1 TRAINING SESSION ACCEPTANCE SAMPLING CONFIDENCE INTERVALS.
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Transcript of 1 TRAINING SESSION ACCEPTANCE SAMPLING CONFIDENCE INTERVALS.
![Page 1: 1 TRAINING SESSION ACCEPTANCE SAMPLING CONFIDENCE INTERVALS.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649da95503460f94a95f02/html5/thumbnails/1.jpg)
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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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EXAMPLE: SNAP CAPSThe 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
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EXAMPLE: SNAP CAPSThe Way You Normally Do It!
• 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
•
• 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?
![Page 37: 1 TRAINING SESSION ACCEPTANCE SAMPLING CONFIDENCE INTERVALS.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649da95503460f94a95f02/html5/thumbnails/37.jpg)
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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!
![Page 49: 1 TRAINING SESSION ACCEPTANCE SAMPLING CONFIDENCE INTERVALS.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649da95503460f94a95f02/html5/thumbnails/49.jpg)
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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
• ???
![Page 50: 1 TRAINING SESSION ACCEPTANCE SAMPLING CONFIDENCE INTERVALS.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649da95503460f94a95f02/html5/thumbnails/50.jpg)
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CONFIDENCE INTERVALS
• 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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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.
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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%
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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