LESSON 2 Statistical Sampling 15 November 2013 Lesson

LESSON 2 Statistical Sampling 15 November 2013

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) Z 1. 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/ASQZ 1. 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 Z 1. 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 Z 1. 4 -2008) DCMA Policy: The QAS will use zero-based sampling unless otherwise stated in a QALI. Sampling System Sample Plan 1 Sampling Scheme Sample Plan 2 Sample Plan 3 Sample Plan 4 Module 4, Lesson 2: Statistical Sampling Sample Plan 1 Sampling Scheme Sample Plan 2 Sample Plan 3 Sample Plan 4 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 Plan 1 Sampling Scheme Sample Plan 2 Sample Plan 3 Sample Plan 4 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 Z 1. 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 Z 1. 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 Z 1. 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) - 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 = Number Nonconforming Number of Units Inspected X 100 Nonconformities per Hundred Units X Number Nonconformities Number of Units Inspected 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/ASQZ 1. 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

Topic 1: 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 Sampl e 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 Assessme nt of the Population Saves Time 100% Not Always Possibl e Module 4, Lesson 2: Statistical Sampling Why Samplin g Cost Effectiv e Custom er Request s 17

Random Sampling Mr. Shields: Random Sampling Example Module 4, Lesson 2: Statistical Sampling 18

What is Random Sampling? Produc t § § Random Sample 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 (Ao. Z) § 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 Customer’s Risk Producer’s Risk 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/ASQZ 1. 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 Z 1. 4 -2008) 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 Lesson Topics: PLAN 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/ASQZ 1. 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 Z 1. 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 Z 1. 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 Z 1. 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/ASQZ 1. 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 Population • Define the population to be examined Criteria • Identify inspection/acceptance criteria Method • Determine the sample system and size Sample • Determine the random-sampling technique Execute • Perform the examination and document results Decisions • Initiate acceptance or non-acceptance actions Module 4, Lesson 2: Statistical Sampling 31

Zero-Based Sampling Process Details Populatio n • Define the population to be examined 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 Criteria • Identify inspection/acceptance criteria 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) Method • Determine the sample system and size Determine contractual (supplier) sampling requirement: § ANSI/ASQ Z 1. 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) 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 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) 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 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 Examination 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 Sample • Determine the sampling technique 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/ASQZ 1. 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 Sample • Simple random sampling technique 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/ Module 4, Lesson 2: Statistical Sampling 54

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/ASQZ 1. 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 Sample • Simple random sampling technique 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 Sample • Systematic sampling technique 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. ) Sample • Systematic sampling technique, example 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 Sample • Cluster sampling technique 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. ) Sample Size • Cluster sampling technique, example 40 K Gloves (population) 400 0 400 400 400 0 0 0 10 Crates (clusters) containing 4000 gloves each 400 0 Sample size = 3 10 10 9 Total of 29 samples Module 4, Lesson 2: Statistical Sampling 62

Zero-Based Sampling Process Details: Stratified Sample • Stratified sampling technique 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. ) Sample • Stratified sampling technique example 40 K Gloves (population) Strata 20 K 10 K L M S 29 22 22 Sample Size The entire lot (40 K) 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/ASQZ 1. 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/ASQZ 1. 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/ASQZ 1. 4 -2008 Sampling System Tables ANSI/ASQZ 1. 4 -2008 Sampling is another sampling plan used in some contracts. Module 4, Lesson 2: Statistical Sampling 73

ANSI/ASQZ 1. 4 -2008 Sampling System Table Interpretation ANSI/ASQZ 1. 4 -2008 is a sampling specification often specified in contractual documents that: § § Is considered the replacement of MIL-STD-105 E 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/ASQZ 1. 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/ASQZ 1. 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 Z 1. 4 System) Module 4, Lesson 2: Statistical Sampling 76

ANSI/ASQZ 1. 4 -2008: Choose AQL Which AQL should be used? Module 4, Lesson 2: Statistical Sampling 77

ANSI/ASQZ 1. 4 -2008: Number of Samples Required Module 4, Lesson 2: Statistical Sampling 78

ANSI/ASQZ 1. 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 REDUCE D START 2 of 5 or fewer consecutive lots are not accepted NORMA L • Lot not accepted • Lot accepted but nonconformities found lie between Ac and Re of plan • Production irregular • Other conditions warrant TIGHTEN ED 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 Z 1. 4 80

ANSI/ASQZ 1. 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 T C E J E R NORMA L T C E J E R TIGHTEN ED 1 defective lot 2 defective lots Module 4, Lesson 2: Statistical Sampling 81

ANSI/ASQZ 1. 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 Z 1. 4 Sampling Example § § Students read the scenario and use the associated tables to determine answers. Open CMQ 101_M 4_L 2_E 1_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/ASQZ 1. 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 Z 1. 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 CMQ 101_M 4_L 2_E 2_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 Lesson Topics: ACCEPTANCE ACTIVITIES 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/ASQZ 1. 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) Execut e • 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 Module 4, Lesson 2: Statistical Sampling 99

Sampling Process Details (2 of 4) Decisio ns • 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 Module 4, Lesson 2: Statistical Sampling 100

Sampling Process Details (3 of 4) Decisio ns • 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 Module 4, Lesson 2: Statistical Sampling 101

Sampling Process Details (4 of 4) Decisio ns • Initiate acceptance or non-acceptance actions (cont. ) 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 Inspection Normal 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: § § § Module 4, Lesson 2: Statistical Sampling is important to ensure acceptance of conforming product. 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 Z 1. 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 Z 1. 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 Z 1. 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 CMQ 101_M 4_L 2_E 3_Sampling. Plan. pdf file. Module 4, Lesson 2: Statistical Sampling 118