1 training session acceptance sampling confidence intervals

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TRAINING SESSION

ACCEPTANCE SAMPLING

CONFIDENCE INTERVALS

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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

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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

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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”

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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

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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

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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??????

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HOW DO WE KNOW WHAT THE LOT % DEFECTIVE IS?

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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)

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MANAGEMENT DECISION

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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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EXAMPLE: SNAP CAPSThe 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”

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• ACCEPTABLE CAN BE DEFINED MANY DIFFERENT WAYS

• VARIABLES (DIMENSIONS) VERSUS ATTRIBUTES (GOOD/BAD)

• FOR ATTRIBUTES, WE NORMALLY TALK ABOUT THE % DEFECTIVE

• “ACCEPTABLE” = MAX % DEFECTIVE

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• REFERENCE: ANSI Z1.4• INSPECTION BY ATTRIBUTES• LOT SIZES = 35,001-150,000• SAMPLE SIZE CODE LETTER “N”• SINGLE, NORMAL, LEVEL 2• AQL = 1.5%• SAMPLE SIZE = N = 500• ACCEPT IF # DEFECTIVES < 14 (C = 14)

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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.

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OTHER ACCEPTANCE SAMPLING PLANS

• DOUBLE SAMPLING

• MULTIPLE SAMPLING

• SEQUENTIAL SAMPLING

• CONDITIONAL SAMPLING

• ETC.

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SNAP CAPS

• IS N = 500, C = 14 A GOOD ACCEPTANCE SAMPLING PLAN??????

• HOW DO YOU DECIDE??????

• WELL, IT DEPENDS!!!!!!

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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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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.

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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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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

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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.

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THIS IS THE PRIMARY ROLE ACCEPTANCE SAMPLING

PLAYS!

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REALITY OF AQL AND RQL

• IF WE CHOOSE

• AQL = 1.5%

• RQL = 3%

• WHAT DOES THAT REALLY MEAN?

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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%

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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.

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RQL = 3% : WHAT DOES IT MEAN

• LOT SIZE = 100,000 SNAP CAPS

• 97,000 ARE GOOD

• 3,000 ARE BAD

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• LOT IS UNACCEPTABLE

• LOT QUALITY: (3000/100,000 = 3%)

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BY DEFINITION

• THIS LOT IS UNACCEPTABLE TO USE IN PRODUCTION (3% ARE DEFECTIVE)

• YOU WOULD NOT WANT TO ACCEPT THIS LOT!!!!!!

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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%)

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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

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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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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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HOW TO FIND RIGHT SAMPLING PLAN

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COMMUNICATION

IS THE KEY TO UNDERSTANDING

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WHAT HAPPENS IF?

• YOU FIX THE AQL AT 1.5%

• AND VARY THE SAMPLE SIZE AND ACCEPT/REJECT NUMBER

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WHAT HAPPENS IF?

• YOU FIX THE SAMPLE SIZE

• AND VARY THE ACCEPT/REJECT NUMBER

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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!

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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

• ???

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

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WHAT’S GOING ON HERE?

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• 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.

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• 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%

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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.

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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.

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EXAMPLEINPUT FOLLOWING DATA:

CONFIDENCE = C ={.90, .95, …) 0.9

SAMPLE SIZE = n = 20

# DEFECTIVES = 1 - x0 = 2

# SUCCESSES = x0 = 18

RESULTS:PROPORTION

DEFECTIVE

OBSERVED PROBABILITY = Ro = 0.100000

UPPER CONFIDENCE LIMIT = RU = 0.282618

LOWER CONFIDENCE LIMIT = RL = 0.018065

RESULTS:PROPORTION ACCEPTABLE

OBSERVED PROBABILITY = Ro = 0.900000

UPPER CONFIDENCE LIMIT = RU = 0.981935

LOWER CONFIDENCE LIMIT = RL = 0.717382

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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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Operating Characteristic (OC) Curven=800, c=0

True percent defective

Prob. o

f accep

tance

0 0.1 0.2 0.3 0.40

0.2

0.4

0.6

0.8

1

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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:

Operating Characteristic (OC) Curve (LOT = 100,000)n=800, c=0

True percent defective

Prob

. of a

ccep

tance

0 0.04 0.08 0.12 0.16 0.20

0.2

0.4

0.6

0.8

1

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THE END

1 training session acceptance sampling confidence intervals

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