1 TRAINING SESSION ACCEPTANCE SAMPLING CONFIDENCE INTERVALS

2 THESE BOXES CONTAIN 1000 PERFECT SNAP CAPS EACH THE V.P. FOR CORPORATE QUALITY APPROVED A $250,000 BUDGET TO INSPECT, X-RAY, MRI, ETC. EACH SNAP CAP IN THE BOX TO INSURE THAT EACH ONE IS ACCEPTABLE TO USE IN PRODUCTION I.E. GUARANTEED 100% PERFECT QUALITY

3 BOX WITH 1000 PERFECT SNAP CAPS WHO WANTS TO MAKE THE DECISION TO RELEASE THESE 1000 SNAP CAPS FOR USE IN PRODUCTION????? EASY DECISION!!!!! BOX CONTAINS 0% DEFECTIVE

4 NOW! WHAT IF? EXACTLY ONE SNAP CAP IS DEFECTIVE NOW, WHO WANTS TO MAKE THE DECISION TO RELEASE THE LOT, CONTAINING “ONE” DEFECTIVE SNAP CAP, FOR USE IN PRODUCTION????? ONE DEFECTIVE OUT OF 1000 IS WHAT WE WOULD REFER TO AS “.1% DEFECTIVE”

5 THE REAL DECISION! ARE YOU WILLING TO LIVE WITH THIS QUALITY LEVEL (.1% DEFECTIVE) ? IF YES, WHAT ABOUT? TWO DEFECTIVES OUT OF 1000 OR.2% DEFECTIVE

6 WHAT ABOUT? 3 DEFECTIVES OUT OF 1000 OR.3% DEFECTIVE 4 DEFECTIVES OUT OF 1000 OR.4% DEFECTIVE ……… WHAT ABOUT 500 DEFECTIVES OUT OF 1000 OR 50% DEFECTIVE

7 REALITY WHO WANTS TO PLAY THE SHELL GAME? “A” BOX SHOWS UP AND YOU MUST MAKE THE DECISION WHETHER OR NOT TO RELEASE THE BOX TO PRODUCTION WHAT IS YOUR DECISION?????? HOW DO YOU DECIDE??????

8 HOW DO WE KNOW WHAT THE LOT % DEFECTIVE IS?

9 Definition of the terms AQL and RQL: AQL = ACCEPTABLE QUALITY LEVEL (THE MAXIMUM % DEFECTIVE YOU CONSIDER ACCEPTABLE) RQL = REJECTABLE QUALITY LEVEL (THE MINIMUM % DEFECTIVE YOU CONSIDER UNACCEPTABLE)

10 MANAGEMENT DECISION

11 ANOTHER ISSUE! YOU’RE USING A SAMPLING PLAN WITH A 1.5% AQL (SHIPPERS) THE SAMPLE SIZE IS N=32 AND YOU ACCEPT ON 1 OR FEWER DEFECTIVES YOU CONDUCT THE TEST, FIND 1 DEFECTIVE, AND ACCEPT THE LOT 1 DEFECTIVE IN A SAMPLE OF 32 IS 3.1%, NOT 1.5% (AQL) HOW CAN THIS BE?

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13 EXAMPLE: SNAP CAPS The Way You Normally Do It! YOU JUST RECEIVED A “LOT” OF SNAP CAPS FROM YOUR SUPPLIER DO YOU WANT TO ACCEPT THE LOT AND RELEASE IT TO PRODUCTION? HOW DO YOU DECIDE IF THE LOT IS ACCEPTABLE? DEFINE “ACCEPTABLE”

14 EXAMPLE: SNAP CAPS The Way You Normally Do It! ACCEPTABLE CAN BE DEFINED MANY DIFFERENT WAYS VARIABLES (DIMENSIONS) VERSUS ATTRIBUTES (GOOD/BAD) FOR ATTRIBUTES, WE NORMALLY TALK ABOUT THE % DEFECTIVE “ACCEPTABLE” = MAX % DEFECTIVE

15 EXAMPLE: SNAP CAPS The Way You Normally Do It! REFERENCE: ANSI Z1.4 INSPECTION BY ATTRIBUTES LOT SIZES = 35, ,000 SAMPLE SIZE CODE LETTER “N” SINGLE, NORMAL, LEVEL 2 AQL = 1.5% SAMPLE SIZE = N = 500 ACCEPT IF # DEFECTIVES < 14 (C = 14)

16 SINGLE ATTRIBUTE ACCEPTANCE SAMPLING PLAN CHARACTERIZED BY A SAMPLE SIZE (n) AND ACCEPT NUMBER (C) SUCH THAT IF YOU HAVE C OR FEWER DEFECTIVES IN THE SAMPLE OF SIZE n, YOU WILL ACCEPT THE LOT. OTHERWISE, YOU REJECT THE LOT.

17 OTHER ACCEPTANCE SAMPLING PLANS DOUBLE SAMPLING MULTIPLE SAMPLING SEQUENTIAL SAMPLING CONDITIONAL SAMPLING ETC.

18 SNAP CAPS IS N = 500, C = 14 A GOOD ACCEPTANCE SAMPLING PLAN?????? HOW DO YOU DECIDE?????? WELL, IT DEPENDS!!!!!!

19 ASSOCIATED WITH EVERY ACCEPTANCE SAMPLING PLAN IS AN OPERATING CHARACTERISTIC CURVE THE “OC” CURVE FOR SAMPLE SIZE = 500 ACCEPT LOT IF # DEFECTIVES < 14 REJECT LOT IF # DEFECTIVES > 15 CAN BE SHOWN TO BE:

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21 ROLE FOR ACCEPTANCE SAMPLING PLANS ACT AS A GATE KEEPER! IF INCOMING QUALITY (% DEFECTIVE) IS WHAT YOU DEFINE AS ACCEPTABLE (in this case 1.5% defective or less), YOU WANT THE GATE TO STAY OPEN AND ACCEPT ALL (MOST) OF THE LOTS.

22 WHAT HAPPENS? WHEN A LOT IS ACCEPTED AND LATER EVENTS INDICATE A PROBLEM (OPEN CAPS) AFTER 100% INSPECTION, YOU FOUND 3000 DEFECTIVE CAPS IN THE LOT OF 100,000 SNAP CAPS!!!!!!! (3000/100,000) = 3% WHY DID YOU ACCEPT THE LOT????

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24 WE NEED TO MAKE A MANAGERIAL DECISION! DO YOU WANT TO RELEASE THIS LOT TO PRODUCTION? WELL, IT DEPENDS! DO YOU CONSIDER A LOT WITH 3% DEFECTIVES JUST UNDESIRABLE, OR DEFINITELY UNACCEPTABLE

25 NEW ROLE FOR ACCEPTANCE SAMPLING PLANS IF INCOMING QUALITY (% DEFECTIVE) IS WHAT YOU DEFINE AS UNACCEPTABLE (let’s say 3% in this case, RQL = 3%) YOU WANT THE GATE TO STAY CLOSED AND REJECT ALL (MOST) OF THE LOTS.

26 THIS IS THE PRIMARY ROLE ACCEPTANCE SAMPLING PLAYS!

27 REALITY OF AQL AND RQL IF WE CHOOSE AQL = 1.5% RQL = 3% WHAT DOES THAT REALLY MEAN?

28 AQL = 1.5% : WHAT DOES IT MEAN LOT SIZE = 100,000 SNAP CAPS 98,500 ARE GOOD 1,500 ARE BAD LOT IS ACCEPTABLE!!!! LOT QUALITY: (1500/100,000)= 1.5%

29 BY DEFINITION THIS LOT IS ACCEPTABLE TO USE IN PRODUCTION ??? (1.5% ARE DEFECTIVE) QUESTION? AS A MANAGER, WOULD YOU REALLY RECOMMEND THAT PRODUCTION USE THIS LOT TO PRODUCE PRODUCT AND SHIP TO THE CUSTOMER? “YES OR NO” IF “NO” THEN WE NEED TO START OVER.

30 RQL = 3% : WHAT DOES IT MEAN LOT SIZE = 100,000 SNAP CAPS 97,000 ARE GOOD 3,000 ARE BAD LOT IS UNACCEPTABLE LOT QUALITY: (3000/100,000 = 3%)

31 BY DEFINITION THIS LOT IS UNACCEPTABLE TO USE IN PRODUCTION (3% ARE DEFECTIVE) YOU WOULD NOT WANT TO ACCEPT THIS LOT!!!!!!

32 MANAGERIAL CONCLUSION A LOT OF 100,000 SNAP CAPS CONTAINING 1500 OPEN CAPS IS ACCEPTABLE (1.5%) HOWEVER, A LOT OF 100,000 SNAP CAPS CONTAINING 3000 OPEN CAPS IS UNACCEPTABLE (3%)

33 IS (n = 500, C = 14) A GOOD SAMPLING PLAN? IF OUR QUALITY IS AT THE AQL (1.5%) WE ACCEPT MOST LOTS HOWEVER, IF OUR QUALITY IS AT THE RQL (3%) WE STILL ACCEPT 45% OF THE LOTS

34 CONCLUSION NOT A GOOD SAMPLING PLAN! WHAT SHOULD WE DO?????? INCREASE THE SAMPLE SIZE!! TENDENCY IS TO USE Z1.4 AND SELECT A LARGER SAMPLE SIZE FOR THE SAME AQL = 1.5% N = 800, C = 21 PROBLEM SOLVED, OR IS IT?????

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36 WHAT DID WE GET FOR OUR MONEY? IS A REDUCTION (FROM 45% TO 32%) IN THE PROBABILITY OF ACCEPTING LOTS WITH 3% DEFECTIVES WORTH A 60% INCREASE IN SAMPLE SIZE (FROM 500 TO 800) HOW DO WE REDUCE THIS PROBALILITY OF ACCEPTING LOTS WITH 3% DEFECTIVE EVEN LOWER?

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40 HOW TO FIND RIGHT SAMPLING PLAN

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43 COMMUNICATION IS THE KEY TO UNDERSTANDING

44 WHAT HAPPENS IF? YOU FIX THE AQL AT 1.5% AND VARY THE SAMPLE SIZE AND ACCEPT/REJECT NUMBER

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46 WHAT HAPPENS IF? YOU FIX THE SAMPLE SIZE AND VARY THE ACCEPT/REJECT NUMBER

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48 WRAP-UP THOUGHTS!! ONLY YOU CAN DECIDE WHAT QUALITY LEVELS YOU’RE WILLING TO LIVE WITH. ONLY YOU CAN DECIDE WHAT QUALITY LEVELS YOU’RE NOT WILLING TO LIVE WITH. ONLY YOU CAN DECIDE IF THE COST OF ACCEPTANCE SAMPLING IS THE WISEST WAY TO SPEND YOUR LIMITED QUALITY ASSURANCE DOLLARS!

49 WHAT ARE YOUR QUESTIONS ABOUT? SPECIFIC SAMPLING PLANS YOU ARE CURRENTLY USING EFFECT OF CHANGING SAMPLE SIZE FOR YOUR PLAN COMPARISON BETWEEN TWO DIFFERENT PLANS ???

50 CONFIDENCE INTERVALS A TOOL USED TO ESTIMATE (GUESS) WHAT YOU THINK THE TRUE PERCENT DEFECTIVE IS IN A LOT (PROCESS).

51 WHAT’S GOING ON HERE?

52 CONFIDENCE INTERVALS THE TWO TYPES OF ESTIMATORS FOR PERCENT DEFECTIVE ARE POINT ESTIMATE = % DEFECTIVE IN THE SAMPLE (BEST GUESS) UPPER 95% CONFIDENCE INTERVAL ESTIMATE = A NUMBER (PERCENT DEFECTIVE) IN WHICH THE ODDS (PROBABILITY) ARE 95% THAT THE “TRUE PERCENT DEFECTIVE IN THE LOT (PROCESS)” IS LESS THAN THAT NUMBER.

53 CONFIDENCE INTERVALS EXAMPLE: IN A SAMPLE OF 20 UNITS, 2 DEFECTIVES ARE FOUND. POINT ESTIMATE = 2/20 =.10 (OR 10%) UPPER 95% CONFIDENCE LIMIT FOR % DEFECTIVE = 28%

54 CONFIDENCE INTERVALS FOR PERCENT DEFECTIVE: FORMULAS FOR OBTAINING CONFIDENCE INTERVALS FOR THE PERCENT DEFECTIVE CAN BE FOUND IN REFERENCE LITERATURE AND ARE AVAILABLE FROM CORPORATE QUALITY AS AN EXCEL SPREADSHEET.

55 CONFIDENCE INTERVALS FOR PERCENT DEFECTIVE: INPUTS TO THIS SPREADSHEET ARE THE CONFIDENCE LEVEL, SAMPLE SIZE AND NUMBER OF DEFECTIVES. THE SPREADSHEET WILL THEN RETURN A POINT ESTIMATE AND CONFIDENCE INTERVAL AS SEEN BELOW.

56 EXAMPLE

57 INTERPRETATION OF (LOT) PERCENT DEFECTIVE AND EFFECT ON SAMPLING PLAN ASSUME PERCENT DEFECTIVE IS DEFINED AS THE ACTUAL PERCENT DEFECTIVE OF THE LOT BEING SAMPLED FOR A LOT SIZE OF 1000, A SAMPLING PLAN WHERE N = 800, AND YOU ACCEPT IF THE NUMBER OF DEFECTIVES IS ‘0’, THE OC CURVE IS GIVEN BY:

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59 FOR A LOT SIZE OF 100,000, A SAMPLING PLAN WHERE N = 800, AND YOU ACCEPT IF THE NUMBER OF DEFECTIVES IS 0, THE OC CURVE IS GIVEN BY:

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61 THE END