CHAPTER 10 ACCEPTANCE SAMPLING AS

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CHAPTER 10 ACCEPTANCE SAMPLING (AS)

• INSPECTION AFTER PRODUCTION.
• HOWEVER - SHOULD NOT TRY TO INSPECT QUALITY INTO
  PRODUCT.
• AS IS AN AUDITING TOOL.
• OUR APPROACH - CONCEPTS ARE MOST IMPORTANT -
  FORMULAS FOR APPLICATIONS.

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Basic Forms of Statistical Sampling for Quality
Control
Sampling to accept or reject the immediate lot of
product at hand (Acceptance Sampling). Sampling
to determine if the process is within acceptable
limits (Statistical Process Control)
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Acceptance Sampling

• Purposes
• Determine quality level
• Ensure quality is within predetermined level
• Advantages
• Economy
• Less handling damage
• Fewer inspectors
• Upgrading of the inspection job
• Applicability to destructive testing
• Entire lot rejection (motivation for improvement)

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Statistical Sampling--Data

• Attribute (Go no-go information)
• Defectives--refers to the acceptability of
  product across a range of characteristics.
• Defects--refers to the number of defects per
  unit--may be higher than the number of
  defectives.
• Variable (Continuous)
• Usually measured by the mean and the standard
  deviation.

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Acceptance Sampling--Single Sampling Plan
A simple goal Determine (1) how many units, n,
to sample from a lot of size N and (2) the
maximum number of defective items, c, that can
be found in the sample before the lot is rejected.
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DESIGNING THE PLAN

• Acceptable Quality Level (AQL) Max. acceptable
  percentage of defectives defined by producer.
• ??(Producers risk) The probability of
  rejecting a good lot.
• Limiting Quality Level (LQL) Lot Tolerance
  Percent Defective (LTPD) Percentage of
  defectives that defines consumers rejection
  point.
• ? (Consumers risk) The probability of
  accepting a bad lot.

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Operating Characteristic Curve
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The OC Curve

• Why is OC Curve So Important?
• It Provides Trade-Offs between, N, n, c, AQL, ?,
  LTPD, and ?.
• The Resulting OC Curve should achieve the desired
  characteristics for producer and consumer.
• Study the previous OC Curve or Fig. 10-2 versus
  the Ideal of Figure 10-1.

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Example Acceptance Sampling
A manufacturer of computers, PH Electronics
purchases motherboards from a vendor, HAL Inc..
HAL has set an acceptable quality level of 1 and
accepts a 5 risk of rejecting lots at or below
this level. PH Electronics considers lots with
3 defectives to be unacceptable and will assume
a 10 risk of accepting a defective lot. Develop
a sampling plan for PH and determine a rule to be
followed by the receiving inspection personnel.
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DESIGN THE PLAN
For this example, determine AQL ? LTPD ?
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DESIGN THE PLAN
To achieve the design of the plan AQL, ?, LTPD,
and ? , specify N Lot Size, n Sample Size, c
Acceptance ANSI/ASQC, ISO, AND Military
Standards exist to define the desired plan. I.E.,
after Defining AQL, ?, LTPD, and ?, go to these
standards for n and c.
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TYPES OF PLANS

• TYPE A
• FININTE POP ngtN/10
• W/O Replacement
• Hypergeometric Dist.
• Eq. 10-1 Applies

• TYPE B
• LARGE POP n?N/10
• W/O Replacement
• Binomial Dist.
• Eq. 10.3 to 10.4

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POISSON DIST.

• IF n is large and the Prob. of Nonconformance Low
• Poisson Dist. can be used
• This Simplifies Formulas
• Eq. 10-5 Applies

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GENERATING OC CURVES

• OC Curves are not difficult to generate
• Consider Table 10-1 and the resulting Fig. 10-2.
• Consider the Effect of n on OC Curve, Fig.
  10-3.
• Consider the Effect of c on OC Curve Fig.
  10-4

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GENERAL TYPES OF PLANS

• SINGLE - TAKE A SINGLE SAMPLE, ACCEPT (A) OR
  REJECT (R)
• DOUBLE - TAKE A SAMPLE, A, R, OR INSPECT A 2ND
  LOT, THEN A OR R
• MULTIPLE - TAKE 1 TO 7 SAMPLES TO REACH A
  CONCLUSION

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SINGLE PLAN

• SIMPLER
• ON AVERAGE, n IS HIGHER
• INSPECTION COST ARE HIGHER
• MORE INFO FROM A SINGLE PLAN
• CONSIDER TABLE 10-9
• N35,000 J, AQL.65
• n80, IF d ?1, ACCEPT, IF dgt1, REJECT

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DOUBLE SAMPLING PLAN

• CONSIDER TABLE 10-12
• N35,000 J, AQL.65
• n150, IF d ?0, ACCEPT, IF dgt2, REJECT, OTHERWISE
  INSPECT AGAIN.
• n250, IF cumulative d ?1, ACCEPT, IF dgt2, REJECT

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MULTIPLE SAMPLING PLAN

• CONSIDER TABLE 10-15
• N35,000 J, AQL.65
• SAMPLE ACCEPT REJECT INSPECT
• 1 n 20
  2 0 OR 1
• 2 n 20
  2 0 OR 1
• 3 n 20 0
  2 1
• 4 n 20 0
  3 1
• 5 n 20 1
  3 2
• 6 n 20 1
  3 2
• 7 n 20 2
  3 N.A.

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CHARACTERISTICS OF PLANS

• AVG. OUTGOING QUALITY
• AVG. TOTAL INSPECTION
• AVERAGE SAMPLE NUMBER
• THESE STATISTICS BETTER DEFINE EACH PLAN AND THUS
  HELP US BETTER UNDERSTAND THE PLAN.

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AVG. OUTGOING QUALITY

• AVERAGE QUALITY LEVEL OF A LARGE NUMBER OF LOTS
  FROM INCOMING QUALITY OF p PERCENT DEFECTIVES.
• ASSUMES RECTIFICATION (i.e., REJECTED LOTS ARE
  100 INSPECTED).
• SEE TABLE 10-2 AND FIG. 10-5.
• PEAK AOQ IS WORST POSSIBLE AVG QUALITY LEAVING A
  PROCESS.
• THIS IS AN IMPROTANT BENCHMARK - MEASURE OF PLAN
  GOODNESS.

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AVG. TOTAL INSPECTION

• AVER. NUMBER INSPECTED PER LOT
• SEE TABLE 10-3 AND FIG. 10-6.
• CAN BE USED TO ESTIMATE THE AVERAGE INSPECTION
  COST.

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AVG. SAMPLE NUMBER

• AVER. NUMBER INSPECTED OVER MANY LOTS
• FOR SINGLE PLAN ASN n.
• SEE TABLE 10-4 AND FIG. 10-7.
• ASN IS LOWER FOR DOUBLE AND MULTIPLE SAMPLING
  PLANS
• THESE PLANS DISCRIMINATE BETWEEN GOOD AND
  DEFECTIVE EARLIER THAN SINGLE PLAN

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USING STD. PLANS

• Using the previous statistics (AOQ, ATI, ASN), n,
  c, AQL, ?, LTPD, and ? can be selected to achieve
  desired results.
• However, standard plans exists which yield simple
  tables embodying commonly accepted values of AQL,
  ?, LTPD, and ?. Consider these plans.

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STD. SAMPLING PLANS

• ATTRIBUTE PLANS
• MIL-STD-105E ANSI/ASQCZ1.4 ISO2859
• VARIABLE PLANS
• MIL-STD-414 ANSI/ASQCZ1.9

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ANSI/ASQCZ1.4

• ATTRIBUTE PLANS
• TABLES INDEXED BY AQL
• a VARIES FROM 1 TO 10
• USUAL AQLs
• CRITICAL ?.10
• MAJOR 1
• MINOR 2 - 4
• FOCUSES ON AQL AND PRODUCERS SEGMENT OF OC CURVE

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ANSI/ASQCZ1.4

• MANY TABLES EXIST FOR GENERATING OTHER OC CURVES
• TABLES ASSIST WITH SELECTING ?, LTPD, and ?
• COMMON LQL (LTPD) WITH B OF 5 OR 10

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ANSI/ASQCZ1.4

• GENERAL INSPECTION LEVELS
• ABOUT A100 WILL REJECTED
• THREE LEVELS OF CONSUMER PROTECTION (B-RISKS)
• I - LEAST
• II-BETTER
• III-BEST
• SEE FIG. 10-15

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STEPS IN USING ANSI/ASQCZ1.4

• SELECT AQL
• SELECT GEN. LEVEL (USUALLY II)
• SELECT LOT SIZE/CODE FROM TABLE
• SELECT TYPE OF PLAN (S, D, or M)
• IDENTIFY PLAN (C OF A AND R)
• CHOOSE NORMAL PLAN AND SWITCH AS NECESSARY AS
  DEFINED BELOW.

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TYPES OF INSP. AND SWITCHING

• STD. PLANS FACILITATE CONDITIONAL INSPECTIONS
• NORMAL - WITH NORMAL LEVEL OF DEFECTS
• TIGHTENED - WITH HIGH LEVEL OF DEFECTS
• REDUCED - WITH OUTPUT REDUCED DEFECTS
• SEE FIG. 10-16 - OC CURVE OF EACH

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SWITCHING RULES

• FIGURE 10-17 ILLUSTRATES SWITCHING RULES
• N gt T (NORMAL TO TIGHTENED)
• T gt N
• N gt R
• R gt N
• DISCONTINUANCE BECAUSE OF POOR QUALITY

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DODGE-ROMIG PLANS

• DESIGNED TO PROVIDE HIGHER AQL BY REQUIRING 100
  AS RECTIFICATION STEP.
• THEY ARE SINGLE AND DOUBLE PLANS
• TABLES SET UP BY LQL AND Beta AND
• AVERAGE OUTGOING QUALITY LEVEL

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OTHER PLANS

• CHAIN SAMPLING PLANS
• SEQUENTIAL SAMPLING PLANS
• SKIP-LOT SAMPLING PLANS
• CONTINUOUS PRODUCTION PLANS
• DEMINGS kp RULE
• EACH HAS UNIQUE GOOD AND BAD CHARACTERISTICS

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VARIABLE PLANS

• MIL-STD-414 ANSI/ASQCZ1.9
  ISO 3951
• TWO TYPES OF PLANS
• CONTROL MEAN AND STD. DEV.
• CONTROL OF PROPORTION NOT MEETING SPECIFICATIONS
  OF THE PROCESS

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ADV. OF VARIABLE PLANS

• SAMPLE SIZES ARE SMALLER THAN ATTRIBUTE PLANS
• MORE INFO FROM VAR. PLANS
• THIS MORE INFO PROVIDES INSIGHTS INTO IMPROVED
  METHODS

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DISADV. OF VAR. PLANS

• EACH CHARACTERISTIC REQUIRES A SEPARATE PLAN.
• ADMIN. AND UNIT INSP. COSTS ARE HIGH.
• MEASURING INSTRUMENTS ARE MORE EXPENSIVE.
• MUST KNOW THE UNDERLYING DISTRIBUTION OF PROCESS.

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QUESTIONS YOU SHOULD BE ABLE TO ANSWER

• QUESTIONS 1 TO 5, 7, 8, AND 16
• PROBLEMS 41, 42, AND 43
• AS MENTIONED EARLIER THIS SEMESTER, YOU MUST BE
  ABLE TO GENERATE AN OC CURVE - THIS APPLIES TO
  THIS CHAPTER AS WELL AS PREVIOUS CHAPTERS.
• BE ABLE TO USE TABLES AS IN 41 - 43.