1. LESSON 2 Statistical Sampling
January 2016

2. Lesson Introduction
Given a surveillance requirement, the student will be able to apply statistical sampling techniques to supplier contract activities.

3. Lesson Objectives
Upon completion of this lesson, you should be able to:
Relate the importance of sampling to QA surveillance.
Distinguish between the three types of inspection: Normal, Reduced, and Tightened.
Outline the internal Defense Contract Management Agency (DCMA) process of Zero-based sampling.
Use randomization tools to generate random numbers for a simple random sample.
Determine whether to initiate acceptance or non-acceptance activities based on sampling results.
Lesson 4: Safety Stock

4. Lesson Topics This lesson will cover these topics:
General background (DCMA policy, sampling terms, and Acceptable Quality Level (AQL))
Importance of sampling to QA
Three types of inspection under a Sampling Plan
Zero-based sampling
Generating random sample numbers
Initiating acceptance and non-acceptance activities

5. What’s In It For Me (WIIFM)?
This lesson is important because:
Zero-Based sampling is a tool used to ensure suppliers present and the Quality Assurance Specialist (QAS) accepts conforming product
DCMA policy to use
Zero-based sampling
Random sampling techniques
Statistically valid sampling plan
Multiple sampling plans exist, including:
ANSI/ASQ Z
MIL-STD 1916

6. DCMA Policy Use Zero-Based Sampling Use random sampling techniques
Use statistically valid sampling plans
Ensure supplier:
Meets contractual requirements
Understands and uses statistically valid sampling plans
If product examination is determined to be the appropriate surveillance method, the QAS should verify the supplier’s conformance by sampling.

7. Sampling Terms Sampling System Sampling Scheme Sampling Scheme
Sampling System - collection of sampling schemes indexed by lot-size ranges, inspection levels, and Acceptable Quality Levels (AQLs) (i.e., ANSI/ASQ Z ) DCMA Policy: The QAS will use zero-based sampling unless otherwise stated in a Quality Assurance Letter of Instruction (QALI).
Sampling System
Sampling
Scheme
Sampling
Scheme
Sample Plan 1
Sample Plan 1
Sample Plan 2
Sample Plan 2
Sample Plan 3
Sample Plan 3
Sample Plan 4
Sample Plan 4

8. Sampling Terms, Cont. Sampling Scheme
Sampling Scheme - combination of sampling plans with switching rules and provision for discontinuance of inspection (i.e., Normal, Reduced, or Tightened) Individual Sampling Plan - plan stating sample size(s) and acceptance criteria (i.e., AQL)
Sampling
Scheme
Sample Plan 1
Sample Plan 2
Sample Plan 3
Sample Plan 4

9. Sampling Terms, Cont.
Attribute - a characteristic or property appraised in terms of whether it does or does not exist, (e.g., go or no go) with respect to a given requirement Characteristic - a physical, chemical, visual, functional, or any other identifiable property of a product, material, or unit identified by the product specification, standard, drawing, etc. Defect - a departure of a quality characteristic from its intended level or state that occurs with a severity sufficient to cause an associated product or service not to satisfy intended normal, or foreseeable, usage requirements (ANSI/ASQ Z ) Nonconformity - a departure of a quality characteristic from its intended level or state that occurs with a severity sufficient to cause an associated product or service not to meet a specification requirement; a unit of product that contains one or more defects (ANSI/ASQ Z )

10. Sampling Terms, Cont.
Lot or Batch - shall mean “inspection lot” or “inspection batch,” i.e., a collection of units of product from which a sample is drawn and inspected to determine conformance with the acceptability criteria, and may differ from a collection of units designated as a lot or batch for other purposes (e.g., production, shipment, etc.) (ANSI/ASQ Z ) Lot or Batch Size - the number of units of product in a lot or batch Homogeneity - manufactured under essentially the same conditions and essentially at the same time

11. Acceptable Quality Level (AQL)
Acceptable Quality Level (AQL) - the quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance sampling. Process Average - the average percentage of nonconforming or average number of nonconformities per hundred units (whichever is applicable) of product submitted by the supplier for original inspection.
Percent Nonconforming =
Number Nonconforming X
100
Number of Units Inspected
Nonconformities per Hundred Units X
Number Nonconformities
100
Number of Units Inspected
Note: One or more nonconformities being possible in any unit

12. Importance of sampling to qa
Lesson Topics:
Importance of Sampling to QA
Three Types of Inspection Under a Sampling Plan
Zero-Based Sampling
Generating Random Sample Numbers
Initiating Acceptance and Non Acceptance Activities

13. What is Sampling?
Refers to a portion of a population that is representative of the population from which it was selected. In other words, the sample is a subset of the population.
Population
Sample

14. What is Acceptance Sampling?
Selecting and inspecting only a representative smaller subset (sample) selected from a larger lot or batch (population), for the purpose of making an accept/reject decision of an entire lot or batch based on the inspection results of the sample only.
Used by suppliers and DCMA to validate product quality.

15. Accurate Assessment of the Population
Why Should We Sample?
Why
Sampling
Accurate Assessment of the Population
Cost Effective
Customer Requests
100% Not Always Possible
Saves Time

16. What is Random Sampling?
Product
Random Sample
Refers to a sampling procedure where every unit in the population has an equal chance of being selected as part of the sample
Objective of Random Sampling: To ensure that the final samples to be measured or tested are representative of the population from which they were taken
ILLUSTRATE random sampling procedure
Every item in that population has an equal opportunity to be selected
If the sample taken is not representative of the population, then it is a biased sample, which can lead to misleading results.
Random sample can be drawn in several ways:
When material is packaged or laid out on a bench in groups or rows, each unit may be numbered from 1 to the total and a sample selected using a random number table
For bulk material a numbered area or zone can be used to lay the material out. Samples can be drawn from numbered zones located by using a random number generator.
ASK the question: What is your answer if a contractor comes to you and says, “We are almost done with this lot, only one more skid to go. Can you go ahead and take your sample from this?”
DISCUSS answer: No, because every item has not had the equal opportunity to be selected in the sample.

17. Zero-Based Sampling Plans
Lot is accepted when zero defects are discovered
Lot is not accepted when one defect is discovered
Also referred to as:
Acceptance equals 0 (C=0)
Zero-Based Acceptance (ZBA)
Accept on Zero (AoZ)
During product examination
Use statistically valid sampling systems
Measure product characteristics
Ensure compliance with manufacturing specification requirements

18. Sampling Risks
Customer’s Risk
Producer’s Risk
Acceptance of Nonconforming Product
Non-Acceptance of Conforming Product
Because the “lot” disposition is based on sample results, there is a probability of making an incorrect disposition concerning “lot” acceptance.

19. Three types of inspection under a sampling plan
Lesson Topics:
Importance of Sampling to QA
Three Types of Inspection Under a Sampling Plan
Zero-Based Sampling
Generating Random Sample Numbers
Initiating Acceptance and Non Acceptance Activities

20. Three Types of Inspection Under a Sampling Plan
Normal Inspection
Reduced Inspection
Tightened Inspection

21. Types of Inspection Normal Inspection Reduced Inspection
Inspection under a sampling plan that is used when there is no evidence that the quality of the product being submitted is better or poorer than the specified quality level
Reduced Inspection
Inspection under a sampling plan using the same quality level as normal inspection, but requiring a smaller sample for inspection
Tightened Inspection
Inspection under a sampling plan using the same quality level as normal inspection, but requiring more stringent acceptance criteria

22. Switching Rules
Preceding 10 lots accepted
Total nonconforming less than limit number (optional)
Production steady
Approved by responsible authority
START
2 of 5 or fewer consecutive lots are not accepted
REDUCED
NORMAL
TIGHTENED
Lot not accepted
Lot accepted but nonconformities found lie between Ac and Re of plan
Production irregular
Other conditions warrant
5 consecutive lots accepted
5 lots not accepted while on Tightened inspection
When switching from normal to tightened or reduced inspection, the sample size changes but not the AQL.
Discontinue inspection under Z1.4

23. zero-based sampling Lesson Topics: Importance of Sampling to QA
Three Types of Inspection Under a Sampling Plan
Zero-Based Sampling
Generating Random Sample Numbers
Initiating Acceptance and Non Acceptance Activities

24. Zero-Based Sampling
Process overview includes making determinations of:
Population
Criteria
Method
Sample size
Acceptance Decisions

25. Zero-Based Sampling Process Details
Method
Determine the sample system and size
Determine contractual (supplier) sampling requirement:
ANSI/ASQ Z /MIL-STD-1916/Government approved plan
Use zero acceptance number sampling plans (Squeglia)
Unless directed by the customer [Quality Assurance Letter of Instruction (QALI)]
Use contract or DCMA criteria for determining AQL
Select sample size per the sampling system tables
Identify accept/reject number from system tables
Zero-Based (C=0) when not contractually mandated

26. Zero-Based Sampling Process Details, Cont.
Method
Determine the sample system and size (cont.)
Samples are selected independent of supplier's sample
When AQL is not specified in contract or QALI:
AQL=0.4 - All critical characteristics on a Critical Safety Item (CSI)
AQL=1.0 – Complex/critical products and/or CSI significant characteristics
AQL=4.0 – Non-complex/non-critical product
Sample size is determined by the AQL and lot size

27. Zero-Based Sampling Process Details, Cont.
Method
Determine the sample system and size (cont.)
Sample selection is dependent on lot formation
Identified by product serial number, production number, some other form of identification
Identified by shift, by machine, by operator, by model, by customer designation
Product unit identification
Allows for randomization using tables of random numbers
Random sampling shall be used even without unit identification or traceability

28. Zero-based Sampling Plan: AQL Chart

29. Zero-based Sampling Plan: Example

30. Product Examination Sheet Sampler Tab
Product Examination Sheet also contains an automated Zero-Based AQL chart that identifies sample size.
Product Examination Sheet

31. Question and Answer
What is the sample size if the lot size is 285 and it is a critical characteristic for the product which is a critical safety item?
125 48 29 11
Select the graphic to view the chart.

32. Question and Answer
What is the sample size if the lot size is 35,000 and the product is a non-complex item? 60
315
108 29
Select the graphic to view the chart.

33. Generating random sample numbers
Lesson Topics:
Importance of Sampling to QA
Three Types of Inspection Under a Sampling Plan
Zero-Based Sampling
Generating Random Sample Numbers
Initiating Acceptance and Non Acceptance Activities

34. Generating Random Sample Numbers
The Product Examination Policy page includes Helpful QA Tools:
1711 Random Generator tool
Random Generator 5
(Excel© spreadsheet)
(for other random generators)

35. Using Random.Org Random Number Generator

36. Practice
Practice using to obtain a random sample.
Lot size of 1200.
Sample size of 34.

37. Initiating acceptance and non-acceptance activities
Lesson Topics:
Importance of Sampling to QA
Three Types of Inspection Under a Sampling Plan
Zero-Based Sampling
Generating Random Sample Numbers
Initiating Acceptance and Non Acceptance Activities

38. Initiating Acceptance and Non-acceptance Activities
Execute
Perform sampling
Document results
Decisions
Acceptance
Non-acceptance

39. Sampling Process Details
Execute
Perform the sampling and document results
Perform examination of the product characteristics, features, or specification requirements as identified in the GCQA surveillance plan
Accept/reject number from sampling system tables
Zero-Based (C=0) - accept on 0 defects, reject on 1 defect
Document the results of the examinations in accordance with agency policy requirements
Adjust risk assessment based on results
Update GCQA surveillance plan accordingly

40. Sampling Process Details, Cont.
Decisions
Initiate acceptance or non-acceptance actions
Notify the supplier of the results
Accept/non-accept decision
Verify supplier’s compliance with:
Lot rejection
Requirements concerning lot screening
Defect investigation
Product replacement
Corrective action

41. Sampling Process Details, Cont.
Decisions
Initiate acceptance or non-acceptance actions (cont.)
When using Zero-Based sampling, the entire lot is rejected when one (1) defect is found in the sample
The supplier shall tender to the Government for acceptance only supplies that have been inspected in accordance with the inspection system and have been found by the supplier to be in conformity with contract requirements… The supplier shall remove supplies rejected or required to be corrected.
Adjust sampling levels as provided for in sampling system or policy

42. Summary Having completed this lesson, you should now understand:
Sampling is important to ensure acceptance of conforming product.
Three levels of inspection: normal, reduced, and tightened.
DCMA process for sampling must be used.
Use of a random number generator preferred; DCMA QA policy includes links to random number generator tools.
DCMA policy mandates zero-based sampling unless otherwise specified by the customer.
Lesson 4: Safety Stock

43. Summary, Cont.
Having completed this lesson, you should now understand:
Zero-based sampling system tables:
CSI critical characteristics use AQL of 0.40%
Complex/critical products or DCMA identified significant characteristics use AQL of 1.0%
Non-complex/non-critical products use AQL of 4.0%
When using zero-based sampling, entire lot is rejected when one defect is found.
Lesson 4: Safety Stock

44. Other Training: CMQ200, Statistical Sampling

45. Other Training: CMQ200, Statistical Sampling, Cont.

46. Questions

47. Review Question 1 Which is NOT a reason to sample?
100% inspection is not possible
Saves time and money
Each product must be inspected
Customer requests it

48. Review Question 2
What type of sampling plan is required by DCMA policy?
Simple
Zero-based
ANSI/ASQ Z
MIL-STD 1916

49. Review Question 3
What AQL is required for a Critical Safety Item (CSI) critical characteristic?
.040%
0.40%
4.0%
1.0%

50. Review Question 4
Inspection level for initial inspection starts at _________.
Normal
Reduced
Tightened
Variable

51. Review Question 5
When changing from Normal to Reduced or Tightened inspection, the QAS is changing the:
Criteria
Lot size
Population size
Sample size

52. Review Question 6 When is a lot rejected if using the Zero-based plan?
0 defects
1 defect
2 non critical defects
2 defects