Chapter 5 Acceptance Sampling

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J5124 QUALITY J5124 QUALITY CONTROLCONTROL

CHAPTER 5CHAPTER 5Acceptance SamplingAcceptance Sampling2012/20132012/2013

COURSE OUTLINECOURSE OUTLINE

-- Usage of acceptance samplingUsage of acceptance sampling-- Advantages and disadvantages of Advantages and disadvantages of

acceptance samplingacceptance sampling-- Types of sampling plan (single, double, Types of sampling plan (single, double,

multiple)multiple)-- Formed lotFormed lot-- OC (Operating Characteristics)OC (Operating Characteristics)-- Consumer’s Risk, producer’s risk, AQL Consumer’s Risk, producer’s risk, AQL

(Acceptance quality level), LTPD ( limiting (Acceptance quality level), LTPD ( limiting tolerance percentage defective)tolerance percentage defective)

What is acceptance What is acceptance sampling?sampling?

Acceptance Acceptance sampling is a sampling is a method used to method used to accept or reject accept or reject product based on a product based on a random sample of random sample of the product.the product.

•• PurposesPurposes–– Determine the quality level of an Determine the quality level of an

incoming shipment or, at the end incoming shipment or, at the end productionproduction

–– Ensure that the quality level is Ensure that the quality level is within the level that has been within the level that has been predeterminedpredetermined

•• Can be either 100% Can be either 100% inspection, or a few items of a inspection, or a few items of a lot.lot.

•• Complete inspectionComplete inspection–– Inspecting each item produced to Inspecting each item produced to

see if each item meets the level see if each item meets the level desireddesired

–– Used when defective items would Used when defective items would be very detrimental in some waybe very detrimental in some way

•• Problems with 100% inspectionProblems with 100% inspection–– Very expensiveVery expensive–– When product must be destroyed When product must be destroyed

to testto test–– Inspection must be very tedious Inspection must be very tedious ––

less effective.less effective.

Acceptance SamplingAcceptance Sampling

Acceptance Sampling Acceptance Sampling methodmethod

ACCEPTANCE SAMPLING

ACCEPT LOT

RETURN LOT TO SUPPLIER 100% INSPECTION

DECISION

REJECT LOT SAMPLE AGAIN

DECISION

INSPECT SAMPLEType title here

TAKE SAMPLE

When you would use it?When you would use it?

•• When products in use could be When products in use could be damaged easilydamaged easily

•• When using new suppliersWhen using new suppliers•• When new products producedWhen new products produced•• When current supplier in questionWhen current supplier in question•• Testing whole lot could be harmfulTesting whole lot could be harmful

Acceptance sampling Acceptance sampling explainedexplained

•• Sampling PlanSampling Plan–– Forms after n and c values have been Forms after n and c values have been

foundfound•• nn

–– Sample size taken for your sampling Sample size taken for your sampling planplan

•• cc–– Where rejections would occur when Where rejections would occur when

defects exceeded this percentdefects exceeded this percent

Producer’s Risk and Producer’s Risk and Consumer’s RisksConsumer’s Risks

•• TYPE I ERROR= P(reject good lot)TYPE I ERROR= P(reject good lot)–– αα or Producer’s risk or Producer’s risk –– Risk associated with a lot of Risk associated with a lot of

acceptable quality rejectedacceptable quality rejected

•• TYPE II ERROR= P(accept bad lot)TYPE II ERROR= P(accept bad lot)–– ββ or Consumer’s riskor Consumer’s risk–– Receive shipment, assume good Receive shipment, assume good

quality, actually bad qualityquality, actually bad quality

A LotA Lot--byby--Lot Sampling PlanLot Sampling Plan

•• Specify the plan (n, c) given N Specify the plan (n, c) given N •• For a lot size N, determine For a lot size N, determine

––the sample size n, and the sample size n, and ––the acceptance number c. the acceptance number c.

•• Make a decision to reject or accept lot.Make a decision to reject or accept lot.•• Specify course of action if lot is rejectedSpecify course of action if lot is rejected

•• Sampling Plans specify the lot size, sample size, Sampling Plans specify the lot size, sample size, number of samples number of samples and acceptance / rejection and acceptance / rejection criteria.criteria.

•• Sampling plans involveSampling plans involve. Single sampling. Single sampling. Double sampling. Double sampling. Multiple sampling. Multiple sampling

Single Sampling PlanSingle Sampling Plan

•• The most common and easiest plan to use but The most common and easiest plan to use but not most efficient in terms of average number not most efficient in terms of average number of samples needed.of samples needed.

•• Single sampling planSingle sampling plan-- N = lot sizeN = lot size-- n= sample size (randomized)n= sample size (randomized)-- c= acceptance numberc= acceptance number-- d= number of defective items in sampled= number of defective items in sample

•• Rule: If d ≤ c, accept lot; else reject the lotRule: If d ≤ c, accept lot; else reject the lot

Procedure (Single)Procedure (Single)

Example 1 (Single)Example 1 (Single)•• Decision making has to finalize for product Decision making has to finalize for product

lot N =1000. Consider sampling plan as per lot N =1000. Consider sampling plan as per below:below:

n = 89n = 89c = 2c = 2

Found defect, d = 8Found defect, d = 8Answer Answer -- The lot is rejected because no of product The lot is rejected because no of product

defective is more than accepted lot ( d > c)defective is more than accepted lot ( d > c)

Double Sampling PlanDouble Sampling Plan•• A A Double Sampling Plan allows the opportunity to Double Sampling Plan allows the opportunity to

take a second take a second sample if the results of the original sample if the results of the original sample are inconclusive.sample are inconclusive.

•• Typically, four parameters are specified:Typically, four parameters are specified:

nn11 == number of units in the first samplenumber of units in the first samplecc11 == acceptance number for the first sampleacceptance number for the first samplenn22 == number of units in the second samplenumber of units in the second samplecc22 == acceptance number for both samplesacceptance number for both samples

Double Sampling PlanDouble Sampling Plan

Procedure (Double)Procedure (Double)•Take small initial sample and compare with •Take small initial sample and compare with

c1 and c2c1 and c2––If d1 ≤ c1, acceptIf d1 ≤ c1, accept––If c1 < d1 < r1 take second sampleIf c1 < d1 < r1 take second sample

•• Accept or reject lot based on 2 samplesAccept or reject lot based on 2 samples-- if (d1 + d2) ≤ c2 , acceptif (d1 + d2) ≤ c2 , accept-- if (d1 + d2) > r2 , rejectif (d1 + d2) > r2 , reject

•• Less inspection than in singleLess inspection than in single--samplingsampling

Example 2 (Double)Example 2 (Double)Given: Given: N = 9000, n1 = 60, c1 = 1, r1=4 N = 9000, n1 = 60, c1 = 1, r1=4

d1 = 5 d1 = 5 n2= 150, c2 =6, d2 = n2= 150, c2 =6, d2 = 22

Determine either to accept or reject lot.Determine either to accept or reject lot.

AnswerAnswer

Reject lotReject lot

Multiple Sampling PlanMultiple Sampling Plan

•• A A Multiple Sampling Plan is similar to the Multiple Sampling Plan is similar to the double sampling plan in that double sampling plan in that successive successive trials are made, each of which has trials are made, each of which has acceptance, rejection and inconclusive acceptance, rejection and inconclusive options.options.

Choosing A Sampling Choosing A Sampling MethodMethod

•• Which Plan you choose depends onWhich Plan you choose depends on–– Cost and timeCost and time–– Number of samples needed and number Number of samples needed and number

of items in each of items in each samplesample

•• Single sampling plansSingle sampling plans––high sampling costshigh sampling costs

•• Double/Multiple sampling plansDouble/Multiple sampling plans––low sampling costslow sampling costs

• Lot rejected will be send back to production unit and isolate the nonconforming units with the conforming units. However, this process will delay the production process. But if the products are really required, then this will be a good choice.

ACTION CAN BE TAKEN TO ACTION CAN BE TAKEN TO THE REJECTED UNITTHE REJECTED UNIT

• The rejected lots will be repaired on the spot after installation in the customer’s workplace by the manufacturer or the customer themselves. However, this will leave a psychological effect as the customer realize that the product they bought may be faulty, but will be taken as a good excuse if any complication happen in the future.

• The rejected lot will be send back to the manufacturer for repair. This is the best action as it helps to improve the quality. Usually the cost of transport are counted for two ways (including cost to send back if rejected), therefore this type of cost will also be a motivation for quality improvement. However, this action may cause a complete halt in production and may give an impact to the supplier of raw materials on the important of quality assurance.

Operating Characteristics Operating Characteristics Curve(OC)Curve(OC)

–– An An Operating Characteristic Curve (OCC) is a Operating Characteristic Curve (OCC) is a probability curve for a probability curve for a sampling plan that shows the sampling plan that shows the probabilities of accepting lots with various lot quality probabilities of accepting lots with various lot quality levels (% defectives).levels (% defectives).

EXERCISEEXERCISE

What the probability the lot is accepted and rejected?If lot has:a) 5% defectivesb) 12% defectivesc) 17 % defectives

Customer Acceptance Customer Acceptance LevelsLevels

•• Most customers understand that 100% inspection is Most customers understand that 100% inspection is impractical and are generally willing to accept that impractical and are generally willing to accept that a certain level of defectives will be produced.a certain level of defectives will be produced.

•• TheThe Acceptable Quality Level (AQL) Acceptable Quality Level (AQL) is the is the percentage level of defects at which a customer is percentage level of defects at which a customer is willing to accept as lot as “good”.willing to accept as lot as “good”.

•• The The Lot Tolerance Percent Defective (LTPD) Lot Tolerance Percent Defective (LTPD) is the is the upper limit on the percentage of defectives that a upper limit on the percentage of defectives that a customer is willing to accept.customer is willing to accept.

AQLAQL

•• Acceptable Quality levels(AQL)Acceptable Quality levels(AQL)

–– Number of defect percentage allowed in a lot Number of defect percentage allowed in a lot which can still be considered accepted which can still be considered accepted (Type I error)(Type I error)

–– The percentage is usually between 1 The percentage is usually between 1 --2 % 2 % defective.defective.

–– The producer would like to design a The producer would like to design a sampling plan such that there is a high sampling plan such that there is a high probability of accepting a lot that has a probability of accepting a lot that has a defect level less than or equal to the AQL.defect level less than or equal to the AQL.

•• Lot Tolerance Percent Defective(LTPD)Lot Tolerance Percent Defective(LTPD)

–– Amount of defects that will come with a lot of Amount of defects that will come with a lot of goods(Type II error).goods(Type II error).

–– The range contain indifferent quality items, an The range contain indifferent quality items, an upper limit on the percentage of defectives that a upper limit on the percentage of defectives that a consumer is willing to tolerate in accepted lots. consumer is willing to tolerate in accepted lots.

–– Consumer will not accept any lot with a defective Consumer will not accept any lot with a defective percentage exceeds the LTPD. percentage exceeds the LTPD.

–– LTPD is a designated high defect level that would LTPD is a designated high defect level that would be unacceptable to the consumer. The consumer be unacceptable to the consumer. The consumer would like the sampling plan to have a low would like the sampling plan to have a low probability of accepting a lot with a defect level probability of accepting a lot with a defect level as high as the LTPD.as high as the LTPD.

LTPDLTPD

•• Therefore the sampling plan must be designed to assure Therefore the sampling plan must be designed to assure the customer that they will be receiving the required the customer that they will be receiving the required AQL AQL and LTPD.and LTPD.

•• The The AQL and LTPD are dependent on many things AQL and LTPD are dependent on many things (reliability, liability, (reliability, liability, competitor quality levels, etc.) and competitor quality levels, etc.) and will vary by industry and by customer.will vary by industry and by customer.

•• Typically industry standards are set because suppliers Typically industry standards are set because suppliers have more than one customer and customers have more have more than one customer and customers have more than one supplier.than one supplier.

•• The The Consumer’s Risk is the probability that an Consumer’s Risk is the probability that an unacceptable lot (e.g. unacceptable lot (e.g. above the above the LTPD) will be accepted.LTPD) will be accepted.

•• The The Producer’s Risk is the probability that a “good” lot Producer’s Risk is the probability that a “good” lot will be rejected.will be rejected.

Customer Acceptance Customer Acceptance LevelsLevels

OCC, AQL & Producer’s OCC, AQL & Producer’s RiskRisk

OCC, LTPD & OCC, LTPD & Consumer’s RiskConsumer’s Risk

Producer’s risk Consumer’s risk

i) Represented by symbol .

ii) Probability of non-acceptance of a

conforming lot.

iii) This risk given as 0.05.

iv) Pa= 1- = 1-0.05 = 0.95

i) Represented by symbol .

ii) Probability of acceptance of a

nonconforming.

iii) This risk given as 0.05.

iv) Associated with the consumer’s risk

is a numerical definition of

nonconforming lot, called

LIMITING QUALITY(LQ)

OC CURVE AND MILOC CURVE AND MIL--STDSTD--105D105D

TUTORIALTUTORIAL

EXAMPLE 1EXAMPLE 1

Draw OC Curve for below sample Draw OC Curve for below sample plan:plan:N = 3000, n= 89, c=2N = 3000, n= 89, c=2

STEPSTEP

1)1) Assume Nonconforming, Po Assume Nonconforming, Po Value Value –– 0.01,0.02,0.03….0.070.01,0.02,0.03….0.07

2)2) Calculate Calculate nPonPo valuevalue3)3) Determine Pa value from Table Determine Pa value from Table

C (Poisson Distribution)C (Poisson Distribution)4)4) Plot Graph Pa Vs 100Po (% Plot Graph Pa Vs 100Po (%

defective)defective)Summary all the STEP in Table.Summary all the STEP in Table.

Table for OC CurveTable for OC Curve

Assumed Process Quality Sample Size Nonconforming

Probability of Acceptance

Po 100Po n nPo Pa

0.01 1 89 0.9 0.938

0.02 2 89 1.8 0.731

0.03 3 89 2.7 0.494

0.04 4 89 3.6 0.302

0.05 5 89 4.5 0.174

0.06 6 89 5.3

0.07 7 89 6.2

USE MILUSE MIL--STDSTD--105D TO 105D TO DETERMINE SINGLE SAMPLING DETERMINE SINGLE SAMPLING

PLANPLAN

EXAMPLE 1EXAMPLE 1

•• REFER PAGE 12 (UNIT 5) IN THE REFER PAGE 12 (UNIT 5) IN THE WORKBOOKWORKBOOK

EXAMPLE 2EXAMPLE 2

For a lot of 5000, an AQL of For a lot of 5000, an AQL of 0.65% and inspection level of III, 0.65% and inspection level of III, determine the single sampling determine the single sampling plans for normal, tightened and plans for normal, tightened and reduced inspection.reduced inspection.

AnswerAnswerNormal Tightened Reducedn =Ac =Re =

n =Ac =Re =

From a lot of a random sample of

is inspected. If or less nonconforming units are found, the lot is accepted. If or morenonconforming units are found, the lot is rejected

ExerciseExercise•• Differentiate the number of Ac, Re and n Differentiate the number of Ac, Re and n

for single sampling inspection table for single sampling inspection table according to MILaccording to MIL--STDSTD--105D for three (3) 105D for three (3) cases of inspection levels above (S4c), if cases of inspection levels above (S4c), if you have the following:you have the following:

Lot Size N Lot Size N = 20,000 units= 20,000 unitsAQLAQL = 0.65 %= 0.65 %General Inspection levelsGeneral Inspection levels = II= II

Chapter 5 Acceptance Sampling

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