## Z1.4: Selecting the Sample Size

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:

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

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

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
ASQ CQE
Principal Statistician, BD
http://statisticaloutsourcingservices.com

Related Content:

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

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

Explore ASQ’s website for more case studies, articles, benchmarking reports, and other content about zero defect sampling.

## Dock to Stock

Q: I have been tasked with implementing a dock to stock policy. Does an expert have any advice or information to share towards forming a dock to stock policy?

A: To begin, here is a brief definition of dock to stock (DTS):

Dock to stock is a receiving method whereby materials are delivered directly to point of use (storage or manufacturing), skipping the normal receiving inspection.

For most organizations, parts which are given a DTS status are those which have been “proven” to be compliant. It is common practice to perform a receiving inspection on the parts for a minimum of five deliveries (some companies choose 10).

After a supplier has proven to deliver a compliant product five times, that individual item/part number is given DTS status. It is then general practice for production/assembly departments or line personnel to verify compliance as needed. If a product is found to be noncompliant, it is put on a contingency list and must prove its validity again — usually through five to 10 compliant shipments before it is returned to DTS status.

Keep in mind that the DTS process is rarely used in some industries/companies. For example, a company certified to ISO 13485 (medical devices) would not use DTS due to FDA regulations — here’s an excerpt from 21 CFR 820.80 (b):

“Receiving Acceptance Activities: Incoming product shall be inspected, tested or otherwise verified as conforming to specified requirements.”

In short, determining how many acceptable shipments to qualify a supplier for DTS status is up to the company. Requesting a certificate of compliance with each shipment can tend to encourage a supplier to ensure their own quality, as does a yearly audit of the supplier’s facilities (if appropriate).

I hope using the guidelines above will help lead you toward your goal.

Bud Salsbury
ASQ Senior Member, CQT, CQI

Related Content:

Chinese OEM Reduces Returns With Improved Product Testing, ASQ case study

Cost-Effectiveness Based Performance Evaluation for Suppliers and Operations, Quality Management Journal

## Z1.4 and Z1.9 in Micro Testing and API Chemical Analysis

Q: I work at a cosmetics manufacturing company that produces sunscreen in bulk amounts. When we make 3,000 kg of sunscreen, we will use that in 10,000 units of final sunscreen products which will weigh 300 g each.

How many samples do I need to collect from the 10,000 units to pass the qualification?

The products need to pass both attribute and variable sampling tests such as container damage, coding error, micro testing, and Active Pharmaceutical Ingredients (API)  failure. Almost 100 percent of final products were inspected for appearance error, but a small number of them should be measured for micro testing and API chemical analysis.

For Z1.4-2008: Sampling Procedures and Tables for Inspection by Attributes, we have to collect a sample of 200 (lot size of 3,201-10,000; general inspection level II;  acceptable quality level 4.0 L), and more than 179 should pass for qualification.

For Z1.9-2008: Sampling Procedures and Tables for Inspection by Variables for Percent Nonconforming, we have to collect a sample of 25 (lot size of 3,201-10,000; general inspection level II; acceptable quality level 4.0, L), to meet the requirement of 1.12 percent of nonconformance.

Which sampling plan should we follow for micro testing and API chemical analysis?

A: If the micro test is pass/fail, then you should use Z1.4. The API chemical test  probably yields a numerical result for which you can calculate the average and standard deviation. Then, the proper standard to use is Z1.9. If the micro test gives you a numerical result, then you can use Z1.9 for it as well.

One thing to consider is the fact that the materials are from a
batch. If the batch can be assumed to be completely mixed without settling or separation prior to loading into final packaging, then the API chemical test may only need to be done on the batch, not on the final product. Micro testing, which can be affected by the cleanliness of the packaging equipment, probably needs to be done on the final product.

Brenda Bishop
U.S. Liaison to TC 69/WG3
ASQ CQE, CQA, CMQ/OE, CRE, SSBB, CQIA
Belleville, Illinois

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

## 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
ASQ CQE
Principal Statistician, BD
http://statisticaloutsourcingservices.com

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

## ISO 9001: Product Development and Customer Satisfaction

Q: Does a company certified to ANSI/ISO/ASQ Q9001-2008 Quality management systems — Requirements that produces raw materials for a customer according to their written specification also, as a raw material supplier, have a responsibility under ISO 9001 to meet the customer’s needs for their design intent and intended and known use?

In simple language, I sell a raw material to a customer who takes my raw material and then designs a product and sells it to a customer who uses it in the field. I wonder where does the ISO standard application stop for the raw material supplier?  How can a raw material supplier under ISO 9001 meet the needs of a customer’s trade secret designs, or further down the intended use of the product where the raw material supplier has no control over how it will be used or maintained?

A: Your question is more a legal one than a quality one. You are offering a product to a customer. This is your finished product and their raw material. When both parties agree to the terms and conditions (payment, form, fit, function, shipping, etc.) a contract exists. We call this a purchase order (PO) and part of that PO is the specification for your product. If they place an order to your spec, you have done the design work under ISO 9001 and they are accepting your design. END OF YOUR RESPONSIBILITY for future application and use. If you accept an order to their spec, they have done the design work and you are obligated to make sure your product meets the stated (and often implied) form/fit/function requirements. We call this quality control and you do this by testing in the lab prior to shipment.

Most firms address the issue of application by stating quite clearly in the contract terms that you are selling your product as-is and you do not warrant the product as fit for ultimate use. This is the kind of thing the lawyers require.

Having said all this, there is a requirement in ISO 9001 for you to measure customer satisfaction. You must state in your manual the concept (strategies) for doing this and have some defined processes – usually called procedures – to carry it out. Of course, part of this is the regular management review. Quality, marketing, and sales all provide input on how well the customer needs are being met. Your registrar should be examining how you do this.

If there is a trend showing that customers are unhappy with how the stuff performs under end-use conditions, ISO says you should address those issues. (Ignoring them is an option, if it is deliberate). Mature firms will work on building customer-supplier partnerships, getting their engineers to talk to your engineers. Although this is technically outside of the quality function, it is still part of your overall quality management system.

Charlie Cianfrani
Consulting Engineer
Green Lane Quality Management Services
Green Lane, PA
ASQ Fellow; ASQ CQE, CRE, CQA, RABQSA Certified QMS-Auditor (Q3558)
ASQ Quality Press Author

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

## Six Sigma Case Studies

Q: I would like to browse through detailed Six Sigma Case Studies. I do not mind making a payment for detailed case studies in the fields of manufacturing, services and software.
Kindly direct me to the requisite links please.

A: Thank you for contacting ASQ.  I received your request for case studies on Six Sigma in the fields of manufacturing, services, and software.

“Six Sigma is an organization-wide approach used to achieve breakthrough improvements tied to significant bottom-line results. Unlike previous TQM approaches, Six Sigma specifies exactly how the organization’s managers s hould set up and lead the effort. Key features are the use of data and statistical analysis, highly trained project leaders known as Black Belts and Green Belts, project selection based on estimated bottom-line results, and the dramatic goal of reducing errors to about three per million opportunities” (taken from The Quality Toolbox, 2nd ed. by Nancy R. Tague)

ASQ has around 300 Six Sigma case studies available online.

A host of additional Six Sigma content is also available.

## Variation in Continuous and Discrete Measurements

Q: I would appreciate some advice on how I can fairly assess process variation for metrics derived from “discrete” variables over time.

For example, I am looking at “unit iron/unit air” rates for a foundry cupola melt furnace in which the “unit air” rate is derived from the “continuous” air blast, while the unit iron rate is derived from input weights made at “discrete” points in time every 3 to 5 minutes.

The coefficient of variation (CV), for the air rate is exceedingly small (good) due to its “continuous’ nature” but the CV for iron rate is quite large because of its “discrete nature,” even when I use moving averages for extended periods of time. Hence, that seemingly large variation for iron rate then carries over when computing the unit iron/unit air rate.

I think the discrete nature of some process variables results in unfairly high assessments of process variation, so I would appreciate some advice on any statistical methods that would more fairly assess process variation for metrics derived from discrete variables.

A: I’m not sure I fully understand the problem, But I do have a few assumptions and possibly a reasonable answer for you. As you know, when making a measurement, using a discrete scale (red, blue, green; on/off, or similar), the item being measured is placed into one of the “discrete” buckets. For continuous measurements, we use some theoretically infinite scale to place the units location on that scale. For this latter type of measurement, we are often limited by the accuracy of the equipment to the level of precision the measurement can be accomplished.

In the question, you mention measurements of air from the “continuous” air blast. The air may be moving without interruption (continuously), yet the measurement is probably recorded periodically unless you are using a continuous chart recorder. Even so, matching up the reading with the unit iron readings every 3 to 5 minutes, does create individual readings for the air value. The unit iron reading is a “weights” based reading (not sure what is meant by derived, yet let’s assume the measurement is a weight scale of some sort.) Weight, like mass or length, is an infinite scale measurement, limited by the ability of the specific measurement system to differentiate between sufficiently small units.

I think you see where I’m heading with this line of thought. The variability with the unit iron reading may simply reflect the ability of the measurement process. I do not think either air rate or unit iron (weight based) is a discrete measurement, per se. Improve the ability to measure the unit iron and that may reduce some measurement error and subsequent variation. Or, it may confirm that the unit iron is variable to an unacceptable amount.

Another assumption I could make is that the unit iron is measured for the batch that then has unit air rates regularly measured. The issue here may just be the time scales involved. Not being familiar with the particular process involved, I’ll assume some manner of metal forming, where a batch of metal is created then formed over time where the unit air is important. And, furthermore, assume the batch of metal takes an hour for the processing. That means we would have about a dozen or so readings of unit air for the one reading of unit iron.

If you recall, the standard deviation formula is divided by square root of n (number of samples). In this case, there is about a 10 to 1 difference in n (10 for unit air to one for unit iron). Over many batches of metal, the ratio of readings remains at or about 10 to 1, thus impacting the relative stability of the two coefficient of variations. Get more readings for unit iron or reduce the unit air readings, and it may just even out. Or, again, you may discover the unit iron readings and underlying process is just more variable.

From the information provided, I think this provides two areas to conduct further exploration. Good luck.

Fred Schenkelberg
Voting member of U.S. TAG to ISO/TC 56
Voting member of U.S. TAG to ISO/TC 69
Reliability Engineering and Management Consultant
FMS Reliability
http://www.fmsreliability.com

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

## Visual Fill Requirements

Q: I work for a consumer products company where more than 60% of our products have a visual fill requirement. This means, aside from meeting label claim, we must ensure the fill level meets a visual level.

What is the industry standard for visual fills?

We just launched Statistical Process Control (SPC), and we notice that our products requiring visual fills show significant variability.

A: This is an interesting question. The NIST SP 1020-2 Consumer Package Labeling Guide and the Fair Packaging and Labeling Act, along with any other industry standards, regulate how you must label a product “accurately.” However, it appears you have been burdened with a separate, and somewhat conflicting requirement —  a visual fill requirement.

In most cases, you probably cannot satisfy both requirements without variability. The laws and standards will direct labeling requirements with regard to accuracy, and your company is liable for that. If you choose to use visual fill standards for “in-process” quality assurance, then you would need a fairly broad range between the upper and lower acceptance limits.

Personally, I would use weights and measures as needed to meet customer and legal requirements. These are the data I would use for SPC records.

If your company has a need (or a desire) to use visual fill levels for a gage, then generating a work instruction telling employees where a caution level is would be a way to start. In other words, “If the visual level is above point A or below point B, immediately notify management.” If you are to remain compliant with what you put on a label, visuals will change from run to run. Using them as a guide for production personnel can be a helpful tool, but not as a viable SPC input.

Bud Salsbury
ASQ Senior Member, CQT, CQI

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

## Guidance on Z1.4 Levels

Q: My company is using ANSI/ASQ Z1.4-2008 Sampling Procedures and Tables for Inspection by Attributes, and we need some clarification on the levels and the sampling plans.

We are specifically looking at Acceptable Quality Limits (AQLs) 1.5, 2.5, 4.0, and 6.5 for post manufacturing of apparel, footwear, home products, and jewelry.

Do you have any guidelines to determine when and where to use levels I, II, and III? I understand that level II is the norm and used most of the time. However, we are not clear on levels I and III versus normal, tightened, and reduced.

Are there any recommended guidelines that correlate between levels I, II, III and single sampling plans, normal, tightened, and reduced?

The tables referenced in the standard show single sampling plans for normal, tightened, and reduced, can you confirm that these are for level II (pages 11, 12, 13)?

Do you have any tables showing the levels I and III for normal, tightened, and reduced?

A: Level I is used when you need less discrimination or when you are not as critical on the acceptance criteria. This is usually used for cosmetic defects where you may have color differences, but it is not noticeable in a single unit. Level III is used when you want to be very picky.  This is a more difficult level to get acceptance with, so it needs to be used sparingly or it can cost you a lot of money.

Each level has a normal, tightened and reduced scheme.  I am not sure about what you are asking for with respect to correlation to levels I, II and III and normal, tightened and reduced.  The goal is to simply inspect the minimum amount to get an accept or reject decision. Since inspection costs money, we do not want to do too much. Likewise, we do not want to reject much since that also costs money both in product availability and extra shipping.

Yes, the tables on pages 11, 12 and 13 are for normal, tightened, and reduced, but if you look at the letters for sample size, you will note that in most cases there are different letters for the levels I, II, and III.  Accept and reject numbers are based on the defect level and the sample size. The switching rules tell you when you can switch to either a reduced or tightened level. The tables can handle not just the levels I, II , and III, but also the special levels.

Jim Bossert
SVP Process Design Manger, Process Optimization
Bank of America
ASQ Fellow, CQE, CQA, CMQ/OE, CSSBB, CMBB
Fort Worth, TX

## Delta Triangle

Question

When revising drawings to include the delta triangle in the title block, does the drawing index sheet also contain the triangle in the title block?

Answer

The term “delta” refers to a triangle placed on the drawing for reference. The triangle is commonly placed next to a dimension, such as 2.65, 5, or other locations where it applies to a feature or item. This is used to refer the reader to a general note that relates to this item.

So if the delta triangle is used as a reference in your main title block, then I would say yes, add it to the index sheet if it makes the reference more clear.

In addition to drawing a reader’s attention to notes, the delta triangle is also quite often used with print revisions. For example, if a drawing was a revision 2, and then a new revision is generated. It might say something simple like, Rev. 3- 2.235 dimension changed to 2.240. Then a delta triangle with the number 3 in it would be next to the 2.240 dimension referring to the revision.

Bud Salsbury
ASQ Senior Member, CQT, CQI