# Sampling Question - Random Sample of 100 pcs and 11 pcs. have been rejected

G

#### GRISHAG

I received a batch of 2,300 pcs. I took random sample of 100pcs, and 11 pcs. have been rejected after my inspection. (I have no special customer requirements).
What will be my conclusion regarding the batch?

#### Jim Wynne

Re: sampling question

You may surmise that the uninspected portion of the batch includes a proportion of nonconforming items similar to the proportion in the sample.

#### ScottK

##### Not out of the crisis
Super Moderator
Re: sampling question

what Jim says.
as to whether you reject or accept the lot based on that information must take in a lot of factors and may be more a business decision than a quality decision.

G

#### GRISHAG

I tried to do some calculations, but I can't paste them because I use symbol of root. Here is the beginning multiplicate by root:
Pmax=0.11+Z0.90 x
under root is 0.11x0.89 devided by 100

#### Bill McNeese

##### Involved In Discussions
For a large sample, (n*p>10), you can use the following for confidence levels:

LCL = p - z*sqrt(pq/n)

UCL = p + z*sqrt(pq/n)

where z is the z value for alpha/2 and q = 1 - p. For small samples, the equation is a little more complex.

G

#### GRISHAG

Thank you.
Can you help with calculation for my case?
What will be conclusion regarding the batch?

#### Bill McNeese

##### Involved In Discussions
The calculation is straight forward. p = .11, q = .89, n = 100 and z = 1.645 for 90%. You can use NORMSINV in Excel to find z. What conclusion would you reach about the batch?

G

#### GRISHAG

Thank you.
Using NORM.S.INV I received z=1.282 (not 1.645 as you wrote).
My conclusion is that in batch of 23,000 there is at least 15% rejected parts. Am I right?

#### Bill McNeese

##### Involved In Discussions
All you can get from this is an estimated range. You had 11 parts rejected out of a sample size of 100. You want a confidence of 90%, which means alpha = 10%. Since this is two sided, the z value is based on alpha/2. Z for 0.05 is 1.645. Do the math and the confidence limits range from 6.85% to 17.21%. So, that is the range for % rejects based on this one sample result and size.

G

#### GRISHAG

Thank you very much. I thought that this is one tail test, this is a reason that I choose 1.283.
How do you came to conclusion regarding that probability to find defective is between 6.85% and 17.21%? Could you send me formula for calculation?

S Random Sampling question - taking samples from the same spot! Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
N The question asks about sampling plans and AQL Reliability Analysis - Predictions, Testing and Standards 5
A Acceptance Sampling question (Is there an approach) Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
B AQL Sampling Tables Question Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
V C=0 Zero Acceptance Number Sampling Plan - Question Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
R Six Sigma / DPMO Related Inquiry - A 6 Sigma related Statistical Sampling question Six Sigma 2
R Zero Acceptance Sampling Plans 5th edition by Squeglia - Question Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
M Distributor Sampling Question Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
D Mil-Std-1916 Inspection Sampling question Inspection, Prints (Drawings), Testing, Sampling and Related Topics 5
W Question about sample size code letter and selecting sampling plan Inspection, Prints (Drawings), Testing, Sampling and Related Topics 7
Sampling Probability Question - Difference in % bad parts in a lot of 3100 pieces Inspection, Prints (Drawings), Testing, Sampling and Related Topics 18
Statistics/sampling plan for medical device Inspection, Prints (Drawings), Testing, Sampling and Related Topics 10
Acceptance sampling by variables - Do Minitab use one sided k only? Why? Statistical Analysis Tools, Techniques and SPC 0
Acceptance Inspection Sampling Plan Calculators Misc. Quality Assurance and Business Systems Related Topics 0
Control Plan and the frequency of sampling FMEA and Control Plans 11
Attribute sampling plan ISO 13485:2016 - Medical Device Quality Management Systems 7
What is the Risk of Using Obsolete Versions of C=0 & ANSI/ ASQ Z1.4 Sampling Plans? ISO 13485:2016 - Medical Device Quality Management Systems 8
Customer feedbacks sampling size EU Medical Device Regulations 4
Mixing criteria and sampling Qualification and Validation (including 21 CFR Part 11) 1
What would you consider "representative sampling" for PT/ILC? ISO 17025 related Discussions 2
Calculating Ppk for Design Verification - Variable Sampling Design and Development of Products and Processes 15
Medical Device Component Change - Testing, Sampling Criteria ISO 14971 - Medical Device Risk Management 3
Is sampling allowed for MDR Class III products? EU Medical Device Regulations 0
Inspection of polymer palletes - sampling plan Inspection, Prints (Drawings), Testing, Sampling and Related Topics 0
Class IIb implantable-TD sampling plan EU Medical Device Regulations 0
How to Develop a Sampling Plan for Drug Substance? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 0
Stability sampling for Class 1 medical devices ISO 13485:2016 - Medical Device Quality Management Systems 1
Internal audit random sampling methodology Internal Auditing 2
Sampling strategies/techniques for software QA Software Quality Assurance 3
ANSI/ASQC Z1.9 VS MIL-STD-1916 for Continuous Sampling Lean in Manufacturing and Service Industries 2
Detection rank for sampling vs 100% inspection & 15x vs 400x magnification FMEA and Control Plans 4
IVD sampling sizes for buyer Reliability Analysis - Predictions, Testing and Standards 0
Which Sampling Plan(s) Should I Use? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 13
Sampling - ISO 16269-6 vs ISO 2859 Other ISO and International Standards and European Regulations 0
Sampling Plan Risks AQL - Acceptable Quality Level 6
Sampling plan for in-process QC (medical devices) Inspection, Prints (Drawings), Testing, Sampling and Related Topics 13
Minitab Capability of the Population (no sampling) Using Minitab Software 11
LTPD, AQL, Ppk and Cpk validation sampling plan table Inspection, Prints (Drawings), Testing, Sampling and Related Topics 0
Sampling method for Distributor verification activities EU Medical Device Regulations 1
Change in control plan - Do I have to do sampling? IATF 16949 - Automotive Quality Systems Standard 1
Is using ANSI/ASQ Z1.4-2008 the correct sampling plan to determine Pass/Fail of Apparel measurements? AQL - Acceptable Quality Level 8
Sampling Plan for Internal Audits - ISO 2859 or 3951 - Or Neither? Internal Auditing 6
Product audit sampling plans IATF 16949 - Automotive Quality Systems Standard 12
Reduced sampling plan for sterial products APQP and PPAP 0
ISO 2859-1 - 9.3.3.2 Switching score - Sampling Plans and PPM AQL - Acceptable Quality Level 0
BS EN 12060:1998 - Zinc and zinc alloys Method of sampling Specifications Manufacturing and Related Processes 4
High voltage testing - ISO 17025 - 7.2.2 Validation of methods and 7.3 Sampling ISO 17025 related Discussions 3
Activity Sampling Exercise Lean in Manufacturing and Service Industries 11
Defining sampling plan for different AQL AQL - Acceptable Quality Level 3
AS9100D Sampling Plan AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 2