Sampling Archives - Page 2 of 2 -

Inspection Sample Size

Analysis, Statistics, Control Charts, Statistical Methods, Audit, Auditing

Question

The customer expects certain levels of inspection: pull 157 bottles for visual testing, but then they also want 20 pulled for dimensional testing. Can’t the 20 additional bottles be a subset of the original testing sample?

When calculating the lot, do you pull the samples before or after your calculations? Do the samples get included in the produced quantity or not? For example: If the customer orders 10,000 bottles and the level 2 inspection pulls 200 bottles that drops the total shipped to the customer to 9,800 pieces. If 10,200 bottles are produced then the inspection level increases so that 315 bottles need to be pulled for testing. What is the correct sample size and production number?

Answer

Here are the responses to your questions:

Yes since the first inspection is visual, you can use a subset for the additional testing.

The lot size is 10,000. You should be putting the samples back into the lot if they are not destroyed by the testing. You send what is contracted for. You are sampling with replacement.

Jim Bossert

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

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

Sampling and Daylight Savings Time

Pharmaceutical sampling

Question

We are wondering if there is any generally accepted procedure to account for seemingly duplicate sample times when operating over the time period when clocks ‘fall back’ one hour for the end of daylight savings time? Our standard practice is to analyze a chemistry sample every half hour, so we foresee two each of the 01:00, 01:30 & 02:00 AM samples this next Sunday morning. Please advise on any generally accepted practice to account for such seemingly duplicate samples.

Answer

I do not know an industry accepted standard for this yet.

If used for control charting, just plot as normal, noting when the sample was taken. For the second 2:30am sample, just note it was after the time change… continue monitoring the process as normal.

If used for lot sampling, analyze the results as normal.

If doing a daily average, then adjust the calculation for the two extra samples, i.e. divide by 26 instead of 24.

At most it may require a slight change to calculations based on the number of samples, otherwise it’s just not a big issue that may require at most a comment or note about the seemingly duplicate sample times or two missing times (in spring).

Cheers,

Fred

Fred Schenkelberg
Reliability Engineering and Management Consultant
FMS Reliability
(408) 710-8248
fms@fmsreliability.com
www.fmsreliability.com
@fmsreliability

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

Sampling Schemes

Inventory, Inspection, Review, Suppliers, Supplies

Question

Is there a sampling plan for determining the number of cases to pull in a batch from which you perform the ANSI/ASQ sampling of individual products? For example: you receive 550 cases with 145 product vials/case. Is it proper to sample a total of 500 vials from 25 cases (using square root of n+1) or would applying the ANSI/ASQ single level II be more appropriate? We would then need to pull 500 vials from 80 cases. Or is there a better statistical method?

Answer

There are two ways to answer this. One is to follow the standard and take samples from 80 cases until you get 500. It is assumed that the samples are random so that you do not always take the samples from the same location in the case. That is following the standard.

The second is that you take a sample from 25 cases in a random manner. That is fine also. There are no standards for sampling from cases so either way will work. Years ago, I developed a sampling scheme similar to what is proposed at the employer I was working with at the time. Sometimes you have to be creative.

Jim Bossert

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

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

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 your 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

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

Food Safety and Sampling

Pharmaceutical sampling

Question

I like to know how to sample a finished product or ingredient so that the sample to be tested is representative of the product as a whole so it will increase confidence in subsequent test result. This is needed to verify a particular finished product lot or incoming ingredient lot is allergen free.

Response

Sampling is not a simple process of looking up a sample size in a table. There are many factors that influence how you develop a sampling plan. When I develop a QA program, I always try to develop the program to answer a specific question or develop a null hypothesis. Once I have framed the question, I can then develop a sampling plan to help develop the answer.

It appears that the question you would like to ask is the following:

• Is an allergen present in either a lot of finished product or in a lot of ingredient?
This question deals with an attribute issue.

In developing a plan, one needs to take into account a number of statistical assumptions including the following:

• Is the process relatively stable? In statistical process control terms, the process is rarely affected by special or assignable causes of variation. The following is an alternative way to describe a stable process. Is the allergen evenly distributed in the lot or can the allergen be concentrated in one part of the lot? Answering this question helps defines the unit.

• A random sampling plan must be used to select the units to be tested.

• A unit must be defined. The unit must either possess the characteristic or not possess the characteristic. The presence of the characteristic makes the unit defective. Many times in food sampling, a unit may be difficult to define.

• A test must be available that can determine if the unit contains the characteristic. It is permissible to test a portion of the unit as long as long as that portion of the unit correctly identifies whether the unit is or is not defective.

• A sampling plan must be developed in which the units will be collected. Every unit must have an equal chance of being selected for analysis (random sampling).

• The number of units that possess the characteristic must be small (less than 10%) as compared to the number of units that do not possess the characteristic. The removal of the number of units for analysis cannot affect the portion of defective units in the lot.

• The number of “units” in the lot does NOT affect the sensitivity of the attribute sampling plan.

• The portion of units that are defective is critical to the sampling plan. If the portion of defective units declines there needs to be an increase in the number of units sampled to ensure that the sensitivity or power of the sampling plan does not change.

• The total number of units sampled is critical for the sensitivity or power of the sampling plan. The power increases with an increase in number of units sampled and tested to determine if they are defective.

• If the portion of defective units can be estimated, it is possible to calculate the power of the sampling plan using the binomial distribution. Likewise, if a sampling plan is selected, it is possible to calculate the power of the sampling plan for a specific proportion of defective units.

• Need to define the confidence level that is desired to determine whether a lot contains or does not contain the allergen.

• Acceptance number. The smaller the acceptance number, the less of a risk the lot will contain units that are defective. The smaller the acceptance number the more sensitive the sampling plan.

The alternative method is to develop a QA system based on the concepts of process control. A classical approach is to use HACCP.

John G. Surak, PhD
– Providing food safety and quality solutions –

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

Recommended AQLs for Packaging Material in the Pharmaceutical Industry

Pharmaceutical sampling

Question:

Are there recommended AQLs (critical, major and minor defects) for packaging material (primary and secondary) for the Pharmaceutical Industry?
Thank you

Response:

Though there are no recommended AQLs (or LTPD) for packaging materials, some industry standards have begun to surface. The following table is a guideline that I have seen used successfully for a risk based approach to sampling. Based on the severity and criticality of the packaging materials, these guidelines can be adjusted up to down per your risk management process. Utilizing a c=0 sampling plan based on the binomial distribution, the sample size can be calculated using the following formula.

	Primary			Secondary
	Confidence (%)	Reliability (%)	Sample Size	Confidence (%)	Reliability (%)		Sample Size
Critical	99.5	99	527	99	97	151
Major	99	97	151	97	95	68
Minor	97	95	68	95	90	28

I hope this assists you.

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

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

Statistical Methods and Control Charts

Question:
My question is regarding a threading process. There is 100% inspection for go/no go check and about 5% rejection/rework. The batch size is 5,000 nos and is completed in 3 days of production. Two such batches are produced in a month.

What type of control chart should be used to monitor the process? How should the process capability be calculated in this case?

Answer:
The type of control chart first depends on what type of data you are measuring. If you are doing go/no go then you are limited to a “P” chart or a “C” chart. A “P” chart looks at % good (or bad). A “C” chart looks at the number of defects found.

If you are measuring thickness or strength, (something that can be measured), then you can use a X-bar/R chart or an X-bar/S chart depending on many samples are taken.

That is the simple answer; part of this depends on how you are taking samples and how often. If samples are taken at the start and the finish, then I would probably recommend the “P” chart.

If you can measure throughout the manufacturing process, and you look at the type of defects, then I recommend a “C” chart.

Ideally, if you can get measurement data, you are better off with the X-bar/R or the X-bar/S charts. These tend to be better predictors and it is easier to calculate capability.

With the capability for the go/no go data, you can get % defective, (or % good) and multiply that by 1,000,000 to get your capability estimate in defects per million.

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

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

Pesticide Residues Surveillance Program Sampling

ISO 14004, Environmental Management System, EMS

Question

I am plant production specialist working in government sector. I am the manager of pesticides residues surveillance program, on this program we targeting local commodities of fresh fruits and vegetables (F&V) by sampling the targeted numbers and types of F&V in regular basis around the year and we analyze samples and results and establish the annual report. I have checked many similar program in other countries included USDA program but I didn’t find approach methodology or statistical way to identify the sample size to be targeted in the year taking in account type and number of crops, crop production,…etc. to elaborate annual sampling plan. My question here is how can elaborate sampling plan for mentioned program considering all valuable factors?

Your cooperation is highly appreciated.

Answer

Sampling is a method to estimate population parameters. For example, if the goal is to determine the amount of unacceptable residue on store bought apples, and testing every individual apple is impractical, then we use a sample to estimate the proportion with unacceptable residue.

The sample plan must focus on the goal and balance with the resources and technology available. If the goal is to accurately detect a very low proportion with residue, say 1 in 1 million, then the sample size will be larger than if the goal is to detect 1 in 100 with unacceptable residue. The goal to detect 1 in 100 is easier to accomplish (fewer apples tested) yet does not reveal is there is a 1 in 1000 level or not.

A key element is the specific goal for detection and design a sample plan that is capable to detect at or better than the goal’s level. Capable includes the measurement system errors and an understanding of the nature of how failures occur.

Another consideration is the nature of the measurement and goal. If the test is only pass / fail for presence of residue, then we have to use the relatively inefficient sampling plans based on the binomial distribution. If the data is a variable value, such as part per million residue presence, then we can use more efficient sampling plans based on the appropriate continuous distribution. If the testing is destructive to the item being tested that limits the sampling techniques available.

How is the lot defined? If this is an annual report then the lot may be the annual production of a specific fruit or vegetable, say a specific variety of apples. Define the population clearly and any relevant subgroups of interest. If the data is only for an annual report the sampling plan is marked different than if the goal is a monthly monitoring and warning system.

Another consideration is the thresholds along with confidence. For sampling plan creation we use two specific points of interest. The Producer Risk Point (PRP) made up of the Acceptable Quality Level (AQL) and the producers’ risk (Type I risk or Alpha – which is the probability of rejecting a good lot, or in this case stating the residual level is above a specific AQL or value when it actually is not). The second point is the Consumer’s Risk Point made up of the Lot Tolerance Percent Defective (LTPD) and the consumer’s risk (Type II risk or Beta – which is the probability of accepting a bad lot, or in this case stating the residual level is below the LTPD when it is actually is not.)

The closer the AQL and LTPD are the more difficult (more samples) it is to determine an accurate estimate of the population. Likewise the less risk either the producer or consumer desire to incur again results in higher sample sizes.

One more consideration which is often overlooked is the selection of samples for testing. Most sampling plans are based on the assumption that the samples are taken randomly from the entire population. For example with say 50 million apples of a specific variety we would create a system to select samples that each has an equal change of any specific apply being selected. This is not a trivial matter in most cases. The availability and distribution of apples along with storage, shipping and display of apples all contribute to limited or biasing selecting a random sample. If it is not possible to select test items randomly, then study the impact on the study and means to account for a non-random sample.

In summary, for any sample plan:

Define the population
Define the desire goal of the study
Understand the measurement system
Use variables data if at all possible
Define PRP and CRP
Determine capable sampling plan
Design method to select random sample

This quick summary of consideration is what I consider the essential elements, yet other may impact the sampling plan. For example, seasonal variations in production, location in supply chain when measurements are made, variations in supply chain impact on presence of residual, differing nature of residue commonly found of different fruit or vegetables, and probably a few more. Understanding the goal, measurement system and random sampling will help determine areas that require consideration.

Cheers,

Fred Schenkelberg

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