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Chapter 15: B. Sampling 157• Preceding 10 lotsaccepted, with• Total nonconformingless than limit number(optional), and• Production steady, and• Approved byresponsible authorityStart• Two out of fiveconsecutive lotsnot acceptedReducedNormalTightened• Lot not accepted, or• Lot accepted butnonconformitiesfound lie betweenacceptance andrejection of plan, or• Production irregular, or• Other conditionswarrant• Five consecutivelots accepted• Five consecutivelots remain ontightenedFigure 15.3 Switching rules for normal, tightened, and reduced inspection.• Discontinueinspectionunder Z1.4Part III.BMultiple sampling plans further reduce the average total inspection but alsoincrease the number of decisions to be made. As many as seven samples may berequired before a decision to accept or reject the lot can be made. This type of planrequires the most administration.Appendix H provides some tables from the ANSI/ASQ Z1.4-2003 standardthat are used for the selection of attribute sampling plans.VARIABLES SAMPLING PLANSVariables sampling plans use the actual measurements of sample products fordecision making, rather than classifying products as conforming or nonconformingas in attribute sampling plans. Variables sampling plans are more complex inadministration than attribute plans, thus they require more skill. They providesome benefits, however, over attribute plans. Two of these benefits are:1. Equal protection as with an attribute sampling plan with a muchsmaller sample size. There are several types of variables samplingplans in use, three of these being: 1) s known, 2) s unknown but canbe estimated using sample standard deviation s, and 3) s unknownand range R used as an estimator. If an attribute sampling plan samplesize is determined, the variables plans previously listed can becompared as a percentage to the attribute plan:

158 Part III: Inspection and TestSample sizePlan(percent)Attribute 100s unknown, range method 60s unknown, s estimated from sample 40s known 15Part III.B2. Variables sampling plans allow the determination of how close tonominal or a specification limit the process is performing. Attributeplans either accept or reject a lot; variables plans give information onhow well or poorly the process is performing.Variables sampling plans, such as ANSI/ASQ Z1.9-2003, have some disadvantagesand limitations:1. The assumption of normality of the population from which the samplesare being drawn.2. Unlike attribute sampling plans, different characteristics on the sameparts will have different averages and dispersions, resulting in aseparate sampling plan for each characteristic.3. Variables plans are more complex in administration.4. Variables gauging is generally more expensive than attribute gauging.ANSI/ASQ Z1.9-2003The most common standard for variables sampling plans is ANSI/ASQ Z1.9-2003,which has plans for: 1) variability known, 2) variability unknown—standard deviationmethod, and 3) variability unknown—range method. Using these methods,this sampling plan can be used to test for a single specification limit, a double (orbilateral) specification limit, estimation of the process average, and estimation ofthe dispersion of the parent population.As in ANSI/ASQ Z1.4-2003, several AQL levels are used and specific switchingprocedures for normal, reduced, and tightened inspection are followed. ANSI/ASQ Z1.9-2003 allows for the use of the same AQL value for each specificationlimit of double specification limit plans or the use of different AQL values for eachspecification limit. The AQL values are designated ML for the lower specificationlimit and MU for the upper specification limit.Figure 15.4 summarizes the structure and organization of ANSI/ASQZ1.9-2003.Appendix H provides some tables from the ANSI/ASQ Z1.9-2003 standardthat are used for the selection of variables sampling plans.SEQUENTIAL SAMPLING PLANSWhen tests are either destructive in nature or very costly, it may be advantageousto use sequential sampling plans popularized by Wald (1973). These plans havethe advantage of greatly reduced sample sizes while providing good protection.

Chapter 15: B. Sampling 157

• Preceding 10 lots

accepted, with

• Total nonconforming

less than limit number

(optional), and

• Production steady, and

• Approved by

responsible authority

Start

• Two out of five

consecutive lots

not accepted

Reduced

Normal

Tightened

• Lot not accepted, or

• Lot accepted but

nonconformities

found lie between

acceptance and

rejection of plan, or

• Production irregular, or

• Other conditions

warrant

• Five consecutive

lots accepted

• Five consecutive

lots remain on

tightened

Figure 15.3 Switching rules for normal, tightened, and reduced inspection.

• Discontinue

inspection

under Z1.4

Part III.B

Multiple sampling plans further reduce the average total inspection but also

increase the number of decisions to be made. As many as seven samples may be

required before a decision to accept or reject the lot can be made. This type of plan

requires the most administration.

Appendix H provides some tables from the ANSI/ASQ Z1.4-2003 standard

that are used for the selection of attribute sampling plans.

VARIABLES SAMPLING PLANS

Variables sampling plans use the actual measurements of sample products for

decision making, rather than classifying products as conforming or nonconforming

as in attribute sampling plans. Variables sampling plans are more complex in

administration than attribute plans, thus they require more skill. They provide

some benefits, however, over attribute plans. Two of these benefits are:

1. Equal protection as with an attribute sampling plan with a much

smaller sample size. There are several types of variables sampling

plans in use, three of these being: 1) s known, 2) s unknown but can

be estimated using sample standard deviation s, and 3) s unknown

and range R used as an estimator. If an attribute sampling plan sample

size is determined, the variables plans previously listed can be

compared as a percentage to the attribute plan:

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