## Question

Our customers require that we follow the ANSI Z1.4 standard for attribute sampling plans; however, it is not feasible to wait until lots are completed to perform inspections. Lots can be large and run for many days and waiting until lot completion to determine the sample size, based on the finished lot size, is too late because we will have missed our chance to correct any production issues that may result in defective parts. Another limitation is a lack of space to stage product while waiting for the final inspection of the completed production lots. Product is made as orders are received, and not typically stored as inventory, so our on-time delivery demands also hinder our ability to hold product for final inspections of completed production lots. Therefore, we are seeking guidance on a practical way to implement a in-process inspection during production that follows the ANSI Z1.4 standard.

Yes, you can sample as you produce to get to the sample size.  It is important that you keep track of your accept/reject items.  Since you know how long you are running the product, you can project the approximate lot size to get the sample size.  Work with your scheduler before the product starts so you can take samples early and continue on in the process.

In addition, if you have material changes as the product is running, I am sure that you are sampling then to make sure everything is set correctly, you can use those samples also.  As an example, let’s say your product is running 4 days and based on the projected lot size, you have a sample of 28 to take, you could take 7 samples each day spaced throughout the day or you take 10 samples the first day, 7 the second day, 6 the third day and 5 the last day of production.  You need to figure the right sequence that fits your history of the product.

Jim Bossert

For more on this topic, please visit ASQ’s website.

## Question

Regarding part of your answer to a post found here, you state:

“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.”

Can you explain for the non-statistical folks like me people how that math works? Specifically, I am wondering what the minimum sample size would be for an AQL of 0.25, when using Special Inspection level S2? Would it be a minimum of 50, no mater what the lot size is?

Acceptance sampling procedures were developed during the early 1920s at Western Electric Company and later formalized at Bell Telephone Laboratories where terms like producer’s risk and consumer’s risk were established.  Later, during World War II, sampling plans such as MIL-STD-105 were developed by Harold F. Dodge and others working with the Army Quartermaster Corps (Dodge, 1967).

Two special features were employed in order to gain agreement with the large body of military suppliers.  One was the use of the acceptable quality limit (AQL) as opposed to the RQL in presenting the plans.  The goal at the time was to focus on rewarding suppliers for production whose quality levels were considered good.  RQLs were recognized but not often brought to the surface during discussions. Also, at that time, the term “AQL” was deliberately vague or inexact.  It was a close approximation, not an exact probability statement.

The other feature was the practice of increasing sample sizes with increased lot sizes.  As noted in Section 3, in most situations, the lot size does not factor in plan construction (based on the binomial).  For many, however, this lacks intuitive appeal.  Therefore, in the development of MIL-STD-105 and its derivatives a deliberate increase in sample sizes for higher lot sizes was introduced, with corresponding increases in acceptance numbers for similar AQLs.  Clearly, this practice resulted in over-sampling and consequent increased inspection costs.  Government operatives believed that the increased sampling cost was of small consequence relative to the power to persuade.

For the binomial distribution you solve for the AQL that gives a high probability of passing.  Usually this probability is set at 95%.  For example if you have a sample size of 80 units with an accept/reject of 1, an AQL of 0.65% would have a 90% probability of passing the sampling plan.

You can use Excel to solve this with the function

=BINOMDIST(1,80,0.0065,1)

Hope this helps,

Steven Walfish

For more on this topic, please visit ASQ’s website.

## Sampling Plan Review?

Question

When following ANSI/ASQ Z1.4-2003 (R2018), if a product has been placed in a “reduced” sampling plan based on the previous 10 lots results, is it a requirement to convert back to a “normal” sampling plan on an annual basis, or should that decision remain based on supplier performance? I have been told that we should revert to normal sampling each year, but I do not see that in the AQL inspection manual.

The standard does not require annual (or periodic) review of the sampling plan.  The switching rules are time invariant, and reflects just the normal flow of lots, which can span more than a year.  Unless the supplier requires a change in the inspection level, the standard is silent on resetting to the normal level annually.

Steven Walfish

For more on this topic, please visit ASQ’s website.

## Z 1.4 Inspection Levels

Question

I am using a reduced switching rule and I don’t understand the meaning of the numbers in the first box. Total noncomforming less than limit number? What’s my limit number?Does production stability mean capability? Would I use 1.33?  The table has an arrow to reduced, so would I move to the next box?

The ANSI/ASQ Z1.4 standard has three inspection levels: normal, reduced and tightened inspection.  Initially you start at normal inspection, and can move to either tightened or reduced inspection depending on how lots are dispositioned.  Based on Figure 1 of the standard, the determination to move amongst the levels can be ascertained.  When you get to the reduced inspection level (Table II-C), you need to read the footnote (†).  It states “If the acceptance number has been exceeded, but the rejection number has not been reached, accept the lot, but reinstate normal inspection.”

A stable process or production is less about a capability index, and more about the control chart of the data showing a stable process.  In other words, the process is stable over time.

Steven Walfish

## Confidence Levels

Question

I would like to confirm if ASQ Z1.4-2008 attribute tables are calculated based on 95% confidence level? I am using Table II-A, on page 11.

ANSI/ASQ Z1.4 tables are not technically calculated based on a 95% confidence level.  The technical definition of AQL is the quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance sampling.  Some interpret it to mean if a lot has AQL percent defective or less, a lot would have a high probability of being accepted based on the sampling plan.  The standard does not specify the probability of acceptance explicitly.  The operating characteristic curve (OC Curve and the tables define the AQL as the percent defective that has a 95% probability of acceptance.  So though it is not a 95% confidence level, it is a 95% probability of acceptance.

Steven Walfish

## Sampling Foils, Films, and Labels

Question

My question is about sampling aluminium foils, films used in packaging and sticker labels received in rolls which are wound around a core. I can decide to chose the number of rolls to sample from using the tables given in Z1.4, but how should I decide on the amount of stickers and aluminium foil and film to be sampled? I ask this question since it is practically impossible to sample from within a wound roll.

The ANSI Z1.4 and Z1.9 standards might be applicable when all units do not have the same probability of being selected.  Since you cannot sample units closer to the core, and defects would never be detected unless they occur at the end of the roll, I would recommend a different strategy, either using a vision system (100% inspection) or in process inspection.

If you want to use the standard, the sample size should be based on the number of samples, not the number of rolls.  For example, a roll with 5000 labels would be an N=5000 not N=1.

Steven Walfish

For more on this topic, please visit ASQ’s website.

## ANSI Z1.4 Reduced Inspection

Question

If you have Ac=0 and Re=2 what do you do for 1? I have not used the reduced sampling before, so am curious what should be done in this instance.

If you review the footnotes for Table II-C of ANSI Z1.4, you will see that there is a note (†) that states: If the acceptance number has been exceeded , but the rejection number has not been reached, accept the lot, but reinstate normal inspection (see 10.1.4).  So in your case, with a single reject, you would accept and reinstate normal inspection.

Steven Walfish

## Defective Parts Per Million (DPPM) Calculation

Question

Recently, there is a debate in my organization about Defective Parts Per Million (DPPM) computation.

Camp 1 - DPPM = (No of parts rejected / No of parts inspected) * 1,000,000
Camp 2 - DPPM = (No of parts rejected / No of parts received) * 1,000,000

We perform sampling inspection based on AQL.
Camp 1 insists they are correct and likewise for Camp 2.  Which is correct or more appropriate to reflect supplier quality?

This is not an uncommon question. If you look at the standard, they define the % nonconforming as the number of parts nonconforming/number of parts inspected x 100. If you are looking at DPPM, instead of multiplying by 100, you put in 1,000,000.

This means that by your definition, Camp 1 is correct. This is also what was intended by the creators of the sampling scheme.

Jim Bossert
Sr Performance Improvement Specialist
JPS Hospital
ASQ Fellow, CQE, CQA, CMQ/OE, CSSBB, CSSMBB
Fort Worth, TX

For more on this topic, please visit ASQ’s website.

## Zero Acceptance Number Sampling Plans and the FDA

Question

There has been some debate over using the MIL-STD-1916 acceptance sampling plan over the ANSI/ASQ Z1.4-2003 (R2018) sampling plans.  The opinion is that the ANSI/ASQ Z1.4-2003 (R2018) is outdated and no longer an acceptable method of determining a qualification sample plan and the MIL-STD-1916 should be used in place of ANSI/ASQ Z1.4-2003 (R2018). Do you have information around this debate over which sampling plans are acceptable by the FDA?

FDA does not (and can not) tell you what sampling plan is to be used.  The FDA requirement is that the plan be statistically valid.  As long as you follow the regulation, you are meeting FDA requirements.

In medical device manufacturing the key point is to have the plan accept on zero defectives.  This point is not FDA but legalese.  It is based on past lawsuits.  The plan “Zero Acceptance Number Sampling Plans” by Nicholas L. Squeglia (available from ASQ) has been widely adopted for this reason.

ANSI/ASQ Z1.4 in not outdated and continues to be widely used.  It is the American National Standard Institute (ANSI) version of MIL-STD-105 which the government discontinued maintaining, allowing ANSI to maintain it along with many, many other MIL-STD’s as a government cost reduction.

MIL-STD-1916 can be used but it is not widely used because of its difficulty and practical use.

James Werner

## AQL Clarifications

Question

I am confused about the values used for AQLs. For example in Table II-A the AQL values range from 0.010 to 1000. Where do these values come from and what do they mean?

The table states, “AQLs, in Percent Nonconforming Items and Nonconformities per 100 Items .” At first I thought the values were percentages, but how can you have more than 100, as in 100%, as the values go up to 1000? Also how can there be more than 100 nonconformities per 100 items, unless one part can have multiple nonconformities?

Just looking for clarification on the AQL numbers, what they mean, and how to interpret them.