Acceptance Sampling Inspection

Automotive inspection, TS 16949, IATF 16949


We have an Acceptance sampling inspection in place where we use the ANSI/ASQ Z1.4 – 2013 standard under Normal Inspection, using General Inspection Level II to drive our samples size and accept, reject criteria. We do not uses switching rules as we have always found them too difficult to manage. I have two questions.

If I have one lot that fails Acceptance sampling and I am trying to bound the issue is it suitable to bound it to the one affected lot if the lot before and after pass or do I need to carry out additional sampling.

My second question is if I have a batch that passes acceptance sampling but at a subsequent downstream process a defect being inspected for by the upstream acceptance sampling inspection is found how do I determine if the lot is acceptable? Do I trust the acceptance sampling inspection or react?


The first question is not an uncommon one and actually it is a good practice to isolate the lot and do 100% inspection of it.  That way you can estimate the % defective and if another failure occurs in the next 5 lots, then increase the sampling until you have some confidence that the supplier has fixed the problem.  Once that confidence is restored, then you go back to what you inspected originally.

The second question, is one that you have to understand how well do you follow the acceptance sampling process?  If your alpha level is at 95%, 5% of the time, you can accept a bad batch as good. That is the pure definition of the alpha risk.  If this failure falls within the 5%, your process is working and while you sort through the lot, and notify the supplier, it is not something that you over react to.

I hope this helps.


James Bossert, PhD, MBB, CQA, CQE, CqM/OE
Sr Performance Improvement Consultant

Z1.4: 2008 Sampling

Audit, audit by exception


We are having an interpretation issue regarding the ANSI/ASQ Z1.4:2008 standard with some of our component vendors. We have a number of different defects that fall into an AQL of 1.0.

Please note that the same question applies to all AQL levels, as our critical and minor defects can also have multiple defects.

Our interpretation of the standard is that if the sampling plan table (based on sample size and inspection level) shows Accept 7 / Reject 8 then all defects in this major category would be cumulative for the accept / reject criteria. (i.e. 3 that fail outer diameter, 3 that fail height of the bottle finish and 3 that fail weight – total of 9 – would constitute a rejection of the lot). The vendor’s interpretation is that each of the items within the major category should have an accept / reject allowance of 7 / 8 (so potentially, in this case, 56 defects would still be accepted).

Can you please forward my question onto a suitable SME at ASQ for help with this matter? Please let me know if you need any further information or clarification.

Thank you again.


In this case, it depends on the question the lot sampling is trying to answer. If they want to know if individual units within the lot are acceptable – based on all criteria that is considered acceptable, then the tally of all defects found is correct. This is further supported by any item with one of the many specifications out of range would be deemed a failure.

On the other hand, if the lot sampling is to detect lots with specific faults, isolated to a specific specification then the defect types would be considered separately. If the AQL 1.0 is suitable for the specific defects, then considering them separate for the 8 criteria would no longer be an overall ASQ 1.0 protection; it would be much less.

Your example of 56 defects being accepted underscores the point that the AQL protection is no longer 1.0.

I’m assuming the specifications and causes of the defects are independent, yet that may not be the case. When not independent I’m not sure how to adjust the sample size to a present the same AQL protection. When independent you would need separate draws of samples for each defect of interest, then apply the Accept 7/Reject 8 criteria judging only the one specification.

In practice, if you want to inspect for isolated specifications, one should allocate the acceptable AQL and LPTD points and develop your sampling plan from there. Instead of a 1.0% defect rate for AQL it would need to less for one of the Reject 8 specifications; try 0.125 so that the tally of failure rates across the various specification of interest (assuming the possibility of failing any specifications is equal). This will lead to much larger sample sizes that may be useful when troubleshooting specific faults.


Z1.4: Selecting the Sample Size

Pharmaceutical sampling

Q: I work for a pharmaceutical company that manufactures soft gel capsules. What is the proper way to select a sample size when using ANSI/ASQ Z1.4-2008: Sampling Procedures and Tables for Inspection by Attributes?

I’ll further illustrate my question with an example.  If one were to have a batch size of 20,000 units, according to General Inspection Level II, Normal, the corresponding letter code is “M.” In the master table for Acceptable Quality Levels (AQLs), the sample size would be 315 units.  If my AQL is 0.010 (with an acceptance/rejection number of 0/1 based on the table), does my sample size change to 1250 units? Or does it remain at 315 units?

Your assistance is greatly appreciated.

A: The simple answer is 1250, not 315 suggested for sample size letter M.  General Inspection Level II, Normal, shows that for a lot size of 20,000, a sample size code level of M corresponds to a sample size of 315.  For an AQL of 0.01, the arrow points to a sample size of 1250 (sample size letter code Q) to have the required AQL of 0.01.

The calculation of AQL is not dependent on lot size.  In other words, a sample size of 315 gives a minimum AQL of 0.04, so a larger sample is required to estimate an AQL of 0.01.

Q2: Could you please add another layer to your response? The reason I’m seeking additional clarification is that the first step in determining the sample size is to find the letter code and the corresponding sample size. To me, it feels like the first step should be to determine the AQL.

A2: Let me expand with a more technical explanation.  Attribute sampling is based on the hypergeometric distribution and is estimated using the binomial distribution (which assumes an infinite population size).

The basic formula for the binomial is:

2.1.2013 1

AQL and LQ for a given sample size (n) and defects allowed (x): 2.1.2013 2

If n=30, x=0; AQL=0.17%; LQ=7.4%:

2.1.2013 3

2.1.2013 4

If you are using Z1.4, your sample size is selected based on your lot size.  Then, you would pick the AQL you need based on the risk you are willing to take for the process average of percent defective.  If you decide to not use Z1.4, but instead use the binomial directly, then you are correct that you would decide on the AQL and lot tolerance proportion defective (LTPD) first, then calculate a sample size for c=0, c=1, c=2, and etc.

Steven Walfish
Secretary, U.S. TAG to ISO/TC 69
Principal Statistician, BD

Related Content:

Acceptance Sampling With Rectification When Inspection Errors Are Present, Journal of Quality Technology, open access

In this paper the authors consider the problem of estimating the number of nonconformances remaining in outgoing lots after acceptance sampling with rectification when inspection errors can occur. Read more.

Zero Defect Sampling, World Conference on Quality and Improvement, open access

Zero defect sampling is an alternative method to the obsolete Mil Std 105E sampling scheme previously used to accept or reject products, and the remaining ANSI Z1.4-1993 which is still in use. This paper discusses the development of zero defect sampling and compares it to Mil Std 105E. Read more.

Explore the ASQ Knowledge Center for more case studies, articles, benchmarking reports, and more.

Browse articles from ASQ magazines and journals here.

Combating contamination

Q: We want to ensure that we are receiving clean containers to package our products. How can we improve our incoming inspection process?

A: You should encourage your vendor to ship only clean containers. Then, be sure that the shipping and receiving process doesn’t cause contamination. If you can determine the source or sources of the contamination, the best fix is to remove the cause.

If that approach is not possible and you have incoming containers that may have some contamination, then consider the following elements in creating an efficient incoming inspection process.

1) How do you detect the contamination?

Apparently, you are able detect the container contamination prior to filling them, or are able to detect the effect of the contamination on the final product. Given that you are interested in creating an incoming test, let’s assume you have one or more ways to detect faulty units.

As you may already know, there are many ways to detect contamination. Some are faster than others, and some are non-destructive. Ideally, a quick non-destructive test would permit you to inspect every unit and to divert faulty units to a cleaning process. If the testing has to be destructive, then you’ll have to consider lot sampling of some sort.

There are many testing options. One is the optical inspection technique, which may find gross discoloration or large debris effectively. Avoid using human inspectors unless it’s only a short term solution, as we humans are pretty poor visual inspectors.

Another approach is using light to illuminate the contamination, such as a black light (UVA). Depending on the nature and properties of the contamination, you may be able to find a suitable light to quickly spot units with problems.

Another approach, which is more time consuming, is conducting a chemical swab or solution rinse and a chemical analysis to find evidence of contamination. If the contamination is volatile, you might be able to use air to “rinse” the unit and conduct the analysis. This chemical approach may require specialized equipment. Depending on how fast the testing occurs, this approach may or may not be suitable for 100 percent screening.

There may be other approaches for detecting the faulty units, yet without more information about the nature and variety of contamination, it’s difficult to make a recommendation. Ideally, a very fast, effective and non-destructive inspection method is preferred over a slow, error prone, and destructive approach. Cost is also a consideration, since any testing will increase the production costs. Finding the right balance around these considerations is highly dependent on the nature of the issue, cost of failure, and local resources.

2) How many units do you have to inspect?

Ideally, the sample size is zero as you would first find and eliminate the source of the problem. If that is not possible or practical, then 100 percent inspection using a quick, inexpensive, and effective method permits you to avoid uncertainties with sampling.

If the inspection method requires lot sampling, then all of the basic lot sampling guidelines apply. There are many references available that will assist you in the selection of an appropriate sampling plan based on your desired sampling risk tolerance levels.

Another consideration is the percentage of contaminated units per lot. If there is a consistent low failure rate per lot, then lot sampling may require relatively large amounts of tested units. You’ll have to determine the level of bad units permitted to pass through to production. Short of 100 percent sampling, it’s difficult (and expensive) to find very low percentages of “bad” units in a lot using destructive testing.

3) Work to remove original source(s) of contamination to permit you to stop inspections.

I stress this approach because it’s the most cost effective in nearly all cases. In my opinion, incoming inspection should be stopped as soon as possible since the process to create, ship and receive components should not introduce contamination and require incoming inspection to “sort” the good from the bad.

Fred Schenkelberg
Voting member of U.S. TAG to ISO/TC 56 on Reliability
Voting member of U.S. TAG to ISO/TC 69 on Applications of Statistical Methods
Reliability Engineering and Management Consultant
FMS Reliability

Related Resources:

Digging for the Root Cause, Six Sigma Forum Magazine, open access

Many Six Sigma practitioners use the term “root cause” without a clear concept of its larger meaning, and similar situations occur in Six Sigma training programs. As a result, many practitioners overlook root causes. Read more.

The Bug and the Slurry: Bacterial Control in Aqueous Products, ASQ Knowledge Center Case Study, open access

When a customer reported a problem using the polycrystalline diamond (PCD) slurry supplied by Warren/Amplex, the company traced its product through the supply chain in order to identify the cause and quickly implement a solution. Read more.

Explore the ASQ Knowledge Center for more case studies, articles, benchmarking reports, and more.

Browse articles from ASQ magazines and journals here.

Z1.4:2008 inspection levels

Q: I am reading ANSI/ASQ Z1.4-2008: Sampling procedures and tables for inspection by attributes, and there is a small section regarding inspection level (clause 9.2). Can I get further explanation of how one would justify that less discrimination is needed?

For example, my lot size is 720 which means, under general inspection level II, the sample size would be 80 (code J). However, we run a variety of tests, including microbial and heavy metal testing. These tests are very costly. We would like to justify that we can abide by level I or even lower if possible. Do you have any advice?

The product is a liquid dietary supplement.

 A: Justification of a specific inspection level is the responsibility of the “responsible party.” Rationale for using one of the special levels (S-1, S-2, S-3, S-4) could be based on the cost or time to perform a test. Less discrimination means that the actual Acceptable Quality Level (AQL) on the table underestimates the true AQL, as the sample size has been reduced from the table-suggested sample size (i.e. Table II-A has sample level G of 32 for a lot size of 151 to 280, while General Inspection level I would require Letter E or 13 samples for the same lot size).

Justification of a sampling plan is based on risk and a sampling plan can be justified based on the cost of the test, assuming you are willing to take larger sampling risks. If you use one of the special sampling plans based on the cost of the test, it is helpful to calculate the actual AQL and Limiting Quality (LQ) using the following formulas.

You solve the equation for AQL and LQ for a given sample size (n) and defects allowed (x):

Steven Walfish
Secretary, U.S. TAG to ISO/TC 69
Principal Statistician, BD

Related Content:

Acceptance Sampling With Rectification When Inspection Errors Are Present, Journal of Quality Technology

In this paper the authors consider the problem of estimating the number of nonconformances remaining in outgoing lots after acceptance sampling with rectification when inspection errors can occur. Read more.

Zero Defect Sampling, World Conference on Quality and Improvement

Zero defect sampling is an alternative method to the obsolete Mil Std 105E sampling scheme previously used to accept or reject products, and the remaining ANSI Z1.4-1993 which is still in use. This paper discusses the development of zero defect sampling and compares it to Mil Std 105E. Read more.

Sampling Employee Tasks

Q: We are collecting data on what tasks our employees in various departments do each day. We hope to eventually get a representation of what each employee does all year long.  Randomly, throughout the day, employees record the tasks they are doing.  We are not sure how to calculate an appropriate sample size and we are not sure how many data points to collect.

A: I wish there was a simple answer.  We need to consider:

  • If it makes a difference on how long an employee has been performing a job?
  • Are the departments are equivalent in terms of what they are doing?
  • What is the difference that you  want to detect?

The simple rule is that the smaller the difference, then the larger the sample size. By smaller, it is less than 1 standard deviation from the data that has been detected.

Random records are O.K., but really, shouldn’t you want a record for everyone for at least a week? That would give you an idea of what is done across the board and, then, if you are trying to readjust the workloads, you have some basis for it based on the logs.  My concern with the current method is that you may have a lot of extra paperwork to account for everyone for a certain time.

Additional information provided by the questioner:

The goal of this project is to establish a baseline of activities that occur in the department and to answer the question “What does the department do all day?”

The amount of time an employee has been performing a job does not make a difference. The tasks performed in each department are considered equivalent.  We are not accounting for the amount of time it takes to complete a task — we are more interested in how frequently that task is required/requested.

The results will be used to identify enhancement opportunities to our database and identifying improvements to the current (and more frequent) processes.  The team will use a system (form in Metastorm) to capture activities throughout the day.  Frequency is approximately 5 entries an hour at random times of the hour.

I have worked with the department’s manager to capture content for the following fields using the form:

  1. Department (network management or dealer relation)
  2. Task (tier 1)
  3. Why (tier 2 – dependent on selection of task)
  4. Lessee/client name
  5. Application
  6. Country
  7. Source of request (department)

We are looking for a reasonable approach to calculate the sample size required for a 90 – 95% confidence level.  The frequency of hourly entries and length of period to capture the data can be adjusted to accommodate the resulting sample size.

A: The additional information helps.  Since you have no previous data and you are getting 5 samples an hour from each employee, (assuming a 7 hour workday, taking out lunch and two breaks), that will give you approximately 35 samples a day. Assuming a five-day week, that gives you approximately 175 data points per employee.  This should give you enough information to get an estimate of what is done for a week.

Now, you will probably want to extend this out another three weeks so that you have an idea of what happens over a month.  If you can assume that the data collected is representative of all months, then you should be O.K.  If you feel that some months are different, then you may want to look at taking another sample during the months where you anticipate different volumes from the one you have. You can use the sample size calculation for discrete data using the information that you have already collected and not look at all employees, but target your average performers.

Jim Bossert
SVP Process Design Manger, Process Optimization
Bank of America
Fort Worth, TX

Learn more about sampling with open access articles from ASQ publications:

Explore more in the ASQ Knowledge Center.


Random sampling

Q: When inspecting components on tape and reel, pulling parts at random can present a problem in a pick and place operation.  Also once removed, the samples would have to be put back on tape for use.

Is there a practical or common sense procedure to follow?

A: This is not an uncommon problem and I know that I’ve been in a similar situation. What we did was to inspect at the beginning and the end of each tape. That way we were not causing disruption to the process.  It worked pretty well with the suppliers we had. But prior to doing that, we certified our suppliers by going to their facility and performing a process audit to make sure that the process was meeting our requirements.

Jim Bossert
ASQ Fellow

Z1.4:2008, Using Acceptance Quality Limit (AQL)

Pharmaceutical sampling

Q: I have a question about how to use ANSI/ASQ Z1.4-2008 Sampling Procedures and Tables for Inspection by Attributes.

I am looking to achieve a 99.5% production yield.  How do I calculate that using the Acceptance Quality Limit (AQL) in this standard?  Is it as simple as taking (100-AQL) to calculate the expected yield?

A: The ANSI Z1.4-2008 standard is not intended for calculating production yield or expected production yield.  The AQL is the maximum percent non-conforming that can be considered acceptable as a process average.  Typically we set this as the percent defective that would be accepted at a 95% confidence.  If you want to sample such that you have 95% confidence that the average production yield is 99.5%, you can find a sampling plan with an AQL of 0.5%.  Also, please understand that the tables in the standard are not exact value for AQL.  Using the binomial distribution (or hypergeometric for sampling with no replacement) you can calculate the exact probability.

Steven Walfish
Secretary, U.S. TAG to ISO/TC 69
Statistician, GE Healthcare