Cmq101 M4 L2 Psg Final

LESSON 2 Statistical Sampling

15November2013

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

Module 4, Lesson 2: Statistical Sampling

2

Lesson Objectives Upon completion of this lesson, you should be able to:

    

Relate the importance of sampling to Quality Assurance (QA) surveillance responsibilities. Distinguish between Inspection by Attributes and Inspection by Variables. 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.

Module 4, Lesson 2: Statistical Sampling

3

Lesson Objectives (cont.) Upon completion of this lesson, you should be able to:

    

Differentiate between simple, systematic, cluster, and stratified sampling techniques. Interpret information presented on Zero-based sampling system tables. Interpret information presented on American National Standards Institute (ANSI)/American Society for Quality (ASQ) Z1.4-2008 sampling system tables. Interpret information presented on Military Standard (MILSTD)-1916 sampling system tables. Determine whether to initiate acceptance or non-acceptance activities based on sampling results.

Module 4, Lesson 2: Statistical Sampling

4

Lesson Topics This lesson will cover the following topics:  Importance of Sampling to QA  Inspection by Attribute vs. Inspection by Variable  Three types of Inspection Under a Sampling Plan  Zero-Based Sampling  Generating Random Sample Numbers  Simple, Systematic, Cluster, and Stratified Sampling Techniques  Interpreting Zero-Based Sampling System Tables  Interpreting ANSI/ASQZ1.4-2008 Sampling System Tables  Interpreting MIL-STD-1916 Sampling System Tables  Initiating Acceptance and Non acceptance Activities

Module 4, Lesson 2: Statistical Sampling

5

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 Z1.4-2008 – MIL-STD 1916

Module 4, Lesson 2: Statistical Sampling

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 the appropriate surveillance method, the QAS should verify supplier’s conformance by sampling. Module 4, Lesson 2: Statistical Sampling

7

Sampling Terms (1 of 4) Sampling System - collection of sampling schemes indexed by lot-size ranges, inspection levels, and Acceptable Quality Levels (AQLs) (i.e., ANSI/ASQ Z1.4-2008) DCMA Policy: The QAS will use zero-based sampling unless otherwise stated in a QALI.

Sampling System Sample Sample Plan Plan 11

Sampling Scheme

Sample Sample Plan Plan 22 Sample Sample Plan Plan 33 Sample Sample Plan Plan 44

Module 4, Lesson 2: Statistical Sampling

Sample Sample Plan Plan 11

Sampling Scheme

Sample Sample Plan Plan 22 Sample Sample Plan Plan 33 Sample Sample Plan Plan 44 8

Sampling Terms (2 of 4) 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) Sample Sample Plan Plan 11

Sampling Scheme

Sample Sample Plan Plan 22 Sample Sample Plan Plan 33 Sample Sample Plan Plan 44

Module 4, Lesson 2: Statistical Sampling

9

Sampling Terms (3 of 4) 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 Z1.4-2008) 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 Z1.4-2008) Module 4, Lesson 2: Statistical Sampling

10

Sampling Terms (4 of 4) 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 Z1.4-2008) 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

Module 4, Lesson 2: Statistical Sampling

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 percent of nonconforming or average number of nonconformities per hundred units (whichever is applicable) of product submitted by the supplier for original inspection. Percent Nonconforming

=

Nonconformities per Hundred Units

X

Number Nonconforming Number of Units Inspected Number Nonconformities Number of Units Inspected

X

100

X

100

Note: One or more nonconformities being possible in any unit

Module 4, Lesson 2: Statistical Sampling

12

IMPORTANCE OF SAMPLING TO QA Lesson Topics: 1) Importance of Sampling to QA 2) Inspection by Attribute vs. Inspection by Variable 3) Three Types of Inspection Under a Sampling Plan 4) Zero-Based Sampling 5) Generating Random Sample Numbers 6) Simple, Systematic, Cluster, and Stratified Sampling Techniques 7) Interpreting Zero-Based Sampling System Tables 8) Interpreting ANSI/ASQZ1.4-2008 Sampling System Tables 9) Interpreting MIL-STD-1916 Sampling System Tables 10) Initiating Acceptance and Non Acceptance Activities Module 4, Lesson 2: Statistical Sampling

13

Topic1: Importance of Sampling to QA

Mr. Shields: Statistical Sampling Importance Module 4, Lesson 2: Statistical Sampling

14

What is Sampling? The term, “Sample,” refers to a portion of a population that is representative of the population from which it was selected. The sample is a subset of the population.

Population

Sample

Module 4, Lesson 2: Statistical Sampling

15

What is Acceptance Sampling? 



Acceptance sampling is 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. Acceptance sampling is used by suppliers and DCMA to validate product quality.

Module 4, Lesson 2: Statistical Sampling

16

Why Should We Sample? Accurate Assessment of the Population

Saves Time

100% Not Always Possible Module 4, Lesson 2: Statistical Sampling

Why Sampling

Cost Effective

Customer Requests 17

Random Sampling

Mr. Shields: Random Sampling Example Module 4, Lesson 2: Statistical Sampling

18

What is Random Sampling?

 

The term Random Sampling refers to a sampling procedure where every unit in the population has an equal chance of being selected as part of the sample The objective of the sampling procedure is to ensure that the final samples to be measured or tested are representative of the population from which they were taken

Module 4, Lesson 2: Statistical Sampling

19

Zero-Based Sampling Plans 

Zero-Based sampling plans – Lot is accepted when zero defects are discovered – Lot is not accepted when one defect is discovered



These type plans are 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

Module 4, Lesson 2: Statistical Sampling

20

Sampling Risks 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. Module 4, Lesson 2: Statistical Sampling

21

INSPECTION BY ATTRIBUTE VS. INSPECTION BY VARIABLE Lesson Topics: 1) Importance of Sampling to QA 2) Inspection by Attribute vs. Inspection by Variable 3) Three Types of Inspection Under a Sampling Plan 4) Zero-Based Sampling 5) Generating Random Sample Numbers 6) Simple, Systematic, Cluster, and Stratified Sampling Techniques 7) Interpreting Zero-Based Sampling System Tables 8) Interpreting ANSI/ASQZ1.4-2008 Sampling System Tables 9) Interpreting MIL-STD-1916 Sampling System Tables 10) Initiating Acceptance and Non Acceptance Activities Module 4, Lesson 2: Statistical Sampling

22

Topic 2: Inspection by Attribute vs. Inspection by Variable

GO NO GO

Attribute

Module 4, Lesson 2: Statistical Sampling

Variable

23

Inspection by Attributes 



Inspection, whereby either the unit of product is classified simply as conforming or nonconforming, or the number of nonconformities in the unit of products is counted, with respect to a given requirement or set of requirements (ANSI/ASQ Z1.42008) Documentation examples include: – Good/Bad – Pass/Fail – Yes/No – Go/No go

Module 4, Lesson 2: Statistical Sampling

24

Inspection by Variables   

Inspection wherein certain quality characteristics of sample are evaluated with respect to a continuous numerical scale and expressed as precise points along this scale. Variables inspection identifies the degree of conformance or nonconformance of the characteristic to the specified requirements. Documentation examples include: – Dimension – Weight – Pressure

Module 4, Lesson 2: Statistical Sampling

25

THREE TYPES OF INSPECTION UNDER A SAMPLING PLAN

Lesson Topics: 1) Importance of Sampling to QA 2) Inspection by Attribute vs. Inspection by Variable 3) Three Types of Inspection Under a Sampling Plan 4) Zero-Based Sampling 5) Generating Random Sample Numbers 6) Simple, Systematic, Cluster, and Stratified Sampling Techniques 7) Interpreting Zero-Based Sampling System Tables 8) Interpreting ANSI/ASQZ1.4-2008 Sampling System Tables 9) Interpreting MIL-STD-1916 Sampling System Tables 10) Initiating Acceptance and Non Acceptance Activities Module 4, Lesson 2: Statistical Sampling

26

Topic 3: Three Types of Inspection Under a Sampling Plan

  

Normal Inspection Reduced Inspection Tightened Inspection

Module 4, Lesson 2: Statistical Sampling

27

Types of Inspection Normal 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 (ANSI/ASQ Z1.4-2008)

Reduced Inspection  Inspection under a sampling plan using the same quality level as normal inspection, but requiring a smaller sample for inspection (ANSI/ASQ Z1.4-2008)

Tightened Inspection  Inspection under a sampling plan using the same quality level as normal inspection, but requiring more stringent acceptance criteria (ANSI/ASQ Z1.4-2008)

Module 4, Lesson 2: Statistical Sampling

28

ZERO-BASED SAMPLING Lesson Topics: 1) Importance of Sampling to QA 2) Inspection by Attribute vs. Inspection by Variable 3) Three Types of Inspection Under a Sampling Plan 4) Zero-Based Sampling 5) Generating Random Sample Numbers 6) Simple, Systematic, Cluster, and Stratified Sampling Techniques 7) Interpreting Zero-Based Sampling System Tables 8) Interpreting ANSI/ASQZ1.4-2008 Sampling System Tables 9) Interpreting MIL-STD-1916 Sampling System Tables 10) Initiating Acceptance and Non Acceptance Activities Module 4, Lesson 2: Statistical Sampling

29

Topic 4: Zero-Based Sampling Process overview includes making determinations of:

     

Population Criteria Method Sample size Execute Decisions

Module 4, Lesson 2: Statistical Sampling

30

Zero-Based Sampling Process Overview

Module 4, Lesson 2: Statistical Sampling

31

Zero-Based Sampling Process Details

Contractual products or services

 To be provided by contract requirement

Population may represent

 Product during manufacturing or in-process product examination  Product final acceptance

Presented after supplier has determined product quality  After supplier’s inspection or test

May be divided into subsets

 Units by machine/units, by shift/units, by day/units, by customer

Module 4, Lesson 2: Statistical Sampling

32

Zero-Based Sampling Process Details

Identify and document the product characteristics or specification requirements to be examined by sampling Determine the product acceptance criteria for each:  Product characteristic to be examined  Specification requirement to be validated

The product characteristics, features, or specification requirements elected must be present and examinable in/on every product unit in the population and sample

Module 4, Lesson 2: Statistical Sampling

33

Zero-Based Sampling Process Details (1 of 3)

Determine contractual (supplier) sampling requirement:

 ANSI/ASQ Z1.4-2008/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 Module 4, Lesson 2: Statistical Sampling

34

Zero-Based Sampling Process Details (2 of 3)

Samples are selected independent of supplier's sample When AQL is not specified in contract or QALI:  AQL=0.4 - All critical characteristics on 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

Module 4, Lesson 2: Statistical Sampling

35

Zero-Based Sampling Process Details (3 of 3)

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 Module 4, Lesson 2: Statistical Sampling

36

Zero-based Sampling Plan: AQL Chart

Module 4, Lesson 2: Statistical Sampling

37

Zero-based Sampling Plan: Example

Module 4, Lesson 2: Statistical Sampling

38

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

Product Product Examination Examination Sheet Sheet

Module 4, Lesson 2: Statistical Sampling

39

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? A. B. C. D.

125 48 29 11 Select the graphic to view the chart.

Module 4, Lesson 2: Statistical Sampling

40

Question and Answer What is the sample size if the lot size is 35,000 and the product is a non-complex item? A. B. C. D.

60 315 108 29 Select the graphic to view the chart.

Module 4, Lesson 2: Statistical Sampling

41

Random Sampling Process Details

Common techniques include:    

Simple random sampling Systematic sampling Cluster sampling Stratified sampling

The sampling technique will always be random  Randomization is DCMA policy − The use of a random number generator is preferred − The use of Microsoft Excel random number generator is easy

Method used should be documented in surveillance plan Module 4, Lesson 2: Statistical Sampling

42

Zero-Based Sampling Process Details The Product Examination Policy page includes a project for Helpful QA Tools and provides:  1711 Random Generator tool  Random Generator 5 (Excel© spreadsheet)

www.Random.org (for other random generators)

Module 4, Lesson 2: Statistical Sampling

43

GENERATING RANDOM SAMPLE NUMBERS Lesson Topics: 1) Importance of Sampling to QA 2) Inspection by Attribute vs. Inspection by Variable 3) Three Types of Inspection Under a Sampling Plan 4) Zero-Based Sampling 5) Generating Random Sample Numbers 6) Simple, Systematic, Cluster, and Stratified Sampling Techniques 7) Interpreting Zero-Based Sampling System Tables 8) Interpreting ANSI/ASQZ1.4-2008 Sampling System Tables 9) Interpreting MIL-STD-1916 Sampling System Tables 10) Initiating Acceptance and Non Acceptance Activities Module 4, Lesson 2: Statistical Sampling

44

Topic 5: Generating Random Sample Numbers Microsoft Excel Random Generator

Random.org Module 4, Lesson 2: Statistical Sampling

45

Random Sampling Process Details

Simple random sampling is a sample in which every member of the population has an equal chance of being selected  Small sample sizes -

Use Microsoft Excel© Random Generator (preferred) Other forms of random sampling based on probability

 Larger samples sizes -

Use Microsoft Excel© Random Number Generator

Module 4, Lesson 2: Statistical Sampling

46

Using Excel to Generate Random Numbers

Randomization Example Zero Acceptance Number Sampling Plan C=0 AQL = 1.0 Lot Size = 25 Sample Size = 13

Module 4, Lesson 2: Statistical Sampling

47

Using Excel to Generate Random Numbers

Determine a way to individualize the product unit for sampling purposes. This could be a serial number, supplier identified number, or other unique number used to ID or track the unit. Use the copy and paste function to import information from the supplier’s documentation. Randomization Example Zero Acceptance Number Sampling Plan C=0 AQL = 1.0 Lot Size = 25 Sample Size = 13

Module 4, Lesson 2: Statistical Sampling

48

Using Excel to Generate Random Numbers

Enter the random number generator formula =RAND() into the cells adjacent to the serial number used.

Randomization Example Zero Acceptance Number Sampling Plan C=0 AQL = 1.0 Lot Size = 25 Sample Size = 13

Module 4, Lesson 2: Statistical Sampling

49

Using Excel to Generate Random Numbers

Use the mouse to highlight both rows of cells containing the serial numbers (in this example) and the random numbers. Highlighting keeps column A and B together as a pair. Randomization Example Zero Acceptance Number Sampling Plan C=0 AQL = 1.0 Lot Size = 25 Sample Size = 13

Module 4, Lesson 2: Statistical Sampling

50

Using Excel to Generate Random Numbers

After highlighting columns A and B, select the Sort icon and sort on the column containing the random numbers (in the example, it is B). Randomization Example Zero Acceptance Number Sampling Plan C=0 AQL = 1.0 Lot Size = 25 Sample Size = 13

Module 4, Lesson 2: Statistical Sampling

51

Using Excel to Generate Random Numbers

Notice that the list of serial numbers has also been sorted to correspond with the random number sort. The product units have been randomly sorted. Randomization Example Zero Acceptance Number Sampling Plan C=0 AQL = 1.0 Lot Size = 25 Sample Size = 13

Module 4, Lesson 2: Statistical Sampling

52

Using Excel to Generate Random Numbers

Using Simple Random Sampling techniques, this is the sample of 13 product units to be examined.

Randomization Example Zero Acceptance Number Sampling Plan C=0 AQL = 1.0 Lot Size = 25 Sample Size = 13

Module 4, Lesson 2: Statistical Sampling

53

Using Random.Org Random Number Generator

www.random.org/intergers/ www.random.org/intergers/

Module 4, Lesson 2: Statistical Sampling

54

Practice Practice using www.random.org/integers/ to obtain a random sample.  Lot size of 1200.  Sample size of 34.

Module 4, Lesson 2: Statistical Sampling

55

SIMPLE, SYSTEMATIC, CLUSTER, AND STRATIFIED SAMPLING TECHNIQUES Lesson Topics: 1) Importance of Sampling to QA 2) Inspection by Attribute vs. Inspection by Variable 3) Three Types of Inspection Under a Sampling Plan 4) Zero-Based Sampling 5) Generating Random Sample Numbers 6) Simple, Systematic, Cluster, and Stratified Sampling Techniques 7) Interpreting Zero-Based Sampling System Tables 8) Interpreting ANSI/ASQZ1.4-2008 Sampling System Tables 9) Interpreting MIL-STD-1916 Sampling System Tables 10) Initiating Acceptance and Non Acceptance Activities Module 4, Lesson 2: Statistical Sampling

56

Topic 6: Simple, Systematic, Cluster, and Stratified Sampling Techniques Four Sampling Techniques

   

Simple Systematic Cluster Stratified

Module 4, Lesson 2: Statistical Sampling

57

Zero-Based Sampling Process Details: Simple

Simple random sampling is a sampling from an entire population  It is highly representative if each member of the population has an equal chance of being selected  Requires complete list of population numbers

Module 4, Lesson 2: Statistical Sampling

58

Zero-Based Sampling Process Details: Systematic

In systematic sampling, every Kth member of the population is chosen for the sample, with the value of K being approximately: N (size of population) n+1 (n = sample size)

 

=K

Random number generator can be used to determine starting point (unit) of pulling the sample Results in less time and money spent

Module 4, Lesson 2: Statistical Sampling

59

Zero-Based Sampling Process Details: Systematic (cont.)

Example: 700 units in population with 34 as the sample size

N (size of population) n+1 (n = sample size)

=K

700 = 20 35

Module 4, Lesson 2: Statistical Sampling

60

Zero-Based Sampling Process Details: Cluster

A cluster sample is a simple random sample of groups or clusters, of the population



Each unit of the chosen clusters would be part of the final sample



To be effective, it is assumed that each cluster selected for the sample is representative of the population at large



A cluster is a miniaturized version of the overall population

Module 4, Lesson 2: Statistical Sampling

61

Zero-Based Sampling Process Details: Cluster (cont.)

40K Gloves (population) 4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

10 Crates (clusters) containing 4000 gloves each Sample size = 3

10

10

9

Total of 29 samples Module 4, Lesson 2: Statistical Sampling

62

Zero-Based Sampling Process Details: Stratified

A stratified sample is obtained by dividing the population into mutually exclusive groups or strata, and randomly sampling from each of these groups



Independent samples are randomly selected from each strata



Each strata is sampled as an independent sub-population

Module 4, Lesson 2: Statistical Sampling

63

Zero-Based Sampling Process Details: Stratified (cont.)

40K Gloves (population) Strata

20K

10K

10K

L

M

S

29

22

22

Sample Size

The entire lot (40K) must be homogeneous/like products produced under similar conditions Module 4, Lesson 2: Statistical Sampling

64

Question and Answer Using the cluster sampling technique, how many crates would be selected from which to pull your samples? Example: 5000 population, 10 crates of 500 each, AQL of .40 A. B. C. D.

13 10 8 3 Select the graphic to view the chart.

Module 4, Lesson 2: Statistical Sampling

65

Question and Answer How many samples are required to represent the entire population? Example: 5000 population, 10 clusters of 500 each, AQL of 1.0

A. B. C. D.

130 100 50 13 Select the graphic to view the chart.

Module 4, Lesson 2: Statistical Sampling

66

INTERPRETING ZERO-BASED SAMPLING SYSTEM TABLES Lesson Topics: 1) Importance of Sampling to QA 2) Inspection by Attribute vs. Inspection by Variable 3) Three Types of Inspection Under a Sampling Plan 4) Zero-Based Sampling 5) Generating Random Sample Numbers 6) Simple, Systematic, Cluster, and Stratified Sampling Techniques 7) Interpreting Zero-Based Sampling System Tables 8) Interpreting ANSI/ASQZ1.4-2008 Sampling System Tables 9) Interpreting MIL-STD-1916 Sampling System Tables 10) Initiating Acceptance and Non Acceptance Activities Module 4, Lesson 2: Statistical Sampling

67

Topic 7: Interpreting Zero-based Sampling System Tables When using zero-based sampling, use the AQL chart to determine sample size.

Module 4, Lesson 2: Statistical Sampling

68

Zero-Based Sampling Plan, AQL Chart

Module 4, Lesson 2: Statistical Sampling

69

Operating Characteristic Curve Chart

Module 4, Lesson 2: Statistical Sampling

70

Tabulated Values for Operating Characteristic Curves for Single Sampling Plans

Two risks associated with sampling. 1. Producers risk – the risk of rejecting product with satisfactory quality. 2. Consumer risk – the risk of accepting product of unsatisfactory quality. Module 4, Lesson 2: Statistical Sampling

71

INTERPRETING MIL-STD-1916 SAMPLING SYSTEM TABLES Lesson Topics: 1) Importance of Sampling to QA 2) Inspection by Attribute vs. Inspection by Variable 3) Three Types of Inspection Under a Sampling Plan 4) Zero-Based Sampling 5) Generating Random Sample Numbers 6) Simple, Systematic, Cluster, and Stratified Sampling Techniques 7) Interpreting Zero-Based Sampling System Tables 8) Interpreting ANSI/ASQZ1.4-2008 Sampling System Tables 9) Interpreting MIL-STD-1916 Sampling System Tables 10) Initiating Acceptance and Non Acceptance Activities Module 4, Lesson 2: Statistical Sampling

72

Topic 8: Interpreting ANSI/ASQZ1.42008 Sampling System Tables ANSI/ASQZ1.4-2008 Sampling is another sampling plan used in some contracts.

Module 4, Lesson 2: Statistical Sampling

73

ANSI/ASQZ1.4-2008 Sampling System Table Interpretation ANSI/ASQZ1.4-2008 is a sampling specification often specified in contractual documents that:

   

Is considered the replacement of MIL-STD-105E Is not Zero-Based Contains sampling schemes which include sampling plans Contains switching rules that are dependent upon previous lot inspection/test results

Remember: Even though these sampling plans have other accept/reject quantities in them, DCMA uses Accept on Zero/Reject on one unless otherwise directed by the customer.

Module 4, Lesson 2: Statistical Sampling

74

ANSI/ASQZ1.4-2008 Sampling System Example: This is the first time a complex part is being offered for acceptance, and there is a lot size of 100 units.

Find the code letter for this lot under “General Inspection Levels II”

Module 4, Lesson 2: Statistical Sampling

75

ANSI/ASQZ1.4-2008: Choose Sampling Plan Type Since this is the first time the supplier is offering this complex part for acceptance, which sampling plan (normal, tightened, or reduced) should be used? START

NORMAL (Reference Switching Rules for ANSI Z1.4 System) Module 4, Lesson 2: Statistical Sampling

76

ANSI/ASQZ1.4-2008: Choose AQL Which AQL should be used?

Module 4, Lesson 2: Statistical Sampling

77

ANSI/ASQZ1.4-2008: Number of Samples Required

Module 4, Lesson 2: Statistical Sampling

78

ANSI/ASQZ1.4-2008: Number of Samples Required (cont.) The supplier has now produced 10 consecutive lots of this part without nonconformities and its production is steady. The supplier switches to reduced sampling level. How many samples are required?

Module 4, Lesson 2: Statistical Sampling

79

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

NORMAL

REDUCE D • Lot not accepted • Lot accepted but nonconformities found lie between Ac and Re of plan • Production irregular • Other conditions warrant

TIGHTENE D 5 consecutive lots accepted

When switching from normal to tightened or reduced inspection, the sample size changes but not the AQL. Module 4, Lesson 2: Statistical Sampling

5 lots not accepted while on Tightened inspection Discontinue inspection under Z1.4 80

ANSI/ASQZ1.4-2008: Choose Sampling Plan Type The supplier had been doing so well that the Government increased the orders from the supplier. To keep up with demand, the supplier had to purchase another milling machine. Now the last three lots have had defects. The supplier was using Reduced sampling, which sampling plan should the supplier be using now?

REDUCED

JE E R

CT

1 defective lot

NORMAL

JE E R

CT

TIGHTENE D

2 defective lots

Module 4, Lesson 2: Statistical Sampling

81

ANSI/ASQZ1.4-2008: Number of Samples Required (cont.) How many samples will be required for Tightened; Lot of 100?

Module 4, Lesson 2: Statistical Sampling

82

Exercise: ANSI-ASQ Z1.4 Sampling Example

   

Students read the scenario and use the associated tables to determine answers. Open CMQ101_M4_L2_E1_ANSI_ASQ.pdf file. Answer questions on the following screens using the polling device. Time: 15 minutes

Module 4, Lesson 2: Statistical Sampling

83

Question and Answer The initial lot is ready to inspect. What is the sample size? A. B. C. D.

50 125 315 All

Module 4, Lesson 2: Statistical Sampling

84

Question and Answer Ten (10) consecutive lots have been found conforming. According to switching rules, what is the sample size? A. B. C. D.

50 80 125 200

Module 4, Lesson 2: Statistical Sampling

85

Question and Answer After being at reduced inspection, 3 lots have been found nonconforming. According to switching rules, what is the sample size? A. B. C. D.

315 200 125 80

Module 4, Lesson 2: Statistical Sampling

86

INTERPRETING MIL-STD-1916 SAMPLING SYSTEM TABLES Lesson Topics: 1) Importance of Sampling to QA 2) Inspection by Attribute vs. Inspection by Variable 3) Three Types of Inspection Under a Sampling Plan 4) Zero-Based Sampling 5) Generating Random Sample Numbers 6) Simple, Systematic, Cluster, and Stratified Sampling Techniques 7) Interpreting Zero-Based Sampling System Tables 8) Interpreting ANSI/ASQZ1.4-2008 Sampling System Tables 9) Interpreting MIL-STD-1916 Sampling System Tables 10) Initiating Acceptance and Non Acceptance Activities Module 4, Lesson 2: Statistical Sampling

87

Topic 9: Interpreting MIL-STD-1916 Sampling System Tables 

Contains three sampling plans: − Attributes − Variables − Continuous





Separates intensity of sampling into Verification Levels (VL) based upon criticality of product characteristics Normal, Reduced, and Tightened switching rules are the same as ANSI/ASQ Z1.4-2008 2 defective lots

Module 4, Lesson 2: Statistical Sampling

88

MIL-STD-1916: Sample Size What sample size would be used for a 5000 pc lot at Verification Level IV? Step 1:

Module 4, Lesson 2: Statistical Sampling

89

MIL-STD-1916: Sample Size (cont.) What sample size would be used for a 5000 pc lot at Verification Level IV? Step 2:

Module 4, Lesson 2: Statistical Sampling

90

MIL-STD-1916: Nonconformities Solution If this lot and the next lot both contain nonconformities, what must the supplier do, according to MIL-STD-1916?

Initiate Corrective Action and Tighten Sampling

Module 4, Lesson 2: Statistical Sampling

91

MIL-STD-1916: Sample Size for Tightened Plan Still using the D code letter, what would the sample size be for a 5000 pc lot, specified as Verification Level IV, using Tightened Inspection?

Module 4, Lesson 2: Statistical Sampling

92

Exercise: MIL-STD-1916 Sampling Example

   

Students read the scenario and use the associated tables to determine answers. Open CMQ101_M4_L2_E2_MIL_STD.pdf file. Answer questions on the following screens using the polling device. Time: 15 minutes

Module 4, Lesson 2: Statistical Sampling

93

Question and Answer The initial lot is ready to inspect. What is the sample size? A. B. C. D.

48 128 320 All

Module 4, Lesson 2: Statistical Sampling

94

Question and Answer Ten (10) consecutive lots have been found conforming. According to switching rules, what is the sample size? A. B. C. D.

48 80 96 320

Module 4, Lesson 2: Statistical Sampling

95

Question and Answer After being at reduced inspection, 3 of the last 5 lots are found nonconforming. According to switching rules, what is the sample size? A. B. C. D.

48 128 320 All

Module 4, Lesson 2: Statistical Sampling

96

INITIATING ACCEPTANCE AND NON ACCEPTANCE ACTIVITIES Lesson Topics: 1) Importance of Sampling to QA 2) Inspection by Attribute vs. Inspection by Variable 3) Three Types of Inspection Under a Sampling Plan 4) Zero-Based Sampling 5) Generating Random Sample Numbers 6) Simple, Systematic, Cluster, and Stratified Sampling Techniques 7) Interpreting Zero-Based Sampling System Tables 8) Interpreting ANSI/ASQZ1.4-2008 Sampling System Tables 9) Interpreting MIL-STD-1916 Sampling System Tables 10) Initiating Acceptance and Non Acceptance Activities Module 4, Lesson 2: Statistical Sampling

97

Topic 10: Initiating Acceptance and Non acceptance Activities



Execute – Perform sampling – Document results



Decisions – Acceptance – Non-acceptance

Module 4, Lesson 2: Statistical Sampling

98

Sampling Process Details (1 of 4)

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

Module 4, Lesson 2: Statistical Sampling

99

Sampling Process Details (2 of 4)

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

Module 4, Lesson 2: Statistical Sampling

100

Sampling Process Details (3 of 4)

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

Module 4, Lesson 2: Statistical Sampling

101

Sampling Process Details (4 of 4)

Initiated inspection levels will start at normal  Unless specified in the sampling system Switching rules  As specified in the sampling system If not specified 1 Lot nonconforming

Reduced Reduced Inspection Inspection

Normal Normal Inspection Inspection 10 consecutive conforming Lots

2 Lots nonconforming out of 5 or less

Tightened Inspection 5 consecutive conforming Lots

Switching increases or reduces sample size, not quality standards Module 4, Lesson 2: Statistical Sampling

102

Summary (1 of 3) Having completed this lesson, you should now understand:  Sampling is important to ensure acceptance of conforming product.

     Module 4, Lesson 2: Statistical Sampling

Two types of inspection: Attribute and Variable 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. 103

Summary (2 of 3) Having completed this lesson, you should now understand:  Sampling techniques: – – – –



Simple Systematic Cluster Stratified

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%

Module 4, Lesson 2: Statistical Sampling

104

Summary (3 of 3) Having completed this lesson, you should now understand:  ANSI/ASQ Z1.4-2008 sampling system tables: – General inspection levels II is the starting point unless otherwise specified – Separate AQL tables for normal, reduced, and tightened – Switching rules apply



Military Standard (MIL-STD)-1916 sampling system tables: – Includes 3 sampling plans for attributes, variables and continuous – Verification levels instead of AQLs – Same switching rules as ANSI/ASQ Z1.4-2008

 Module 4, Lesson 2: Statistical Sampling

When using zero-based sampling, entire lot is rejected when one defect is found. 105

Questions

Module 4, Lesson 2: Statistical Sampling

106

Review Question 1 Which is NOT a reason to sample?

A. B. C. D.

100% inspection is not possible Saves time and money Each product must be inspected Customer requests it

Module 4, Lesson 2: Statistical Sampling

107

Review Question 2 What type of sampling plan is required by DCMA policy?

A. B. C. D.

Simple Zero-based ANSI/ASQ Z1.4-2008 MIL-STD 1916

Module 4, Lesson 2: Statistical Sampling

108

Review Question 3 What AQL is required for a Critical Safety Item (CSI) critical characteristic? A. B. C. D.

.040% 0.40% 4.0% 1.0%

Module 4, Lesson 2: Statistical Sampling

109

Review Question 4 What sampling technique requires a complete list of population numbers? A. B. C. D.

Simple Systematic Cluster Stratified

Module 4, Lesson 2: Statistical Sampling

110

Review Question 5 What is an appropriate technique when sampling large quantities presented in numerous crates? A. B. C. D.

Simple Systematic Cluster Stratified

Module 4, Lesson 2: Statistical Sampling

111

Review Question 6 Which technique uses the equation displayed here? N (size of population) n+1 (n = sample size)

A. B. C. D.

=K

Simple Systematic Cluster Stratified

Module 4, Lesson 2: Statistical Sampling

112

Review Question 7 Inspection level for initial inspection starts at _________.

A. B. C. D.

Normal Reduced Tightened Variable

Module 4, Lesson 2: Statistical Sampling

113

Review Question 8 At normal inspection with 2 nonconforming lots, what is the next step? A. Continue at normal inspection level; notify supplier B. Switch to reduced inspection level; initiate corrective action C. Initiate corrective action; switch to tightened inspection level D. Switch to tightened inspection level for 1 lot; back to normal Module 4, Lesson 2: Statistical Sampling

114

Review Question 9 After 10 consecutive conforming lots at normal inspection, switch to _____________. A. B. C. D.

Normal Reduced Tightened Variable

Module 4, Lesson 2: Statistical Sampling

115

Review Question 10 When changing from Normal to Reduced or Tightened inspection, the QAS is _______________. A. B. C. D.

Changing the AQL Changing the lot size Changing the population size Changing the sample size

Module 4, Lesson 2: Statistical Sampling

116

Review Question 11 When is a lot rejected if using the Zero-based plan?

A. B. C. D.

0 defects 1 defect 2 non critical defects 2 defects

Module 4, Lesson 2: Statistical Sampling

117

Exercise: Sampling Plan

 

Students work in pairs to answer the questions in the exercise. Open CMQ101_M4_L2_E3_SamplingPlan.pdf file.

Module 4, Lesson 2: Statistical Sampling

118