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

Fully vaccinated are you?
Leader
#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
Quality Runner Continuous monitoring of validated process – sample sizes 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 3
D Locking Control Limits and SPC Sample Sizes (AIAG/Automotive Requirements) Six Sigma 2
S Determining sample sizes for PQ Qualification and Validation (including 21 CFR Part 11) 4
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
K Sample size calculation for the medical device with multiple indications. e.g. suture US Food and Drug Administration (FDA) 3
R 18 different charts? 18 sample points over 28 days Capability, Accuracy and Stability - Processes, Machines, etc. 13
V Sample Size rationale to reduce size and use special levels EU Medical Device Regulations 6
C Sample qualification to be IEC 60601-1 series tested IEC 60601 - Medical Electrical Equipment Safety Standards Series 2
Y DFMEA Sample in Semiconductor FMEA and Control Plans 2
T Cease Production Sample Procedure Manufacturing and Related Processes 1
Q Gage Pin Sets? Calibrate/Verify them all or just a sample size? General Measurement Device and Calibration Topics 22
S How to determine sample size to test when the acceptance criteria is x >= Standard value? 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 7
I Mixing tank sample points Qualification and Validation (including 21 CFR Part 11) 4
T Sample size calculation Using Minitab Software 3
C What Theory is MIL-STD-105E Sample Size Code Letters Based on? Quality Tools, Improvement and Analysis 3
Stefan Mundt AS9100D Engineering sample purchases - Supplier not approved AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 3
U Determining population defect rate from sample defect rate Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
Y FMEA link to Control Plan frequency and sample size FMEA and Control Plans 20
T Noob question regarding sample size Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
S Help needed in choosing the method of calculating the minimum sample size Internal Auditing 12
P Worst case HLD sample for efficacy studies Other US Medical Device Regulations 0
D Estimate Sample Size for very rare event Using Minitab Software 1
M Summative evaluation: how many sample per participant? IEC 62366 - Medical Device Usability Engineering 5
S Determining Sample Size and Method Quality Tools, Improvement and Analysis 12
C Complaint Return Sample Size Question 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 4
shimonv Frequency and sample size for lot release of EtO sterilized products EU Medical Device Regulations 2
X Sample SOC2 audit report (or a redacted one) IEC 27001 - Information Security Management Systems (ISMS) 0
A Clinical assessment sample size - Medical device Class IIb implantable (93/42 directive) EU Medical Device Regulations 2

Similar threads

Top Bottom