Vermont ASQ MeetingOctober 26, 2011

Jeffrey S. SolomonGeneral Dynamics

Armament and Technical Products, Inc.Williston, VT 05495

Advantages and Disadvantages of Sampling

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Outline

I. Definition and ExamplesII. History and the Basic AssumptionIII. 1936 Presidential ElectionIV. Advantages and Disadvantages of SamplingV. Economics of SamplingVI. Theory Behind Sampling: Risks and OC CurvesVII. Common Sampling Plans and TermsVIII. Example Using Z1.4IX. Summary

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I. Definition and Examples

Samplingl The process of selecting a subset of units or

individuals (a portion or sample) from a population of interest so that by examining the sample, we can generalize the results to the whole population

Examplesl Conducting a poll to predict the winner of an

upcoming electionl Inspecting a sample of parts to determine if the entire

lot meets requirements

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II. History

l Sampling is mentioned several times in the Bible

l 1786: Pierre Simon Laplace estimates the population of France by using a sample

l During WWII, use of sampling spreads when sampling plans such as MIL-STD-105 were developed by Harold Dodge and others

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Basic Assumption of Sampling

l Whenever a sample is taken from a population, it must be a RANDOM SAMPLE

l Random sample: Every unit in the population has an equal chance of being included in the sample

l If you don’t have a random sample, you are not allowed to apply the results of the sample to the entire population

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III. The 1936 Presidential Election

l The Literary Digest was an influential weekly magazine; founded in 1890, it flourished in the early 20th century (circulation over 1 million), only to cease operations by 1940

l 1936 presidential election: FDR (D, incumbent) versus Alf Landon (R, Kansas governor); height of the Great Depression

l The Literary Digest conducted a “straw poll” regarding the outcome of the election. They had done this in 1932 and had accurately predicted the outcome. Ten million surveys were sent to Digest subscribers, registered automobile owners and telephone customers

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The 1936 Presidential Election

l Based on the survey, Digest predicted Landon would win 370 – 161

l In the November election, Landon carried only Maine and Vermont; FDR won the other 46 states and won 523 – 8

l Why?

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The 1936 Presidential Election

l Of the 10 million people that were sent surveys, only 2.4 million responded (a very large number for any survey, but a very low response rate)

l Digest’s readers, automobile owners, and telephone users all had disposable incomes well above the national average in 1936

l Voluntary responses to a survey is not a random sample

l George Gallup’s American Institute of Public Opinion correctly predicted the result of the election using a sample of 50,000

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IV. Advantages of Sampling

l 100% inspection does not guarantee 100% compliance

l Economyl Less opportunity for product damagel Fewer inspection personnell Less monotonous for the inspectorl Lot-by-lot examinationl Applicable for destructive testingl Lot rejection versus piece rejection

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Disadvantages of Sampling

l Risk of rejecting a “good” lot (producer’s risk)l Risk of accepting a “bad” lot (consumer’s risk)l Greater administration costsl Requires additional planning and documentationl Yields less actual information about the productl Will not detect all defective product in a lotl Designed to maintain a given level of quality; will not

drive improvement

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V. Economics of Sampling

l Which method of inspection costs the least: No inspection Sampling 100% inspection

l Variables neededLot size Sample size% defective Cost if a defect isn’t caughtInspection cost per unit Probability of accepting a lot

l Example: 100 piece lot; c=0 sampling plan with sample size of 13; $0.50 to inspect a piece; $10 to fix the higher assembly if a defective part is used

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Economics of Sampling

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VI. Theory Behind Sampling

l Sampling is an example of Hypothesis Testingl Null Hypothesis (H0): The lot is acceptable (“good”)l Alternative Hypothesis (Ha): The lot is unacceptablel Process: Given the lot size. . .

Determine the sampling plan (sample size, accept number, reject number)

Select random sample Inspect parts in the sample; count the number of

defective ones Determine whether to accept or reject the lot

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Sampling Risks

l Producer’s risk = risk of rejecting a “good” lot = α = Type I error = level of significance

l Consumer’s risk = risk of accepting a “bad” lot = β = Type II error

l The operating characteristics (OC) curve for a sampling plan shows these risks. It shows the probability of accepting a lot as a function of the percent defective in the lot

l AQL – Acceptance Quality Limit (formerly known as “Acceptable Quality Level”): The quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance sampling

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Ideal OC Curve

AQL

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More Typical OC Curves

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VII. Common Sampling Plans

l ANSI/ASQ Z1.4 (MIL-STD-105)l ANSI/ASQ Z1.9 (MIL-STD-414)l C=0 (“Zero Acceptance Number Sampling Plans” by

Nicholas L. Squeglia) (ASQ H1331)l Dodge-Romig Sampling Tablesl MIL-STD-1916l MIL-STD-1235l Boeing D1-8007

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Common Sampling Terms

l Inspection by Attributes / Variablesl Inspection Levelsl Single / Double / Multiple Samplingl Normal / Tightened / Reduced Samplingl AQL / AOQ / AOQLl Continuous samplingl Sequential samplingl Skip lot sampling (ASQ S1)

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VIII. Example Using Z1.4

l You work in Receiving Inspection and have been given a shipment from Widgets R Us containing 25 widgets

l You are told to inspect it using ANSI/ASQ Z1.4 for

General Inspection Level II

AQL 1.0

Single normal sampling

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Example Using Z1.4

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Example Using Z1.4

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Example Using Z1.4

l Sampling Plan Sample size (n) = 13 Acceptance number (Ac or c) = 0 Rejection number (Re) = 1

l Select a random sample of size 13 from the lot of 25 widgets

l Inspect the parts in the sample

l Accept the entire lot if there are 0 defective pieces in the sample; otherwise reject the lot

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IX. Summary

l Sampling is a good approach – but you need to be aware of its limitations

l Keep it simple – pick the best sampling approach for your needs, set up your own procedures with tables to use, and train everyone

The concept of a random sample is critical

l Set up a Dock-to-Stock or Operator Self-Inspection program for parts with historically very low defect rates

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Questions?