Advantages and Disadvantages of Sampling. Vermont ASQ Meeting October 26, 2011

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1 Advantages and Disadvantages of Samping Vermont ASQ Meeting October 26, 2011 Jeffrey S. Soomon Genera Dynamics Armament and Technica Products, Inc. Wiiston, VT 05495

2 Outine I. Definition and Exampes II. III. IV. History and the Basic Assumption 1936 Presidentia Eection Advantages and Disadvantages of Samping V. Economics of Samping VI. VII. Theory Behind Samping: Risks and OC Curves Common Samping Pans and Terms VIII. Exampe Using Z1.4 IX. Summary 2

and Disadvantages of Samping V. Economics of Samping VI. VII.

3 I. Definition and Exampes Samping The process of seecting a subset of units or individuas (a portion or sampe) from a popuation of interest so that by examining the sampe, we can generaize the resuts to the whoe popuation Exampes Conducting a po to predict the winner of an upcoming eection Inspecting a sampe of parts to determine if the entire ot meets requirements 3

generaize the resuts to the whoe popuation Exampes Conducting a po to predict the winner of

4 II. History Samping is mentioned severa times in the Bibe 1786: Pierre Simon Lapace estimates the popuation of France by using a sampe During WWII, use of samping spreads when samping pans such as MIL-STD-105 were deveoped by Harod Dodge and others 4

using a sampe During WWII, use of samping spreads when samping

5 Basic Assumption of Samping Whenever a sampe is taken from a popuation, it must be a RANDOM SAMPLE Random sampe: Every unit in the popuation has an equa chance of being incuded in the sampe If you don t have a random sampe, you are not aowed to appy the resuts of the sampe to the entire popuation 5

equa chance of being incuded in the sampe If you don t have a random

6 III. The 1936 Presidentia Eection The Literary Digest was an infuentia weeky magazine; founded in 1890, it fourished in the eary 20 th century (circuation over 1 miion), ony to cease operations by presidentia eection: FDR (D, incumbent) versus Af Landon (R, Kansas governor); height of the Great Depression The Literary Digest conducted a straw po regarding the outcome of the eection. They had done this in 1932 and had accuratey predicted the outcome. Ten miion surveys were sent to Digest subscribers, registered automobie owners and teephone customers 6

governor); height of the Great Depression The Literary Digest conducted a straw po regarding the outcome of the eection.

7 The 1936 Presidentia Eection Based on the survey, Digest predicted Landon woud win In the November eection, Landon carried ony Maine and Vermont; FDR won the other 46 states and won Why? 7

8 The 1936 Presidentia Eection Of the 10 miion peope that were sent surveys, ony 2.4 miion responded (a very arge number for any survey, but a very ow response rate) Digest s readers, automobie owners, and teephone users a had disposabe incomes we above the nationa average in 1936 Vountary responses to a survey is not a random sampe George Gaup s American Institute of Pubic Opinion correcty predicted the resut of the eection using a sampe of 50,000 8

owners, and teephone users a had disposabe incomes we above the nationa average in 1936 Vountary responses to a

9 IV. Advantages of Samping 100% inspection does not guarantee 100% compiance Economy Less opportunity for product damage Fewer inspection personne Less monotonous for the inspector Lot-by-ot examination Appicabe for destructive testing Lot rejection versus piece rejection 9

inspection personne Less monotonous for the inspector Lot-by-ot

10 Disadvantages of Samping Risk of rejecting a good ot (producer s risk) Risk of accepting a bad ot (consumer s risk) Greater administration costs Requires additiona panning and documentation Yieds ess actua information about the product Wi not detect a defective product in a ot Designed to maintain a given eve of quaity; wi not drive improvement 10

panning and documentation Yieds ess actua information about the product Wi not detect a

11 V. Economics of Samping Which method of inspection costs the east: No inspection Samping 100% inspection Variabes needed Lot size Sampe size % defective Cost if a defect isn t caught Inspection cost per unit Probabiity of accepting a ot Exampe: 100 piece ot; c=0 samping pan with sampe size of 13; $0.50 to inspect a piece; $10 to fix the higher assemby if a defective part is used 11

Inspection cost per unit Probabiity of accepting a ot Exampe: 100 piece ot; c=0 samping pan

12 Economics of Samping 12

13 VI. Theory Behind Samping Samping is an exampe of Hypothesis Testing Nu Hypothesis (H 0 ): The ot is acceptabe ( good ) Aternative Hypothesis (H a ): The ot is unacceptabe Process: Given the ot size... Determine the samping pan (sampe size, accept number, reject number) Seect random sampe Inspect parts in the sampe; count the number of defective ones Determine whether to accept or reject the ot 13

size... Determine the samping pan (sampe size, accept number, reject number) Seect random sampe

14 Samping Risks Producer s risk = risk of rejecting a good ot = α = Type I error = eve of significance Consumer s risk = risk of accepting a bad ot = β = Type II error The operating characteristics (OC) curve for a samping pan shows these risks. It shows the probabiity of accepting a ot as a function of the percent defective in the ot AQL Acceptance Quaity Limit (formery known as Acceptabe Quaity Leve ): The quaity eve that is the worst toerabe process average when a continuing series of ots is submitted for acceptance samping 14

It shows the probabiity of accepting a ot as a function of the percent defective in the ot AQL Acceptance Quaity Limit (formery known

15 Idea OC Curve AQL 15

16 More Typica OC Curves 16

17 VII. Common Samping Pans ANSI/ASQ Z1.4 (MIL-STD-105) ANSI/ASQ Z1.9 (MIL-STD-414) C=0 ( Zero Acceptance Number Samping Pans by Nichoas L. Squegia) (ASQ H1331) Dodge-Romig Samping Tabes MIL-STD-1916 MIL-STD-1235 Boeing D

18 Common Samping Terms Inspection by Attributes / Variabes Inspection Leves Singe / Doube / Mutipe Samping Norma / Tightened / Reduced Samping AQL / AOQ / AOQL Continuous samping Sequentia samping Skip ot samping (ASQ S1) 18

Samping Norma / Tightened / Reduced Samping AQL / AOQ /

19 VIII. Exampe Using Z1.4 You work in Receiving Inspection and have been given a shipment from Widgets R Us containing 25 widgets You are tod to inspect it using ANSI/ASQ Z1.4 for Genera Inspection Leve II AQL 1.0 Singe norma samping 19

20 Exampe Using Z1.4 20

21 Exampe Using Z1.4 21

22 Exampe Using Z1.4 Samping Pan Sampe size (n) = 13 Acceptance number (Ac or c) = 0 Rejection number (Re) = 1 Seect a random sampe of size 13 from the ot of 25 widgets Inspect the parts in the sampe Accept the entire ot if there are 0 defective pieces in the sampe; otherwise reject the ot 22

23 IX. Summary Samping is a good approach but you need to be aware of its imitations Keep it simpe pick the best samping approach for your needs, set up your own procedures with tabes to use, and train everyone The concept of a random sampe is critica Set up a Dock-to-Stock or Operator Sef-Inspection program for parts with historicay very ow defect rates 23

24 Questions? 24