Sample Sizes and A2, A3, B4, d2 Factor Parameters

K

kristof nuyts

#1
Hello,

I'm a student Industrial Engineer Elektromechanics in Belgium. For a thesis I have to make a study about Statistical Process Control.

Recently I've encountered a small problem. Suppose we have an on-line process and every second we get the value of a measurement. We calculate the moving average and plot it on a chart. The problem is which samplesize I have to take. Usually people take a sample size of 2 but is there a formula to calculate the sample size?

I have noticed that in some books the parameters A2, A3, B4, d2,... are just written down for sample sizes from 2 to 25. Do these parameters exist for larger sample size or isn't it useful to use these. In other words, is it still useful for plotting the points on a chart with a sample size of (for example) 28.

greetings,

Kristof N.
 
Elsmar Forum Sponsor

Marc

Hunkered Down for the Duration
Staff member
Admin
#2
If you get 1 measurement every 1 second, how many pieces are going through in 1 second?
 
D

D.Scott

#3
Kristof - I am not a statistician so this is only information from my limited knowledge. At least we will get the discussion going.

Assumption - you are running an X-bar & R chart.

It depends on why you are using the chart as to the large sample sizes being useful. If you are trying to control process variability for example, you wouldn't want a large sample size. There is a number of 12 somewhere in the back of my head as the point where the range efficiency drops rapidly.

For large sample sizes you would probably want to run an X-bar & s chart.

Dave
 
R

Rick Goodson

#4
kristof,

Let me follow up on Dave's comments.

There are three components of variation in a part, within-piece, piece-to-piece, and time-to-time variation. These are composed of process, material, operator, and miscellaneous components. There are typically two schemes for selecting subgroup samples:

1) Select subgroup samples from product produced at one instant of time or as close to one instant as possible - instant time method.

2) Select product produced over a period of time so that it represents all products - period of time method.

The instant time method will have a minimum of within part variation and a maximum of variation among subgroups. Period of time will have a maximum of within part variation while a minimum of subgroup to subgroup variation. Instant time is the most common used method.

Deciding on the subgroup size is more of a management than a technical decision. As the subgroup size increases, the control limits become closer to the central value which makes the subgroup more sensitive to small variations in the process average. Also, as the subgroup size increases the inspection/test cost increases. When the subgroup size exceeds 10, a sigma chart is used instead of the range chart. Sigma is more sensitive but more difficult to calculate. Range is normally used simply for calculating simplicity.

There is no rule for frequency of subgroups. The inconveniences of factory layout and the cost involved in taking the subgroups have to be balanced against the value of more frequent information. A rule of thumb is to used a variables sampling plan (such as the old MIL-STD-414) to determine the sample size based on daily production. For example, if you produce 3,201 to 8,000 units per day you would take 60 samples per day. If the subgroup size is 5, then the number of subgroups per day would be 60 divided by 5 or 12 subgroups.

With regard to the A2, A3, B4, d2 factors, you need to understand the derivation of the factors to understand why the tables stop at 25. The formula substitutions do not work well in the text based forum format otherwise I would try to show it to you. If you can get hold of a copy of Acheson Duncan's book, Quality Control and Industrial Statistics you can find the background material. Never the less, for the A2 factor for a sample larger than 25 the formula is 3 multiplied times d2 divided by the squart root of the sample size (n). The d2 factor for samples larger than 25 is equal to R divided by sigma. My formula come from an American Society for Testing and Materials standard, ASTM-STP-15D.

Hope this helps.

Regards,

Rick
 
K

kristof nuyts

#5
Thanks to all of you for the answers.

With regard to the A2, A3, B4, d2 factors, Rick wrote me to get a copy of Acheson Duncan's book, Quality Control and Industrial Statistics. Too bad I'm just a (poor) student working on a thesis who hasn't got the money for ordering it.

Maybe someone knows a website where I can find the formulas for all these factors.

Thanks,

Kristof

:bigwave:
 
Thread starter Similar threads Forum Replies Date
N Design Verification & Process Validation - Statistical sample sizes Design and Development of Products and Processes 2
Marc Determination of Sample Sizes when Auditing General Auditing Discussions 13
M Validation Sample Sizes and Selection: An Example Inspection, Prints (Drawings), Testing, Sampling and Related Topics 10
D Sample Sizes for 'Bulk' Fluids/ Materials (Polymer Synthesis Process) Design and Development of Products and Processes 1
M Unequal Sample Sizes - F-Test & T-Test Statistical Analysis Tools, Techniques and SPC 5
H Determining the Correct Sample Size when AQL points to two Sample Sizes AQL - Acceptable Quality Level 7
R Determining Sample Sizes for Testing (Chemistry or Microbiology) Inspection, Prints (Drawings), Testing, Sampling and Related Topics 6
C Sample Size: Why are Sample Sizes not Linear according to the Lot Size? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
E AQL with Multiple Attributes - Sample Sizes AQL - Acceptable Quality Level 8
J Control Charts with different Sample Sizes Reliability Analysis - Predictions, Testing and Standards 2
G Stabilized (Normalized) S Chart for Unequal Sample Sizes Statistical Analysis Tools, Techniques and SPC 5
A AQL Sample Sizes - Explain how Sample Sizes in an AQL table are calculated AQL - Acceptable Quality Level 4
B Sample Sizes for In-Vivo Design Validation Testing Other Medical Device and Orthopedic Related Topics 1
S Single-Stage Cluster Sample of Unequal Sizes & Confidence Limits Statistical Analysis Tools, Techniques and SPC 1
R Chain Sampling Plan explanation and help - Reducing sample sizes (compared to Z1.4) Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
T Sample Sizes for Design Verification of Medical Devices Inspection, Prints (Drawings), Testing, Sampling and Related Topics 16
T Assumptions with Small Sample Sizes Capability, Accuracy and Stability - Processes, Machines, etc. 11
T Hypothesis test help/sample sizes/advice - Two different polycarbonates Statistical Analysis Tools, Techniques and SPC 2
B Destructive Gauge R&R Sample Sizes - Does ANOVA work better for the analysis? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
A Sample Sizes for Process Validation - Medical device manufacturer ISO 13485:2016 - Medical Device Quality Management Systems 6
A Arriving at Sample sizes based on confidence levels Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
M Auditing Statistically - A statistical approach to sample sizes General Auditing Discussions 11
J Statistically Valid Sample Sizes For SPC Statistical Analysis Tools, Techniques and SPC 1
L Sample Procedure from Contract Manufacturer Prospective ISO 14971 - Medical Device Risk Management 1
D Adding a Class I to a sample box Canada Medical Device Regulations 5
P Unrealistic Packaging Validation Sample Size 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 13
M ISO 9001:2015 case study sample ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 2
M Sample of Nonconformity report for ISO 9001:2015 ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 3
A Sample Agreement available for Outsourcing Medical Device Design activity? ISO 13485:2016 - Medical Device Quality Management Systems 1
B Control chart and sample time Statistical Analysis Tools, Techniques and SPC 1
J Control chart for huge sample size Statistical Analysis Tools, Techniques and SPC 9
D How to list multi-product sample pack in GUDID 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 1
S Is there a standard for sample size during R&D phase Other ISO and International Standards and European Regulations 18
M Minitab assistant: 1-Sample % Defective Test Using Minitab Software 1
J Sample size definition in an Automotive SMT pilot lot run Misc. Quality Assurance and Business Systems Related Topics 1
T ISO 27001 sample audit report IEC 27001 - Information Security Management Systems (ISMS) 0
B IATF 16949 - Is a Deviation required for sample components in a prototype build? IATF 16949 - Automotive Quality Systems Standard 13
D Sample Calibration SOP for ISO 13485 General Measurement Device and Calibration Topics 4
T Sample of 1st Article Inspection Report wanted APQP and PPAP 3
E Correct way to certify hydrostatic testing when it is not 100% (and Sample Size) Various Other Specifications, Standards, and related Requirements 6
B Determining sample size for device sterility Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
A In which EU countries would it be okay to use sample labels for registration? EU Medical Device Regulations 0
D Determining of sample size for 'Operational Qualification' AQL - Acceptable Quality Level 3
F Bayes Success run Theorem for sample size during OQ&PQ Qualification and Validation (including 21 CFR Part 11) 4
Watchcat Identification of Test Sample in Test Reports? Design and Development of Products and Processes 22
M AQL table - I need to sample 1250pcs AQL - Acceptable Quality Level 3
K The correct way of doing a 2 Sample T test Reliability Analysis - Predictions, Testing and Standards 7
I Device modifications - Clinical sample size rationale EU Medical Device Regulations 5
M Informational How to perform a clinical evaluation of medical devices – Part 1 – Overview and sample of activities Medical Device and FDA Regulations and Standards News 0
M SOP Sample for BC/ISO22301 (Business Continuity) wanted Business Continuity & Resiliency Planning (BCRP) 4

Similar threads

Top Bottom