acceptance sampling
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StatisticsTRANSCRIPT
Acceptance Sampling- A form of inspection
PRESENTED BY : SENARATHNE D.M.U.S | S/09/598
2Outline Introduction Usage Sampling Plans Single, Double and multiple Sampling Plans Operating Characteristic Curve and Acceptance Levels Sampling Risks Average Outgoing Quality Advantages and Disadvantages Conclusion
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3Introduction
A form of inspection applied to lots or batches of
items before or after a process to judge
conformance to predetermined standards
It is a decision making tool by which a conclusion
is reached regarding the acceptability of lot.
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4Acceptance Sampling Used in…
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When testing is destructive When the cost of 100% inspection is extremely high and it
is not technologically feasible When the vendor has an excellent quality history, and some
reduction in inspection from 100% is desired, but the vendor’s process capability is sufficiently low as to make no inspection an unsatisfactory alternative
5Sampling Plans
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Sampling plans
Attribute sampling
Single sampl
ing
Double
Sampling
Multiple
Sampling
Sequential
Sampling
Variable sampling
Sampling Plans specify the lot size, sample size, number of samples and acceptance/rejection criteria. Sampling plans involve
Random sample
Lot
6Single Sampling Plan
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g A representative sample of n items is drawn from a lot size of N items.
Each item in the sample is examined and classified as good/defective
If the number of defective exceeds a specified rejection number (C - cut off point) the whole lot is rejected; otherwise the whole lot is accepted
Random
sample (n
items)
Lot (N items)
Random
sample (n
items)
Lot (N items)
7Double Sampling Plan
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A Double Sampling Plan allows the opportunity to take a second sample if the results of the original sample are inconclusive.
Specifies the lot size, size of the initial sample, the accept/reject/inconclusive criteria for the initial sample (CL - lower level of defectives, CU - upper level of defectives)
Specifies the size of the second sample and the acceptance rejection criteria based on the total number of defective observed in both the first and second sample (CT- total allowable defectives)
It works like the following example
8Double Sampling Plan…acce
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Compare number of defective found in the first random sample to CL and CU and make appropriate decision.
CL CU
Accept Lot Reject Lot
First sample inconclusive, take second sample
First Random sample
Lot
9Double Sampling Plan…acce
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Compare the total number of defective in both samples to CT and make the appropriate decision
Accept Lot Reject Lot
CT
Lot First Random sample
Second Random sample
10Multiple Sampling Plans
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A Multiple Sampling Plan is similar to the double sampling plan in that successive trials are made, each of which has acceptance, rejection and inconclusive options.
Which Plan you choose depends on
Cost and time
Number of samples needed and number of items in each sample
11Operating Characteristic Curve(OCC) An Operating
Characteristic Curve (OCC) is a probability curve for a sampling plan that shows the probabilities of accepting lots with various lot quality levels (%defectives).
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Lot quality (%defective)
Pro
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Under this sampling plan, if the lot has 2% defective . the probability of accepting the lot is 92% . the probability of re-jecting the lot is 8%
If the lot has 10% defective . it has a small proba-bility (11%) of being accepted . the probability of rejecting the lot is 89%
12Customers Acceptance Levels
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Most customers understand that 100% inspection is impractical and are generally willing to accept that a certain level of defectives will be produced.
The Acceptable Quality Level (AQL) is the percentage level of defects at which a customer is willing to accept as lot as “good”.
The Lot Tolerance Percent Defective (LTPD) is the upper limit on the percentage of defectives that a customer is willing to accept.
Customers want lots with quality better than or equal to the AQL but are willing to live with some lots with quality as poor as the LTPD, but prefer not to accept lots with quality levels worse than the LTPD.
13Defining good and bad lot
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Proportion non-conforming
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AQL LTPD
Very Good
Ok! But not great
Very Bad
Instead of good and bad we will define “really good”, “really bad”, “ok, but not great”
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14Customers Acceptance Levels…
Therefore the sampling plan must be designed to assure the customer that they will be receiving the required AQL and LTPD.
The Consumer’s Risk is the probability that an unacceptable lot (e.g. above the LTPD) will be accepted.
The Producer’s Risk is the probability that a “good” lot will be rejected.
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15Sampling Risks
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AQL LTPD
Producer’s Risk = Probability acceptable is rejected
Consumer Risk = Probability unacceptable is accepted
Acceptable lotUnacceptable lot
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16Average Quality Of Inspected LotsThe result of acceptance sampling (assuming rejected lots are 100% inspected) is that the level of inspection automatically adjusts to the quality of the lots being inspected.
The Average Outgoing Quality (AOQ)is the average of rejected lots (100% inspection) and accepted lots ( a sample of items inspected).
AOQ = where;
= Probability of accepting a lot
= Fraction defective
N = Lot size
n = Sample size
The maximum outgoing quality level is referred to as the AOQL
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17Constructing OC Curve
00.10.20.30.40.50.60.70.80.9
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Proportion non-conforming
Pro
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0.677Proportion non-conforming
Probability of acceptance
0 10.01 0.9860.02 0.9220.04 0.6770.06 0.4160.08 0.226
0.1 0.1120.15 0.014
0.2 0.001OC curve for n=50, c=2
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18Advantages It is usually less expensive because there is less
inspection. There is less handling of the product, hence reduced
damage. It is applicable to destructive testing. Fewer personnel are involved in inspection activities. It often greatly reduces the amount of inspection error. The rejection of entire lots are opposed to the sample
return of defectives often provides a stronger motivation to the vendor for quality improvements.
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19Disadvantages
There are risk of accepting “bad” lots and rejecting “good” lots.
Less information is usually generated about the product or about the process that manufactured the product.
Acceptance sampling requires planning and documentation of the acceptance sampling procedure whereas 100% inspection does not.
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20Conclusion Acceptance sampling is a statistical procedure used to
determine whether to accept or reject a production lot of material.
A wide variety of sampling plans are available. Plans have an accepted AQL & a rejected LTPD & an AOQL.
Acceptance sampling tables are there to supply a set of accepted procedures with known properties &verified results.
Sampling provides rational means of verification that a production lot confirms with requirements of technical specifications.
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21
THANK YOU
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