with an infinite lot size. The same sample sizes can be generated using Stat > Quality Tools > Acceptance Sampling by Attributes by:

  1. Setting RQL at 5% for 95% reliability or 1% for 99% reliability.
  2. Setting the Consumer’s Risk (β) at 0.05, which results in a 95% confidence level.
  3. Setting AQL at an arbitrary value lower than the RQL, such as 0.1%.
  4. Setting Producer’s Risk (α) at an arbitrary high value, such as 0.5 (note, α must be less than 1-β to run).


By changing RQL to 1%, the following C=0 plan can be obtained:

If you want to make the same confidence statements while allowing 1 or more defects in your sample, the sample size required will be larger. For example, allowing 1 defect in the sample will require a sample size of 93 for the 95% reliability statement. This is a C=1 sampling plan. It can be generated, in this case, by lowering the Producer’s risk to 0.05.

As you can see, the sample size for an acceptance number of 0 is much smaller—in this case, raising the acceptance number from 0 to 1 has raised the sample size from 59 to 93.

Check out this post for more information about acceptance sampling



By: Jim Colton
Posted: July 12, 2017, 12:00 pm

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