Z 1.4 Inspection Levels

Pharmaceutical sampling

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?

Answer

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

For more information about inspection, please view the resources found here.

Confidence Levels

 

Data review, data analysis, data migration

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.

Answer

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

For more information about AQL, please view the resources here.

Zero Acceptance Number Sampling Plans

Airplane, aerospace, AS9100

Question

Regarding Nicholas Squeglia’s Zero Acceptance Number Sampling Plans, in the 4th edition for lot size 151-280 (1% AQL), a sample size of 20 is provided.  However, in the 5th edition, for the same lot size 151-280 and AQL of 1%, the sample size is 29. Which is correct – a sample size of 20 or 29?

Answer

In the 5th edition of Nicolas Squeglia’s book, he mentions on page xii the rationale of the change in sample sizes.  From  the 5th edition, “in the early 2000’s, a large aerospace manufacturer was given permission by ASQ to reproduce the c=0 sampling table.  They modified the table by changing several sample sizes, and for convenience it was therefore originally decided to carry those modifications into the fifth edition.”

Table 1a is the original tables (4th edition and previous) which has the sample size of 29.  Use this table unless otherwise specified by contract.

Table 1b is the modified table which has a sample size of 20.

Thanks

Steven Walfish

Sampling Foils, Films, and Labels

Manufacturing, inspection, exclusions

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.
Answer

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

Learn more about visual inspection here.

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.

Answer

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

AQL Clarifications

Automotive inspection, TS 16949, IATF 16949

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.

Answer

Let’s start with the definition of Acceptable Quality Level (AQL).  From Z1.4, the AQL is the quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance sampling.  Although individual lots with quality as bad as the AQL can be accepted with fairly high probability, the designation of an AQL does not suggest that this is necessarily a desirable quality level. The AQL is a parameter of the sampling scheme and should not be confused with a process average which describes the operating level of a manufacturing process. It is expected that the product quality level will be less than the AQL to avoid excessive non-accepted lots.

The columns with percentages greater than 100% should not be included in the standard, but remain as indication of how to interpret lots where the entire sample is defective.  It has some statistical relevance with use of the switching rules, but for the general practitioner, it should be ignored.

Hope this helps.

Steven Walfish

DPMO

Question

My question concerns the process performance metric DPMO (defects per million opportunities). I want to use this to quantify a particular supplier’s performance. My question is, is the number of defects referred to in the calculation the number of defects produced by the supplier (in which case it would involve data I don’t have access to), or is it the number of defects experienced by the customer (which is us)? I of course can count the number of defects we receive from the supplier, but if this metric is supposed to be based on the number of defects produced by an organization, I would have no way of knowing how many defects are produced by the supplier’s process, but contained within the supplier’s facility. My hope is to be able to characterize the supplier’s process performance in terms of sigma level.
Answer

The DPMO metric is not usually considered a point estimate of the true percent defective in the lot (either at the supplier or customer site).  It is a relative performance metric used to equate the observed percent defective from a sample to defective units per million opportunities.  If a supplier culls out all the defective units before shipping to you (i.e. perfect inspection system), your internal DPMO would be 0, even if the supplier DPMO is high. If your goal is to characterize the supplier’s process performance in terms of sigma level, you would need their data, as the data you collect internally is just an estimate for the average outgoing quality from the supplier and not their process performance.

Steven Walfish

Z1.4 Sample Size

Pharmaceutical sampling

Question

I am trying to determine the sampling size using my ANSI/ASQ Z1.4 table and I wanted to get some clarification. If I am using Table II A and my Sample Size Code letter is D, what would be my sample size? If it falls on an arrow does it mean that I have to change to the next sample size based on where the arrow points?

Answers

From Charlie Cianfrani:

If you are using Z1.4, your sample size is selected based on your lot size.  You would pick the AQL you need based on the risk you are willing to take for the process average of percent defective.  It is important to understand what you are doing when using sampling plans, what they are and the protection you are trying to ensure. Thus, the important step is to determine the AQL. Then you select the sample size to provide the level of protection you are striving to ensure. It is more important to understand the theory behind the tables than to mechanically use the tables.

From Fred Schenkelberg:

Use the sample size where the arrow points. In the 2008 and 2013 versions it explains this in section 9.4, “When no sampling plan is available for a given combination of AQL and code letter, the tables direct the user to a different letter. The sample size to be used is given by the new code letter, not by the original letter.”

From Steven Walfish:

The standard sample size for Code Letter D from IIA is a sample size of 8.  But depending on your AQL, a sample size of 8 would be inappropriate, so the standard has arrows to delineate alternative sample sizes to reach the target AQL.  So, you sample size and accept/reject values are changed.  For example, at an AQL of 0.25, you would move down to a sample size of 50, with an accept/reject of 0/1.  If the lot size is less than 50, you would need to do 100% inspection.  In other words, there is no sampling plan that can give an AQL of 0.25 without a minimum sample size of 50.

From James Werner:

Yes.  When using Z1.4 two items need to be known, lot size and the AQL (Acceptance Quality Limit).  You use Table I – Sample size code letters to determine the Sample size code letter based on the Lot or batch size.  In the question below that was determined to be “D”.  Next step is to use Table II-A to find the sample size related to the sample size code letter – D and the AQL.  On Table II-A go across the table’s row for letter D until it intersect the given AQL column heading.  If an arrow is in that intersection point, follow the arrow then go back to the sample size code letter column to find the actual sample size (if a up/down arrow is in there then you choose).

Example 1.  Code letter is D (as in the question below).  Let’s say the AQL is 0.25.  Starting at code letter D, move across that row until you intersect at the AQL 0.25 column.  There’s a down arrow this row/column intersection.  Follow the arrow downward until the “Ac Re” reads ” 0 1″.  Staying on this row go back to the Sample size code letter column and find Code Letter H and Sample size = 50.  This means for the lot size with code letter D and with an AQL of 0.25 the sample size = 50 and accept the entire lot if no nonconformances were found else reject the entire lot if 1 or more nonconformance were found in the sample.

Example 2.  Let’s say the Sample size code letter was determine from Table I to be “F”.  Looking at Table II-A; If the AQL = 0.65, then the sample size would be 20 and the lot would be accepted zero nonconformance.  But if the AQL = 0.15 then the sample size would be 80.

ASQ/ANSI Z1.4 is available for purchase in PDF as well as hard copy.

Six Sigma Statistical Meaning

Reporting, best practices, non-compliance reporting

Question

I need to understand the statement, “Adding a 1.5 sigma shift in the mean results …….”
I’m used to the bell curve and + /- three sigma.
How does the extra +/- three sigma fit in, and what is this about moving the mean?
Does ASQ have a good book that includes this detail in with basic statistics?

Answer

The idea of 6-sigma leading to a process with 3.4 parts per million defective is not a totally statistical statement.  Using the normal distribution, we know that a process that is centered on its mean will have 0.135% of the distribution outside 3 standard deviations on each tail.  That same process would have 0.00000010% outside of 6 sigma, which does not lead to the aforementioned 3.4 million parts per million outside.  Dr. Mikal Harry in 1992 published a book (see chapter 6) entitled Six Sigma Producibility Analysis and Process Characterization, written by Mikel J. Harry and J. Ronald Lawson. In it is one of the only tables showing the standard normal distribution table out to a z value of 6.  Here is where he stated that processes can shift by 1.5 sigma leading to only having 4.5 sigma limits and the 3.4 parts per million outside the “6-sigma” limits.  I would suggest you look at the six sigma division on the ASQ website (http://asq.org/sixsigma) that will help to better explain the rationale for the shift.

Steven Walfish
Secretary, U.S. TAG to ISO/TC 69
ASQ CQE
Principal Statistician
http://statisticaloutsourcingservices.com

Switch from ANSI/ASQ Z1.9 to ANSI/ASQ Z1.4?

PLCs, programmable logic controllers

Question

Hi,

We are using ANSI z1.9 for a dimension test of packaging components. As dimension is under variable, can we switch to ANSI z1.4? The reason for this is to align with our supplier who is using ANSI z1.4.

Can you please advise if this switching is acceptable. If yes, what should be taken into consideration like AQL, etc.?

Answer

The ANSI/ASQ Z1.4 standard is for incoming inspection of attribute characteristics.  As you measurement is a variable measurement, it is appropriate to use ANSI/ASQ Z1.9.  Both plans are indexed by AQL, but have different sample size requirements based on the level of protection you are looking to maintain.  I assume your real question is can you switch from a variable plan (Z1.9) to an attribute plan (Z1.4) for your inspection to align with your supplier’s use of Z1.4.   Though I do not believe harmonizing with the supplier’s use of Z1.4 for your acceptance testing is necessary, it is possible to use Z1.4 by redefining the variable measurements as either good or no-good.  Choosing to move to Z1.4 from Z1.9 will increase your sample size for the same level of protection and same lot size.  For example, a lot size of 5000 would have a sample size of 75 in Z1.4 and 200 for Z1.4 for a General Inspection Level II plan.  Both plans give approximately the same AQL and LTPD, though the Z1.4 will require 2.67x more samples.

Steven Walfish
Chair Z1, U.S. TAG to ISO/TC 69
ASQ CQE
Staff Statistician, BD