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 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”
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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
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EXAMPLE: SNAP CAPS
The 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?
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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
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DOLLARS!
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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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.52
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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EXAMPLE
INPUT FOLLOWING DATA:
CONFIDENCE = C ={.90, .95, …)
SAMPLE SIZE = n =
# DEFECTIVES = 1 - x 0 =
# SUCCESSES = x 0 =
RESULTS:
0.9
20
2
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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) Curve
Prob. of acceptance
n=800, c=0
1
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
True percent defective
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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)
Prob. of acceptance
n=800, c=0
1
0.8
0.6
0.4
0.2
0
0
0.04
0.08
0.12
0.16
0.2
True percent defective
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THE END
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