Statisticalsampling

Cosmo - Statistical Sampling and AQL

1.0. PURPOSE
This procedure describes the processes involved in performing Statistical Sampling for the Inspection of consumer products.

2.0. SCOPE
This procedure must be used by all China Gateway inspectors for the inspection of consumer products

3.0. RESPONSIBILITY
All staff involved in the inspection of consumer products are responsible for understanding and implementing these procedures.

4.0. REFERENCES
Basic Workflow for Inspection Final Random Inspection Product Specific Inspection Procedures

5.0. TERMINOLOGY

IR	Inspection Report
COP	Client Operating Procedure

6.0. PROCEDURE

6.1. Summary – This document contains a summary of those sampling and inspection methods/parameters most commonly applied in the Consumer Products Industry. There do exist other methods/parameters that can be used in place of those mentioned here. What is most important is that the buyer and seller agree on specific sampling and inspection methods/parameters and these are known, understood, and applied by the inspection company. Unless stipulated otherwise, the following methods/parameters will be applied by Cosmo Services for the inspection of consumer products.

NOTE: Client specific or product specific sampling methods/parameters stated in a COP, Product Specification and/or Inspection Protocol for the inspection in concern will always REPLACE the China Gateway Standard Inspection Criteria listed in sections 6.2.5, 6.4.3.4 and 6.6.5 of this document.

6.2. Statistical Sampling

6.2.1. Statistical sampling is a method used to check a large number of items within a limited period of time. This advantage, combined with a known degree of reliability, makes it a preferred practice over examination of every item in a lot/batch. Conducting such a 100% inspection often involves a long and expensive procedure, making it impractical in most cases where there are large numbers of articles.

6.2.2. Statistical sampling involves the selection of individual samples, or units.

6.2.3. Unless otherwise stipulated in the COP, the percentage of units to be taken is based on the following standard: ISO 2859

6.2.4. Sampling Definitions

6.2.4.1. Sample – one unit of product drawn from a lot.

6.2.4.2. Sample Size – total number of samples drawn from a lot.

6.2.4.3. Lot or Batch – a collection of units of a product from which a sample is to be drawn.

6.2.4.4. Lot or Batch Size – total number of units of a product in a lot.

6.2.4.5. Defect – any non-conformance of the inspected unit of product with specified requirements.

6.2.4.6. Defective – a unit of product that contains one or more defects.

6.2.4.7. Acceptance Number – the maximum number of defects or defective units in the sample that will permit acceptance of the inspection lot or batch.

6.2.4.8. Rejection Number – the minimum number of defects or defective units in the sample that will cause rejection of the lot represented by the sample.

6.2.4.9. Sampling Plan – Within ISO 2859 three sampling plans (Single, Double, Multiple) are available to determine the number of samples from each lot to be inspected based on the nature of the product to be inspected.

6.2.4.10. Inspection Procedure – Within ISO 2859, three inspection procedures are available to adjust the severity of inspection based on the accept/reject results.

Normal Inspection – Inspection procedure used when there is no evidence that the quality of product being submitted is better or poorer that the specified quality level.
Tightened Inspection – uses the same quality level as for normal inspection, but requires more stringent acceptance criteria.
Reduced Inspection – uses the same quality level as for normal inspection, but requires a smaller sample for inspection.

6.2.4.11. Inspection Level – Within ISO 2859, three General and four Special Inspection Levels are provided. These seven levels permit the user to balance the cost of inspection against the amount of protection required.

General Inspection Levels (I, II, III) are commonly used for non-destructive inspection. Level II is considered the norm (except for small sample sizes). Level I requires only 40 per cent of the amount of inspection Level II and can be used where less discrimination is needed. Level III equals 160 per cent of the amount of inspection Level II. Level III will give a lower risk of accepting a lot with an excessive number of defects, however, inspection of a larger number of samples is required.
Special Inspection Levels (S-1, S-2, S-3, and S-4) are used where relatively small sample sizes are necessary and large sampling risks can or must be taken.
Examples of this are: destructive or costly (time consuming) types of inspection, where very large lots are involved, and when small sample sizes are desired and large risks can be tolerated. Larger sample sizes are required for inspection levels increasing from S-1 to S-4.

6.2.5Cosmo Services Standard Inspection Criteria: Sampling

Sampling Plan	Single
Inspection Procedure	Normal
Inspection Level	Depending on type of product and/or service

6.3. Inspection by Attributes

6.3.1. Inspection by Attributes is where the unit of product is classified simply as defective or non-defective, the number of defects in the unit of product are counted, with respect to a given requirement or set of requirements. This involves removing a small number of items from a larger lot (through statistical sampling) and, by examining them very closely, assessing the quality of the whole lot/batch. However, as a sample rarely contains exactly the same proportion of defective articles as the lot/batch from which it is taken, any decision about a given lot/batch involves some risk:

6.3.1.1The sample may contain a higher percentage of defective items, which could mean a good-quality lot/batch being rejected – this the Vendor’s risk.

6.3.1.2 The sample may contain a lower percentage of defective items, which could mean a low quality lot/batch being accepted – this is the Buyer’s risk.

6.4 Defects & Defectives

6.4.1 A Defect is defined as any non-conformance of the inspected unit of product with specified requirements. Requirements may be in the form of written specifications, measurement charts, color standards, approved reference samples, etc.

6.4.2 A Defective is defined as a unit of product that contains one or more defects.
6.4.3 Classification of Defects – Defects exhibited by each inspected sample are identified according to their apparent severity as Critical, Major, or Minor

6.4.3.1. Critical Defect – a defect likely to result in a hazardous or unsafe condition for an individual using the product or fails to meet mandatory regulations.

6.4.3.2. Major Defect – a defect that is likely to result in failure, reduce the usability & salability and can easily be detected by the customer.

6.4.3.3. Minor Defect – a defect that does not reduce the usability of the product, can be noticed only after careful examination, and may reduce the salability. A workmanship defect beyond the defined quality standard.

6.4.3.4 Cosmo Services Standard Inspection Criteria: Classification of Defects

Inspection Criteria	Classification
Workmanship/Measurements/Aesthetics	Major or Minor – depending on severity
Packaging/Marking/Labeling	Major or Minor – depending on severity
Color Comparison	Major or Minor – depending on severity
Functional	Major or Critical – depending on severity
Safety Requirements	Critical

6.4.4. Recording of Defects – All defects observed on all samples should be recorded by the inspector. All samples must be checked fully for Critical, Major and Minor defects – an inspection does not stop just because a sample exhibits a Critical defect – the inspection must continue until all defects observed have been classified & recorded.

6.4.5 Counting of Defects & Defectives – When the number of defects is being counted for AQL purposes, a single defect is taken into account, in every case the most serious defect exhibited by the individual sample being inspected regardless of the characteristic.

6.4.5.1 A single inspected sample may not be counted as more than 1 Major defective towards the total number of Major defectives for the inspection lot. When an inspected sample contains both a Major defect and Minor defect for the same characteristic, it should be classified as a defective based on the most severe defect (Major defective).

6.4.5.2 If 3 or more Minor defects are found within the same sample, the sample is then counted as 1 Major defective.

6.4.6. Reporting of Defects & Defectives – It is the standard policy of Cosmo Services to report the number of defectives (units of product that contain one or more defects) found during an inspection.

6.4.6.1 It is critical that the exact number, classification, and description of defectives are clearly stated on the Inspection Report.

6.4.6.2. The number of defects (the individual non-conformances found on the inspected units) is not to be reported unless specifically requested by the client.

6.4.6.3. A summary of “Other Defects Observed but not Counted in AQL Result” is to be included in the Remarks section of the Inspection Report immediately following the Workmanship results. This list should contain the names of the other defects found but not the number of other defects found.

Remarks: Other defects were found but not counted in the AQL result Slight color deviation on program button

6.4.6.4. If 3 or more Minor defects are found within the same sample, the sample is reported as 1 Major defective as follows: “defect 1 + defect + defect 3”
Example: Scratch on LCD + button scratched + gift box dirty

6.5. Sampling From Export Cartons

6.5.2 The total number of cartons to be opened, from which the inspection samples are drawn and internal quantities counted, is determined as follows: Square Root of Total # of Cartons (round the number up)

6.5.1.1 Example: Square root of 300 Cartons = 17.3 (round up to 18 Cartons)

6.5.2 The cartons to be opened should be drawn from the total # of cartons in a representative and random manner
6.5.3 The required sample size should be selected from the opened cartons randomly and proportionally. Do not take all required samples from a few cartons only !

6.5.3.1 Example: Sample Size = 200 units, Opened Cartons = 18 Divide 200 units by 18 cartons = 11.1111 Select 11 samples each of the other 17 cartons and 13 samples from 1 carton

6.5.4 Additional cartons must be opened in the following situations:

6.5.4.1 When the total quantity of units within the selected cartons is less than the required sample size.
6.5.4.2 When the required sample size for all styles/colors/sizes is not represented in the selected cartons.

6.6 Acceptance Quality Limit (AQL)

6.6.1 The Acceptance Quality Limit (AQL) is the maximum percentage of detective items regarded as satisfactory during inspection, which in theory represents the average quality of production.
6.6.2 By designating a specific value of AQL for a certain defect or group of defects, the buyer indicates to the supplier that the great majority of the lots or batches

that the supplier submits will be accepted, provided that the process average level of percent defective (or defects per hundred units) in these lots or batches is no greater than the designated value of AQL.

6.6.3 The sampling plans in ISO 2859 are arranged so that the probability of acceptance at the designated AQL value depends upon the sample size, being generally higher for large samples than for small ones, for a given AQL. The AQL alone does not describe the protection to the buyer or consumer for individual lots or batches but more directly relates to what might be expected from a series of lots or batches. In total there are 26 specific values of AQL
6.6.4 For inspection under ISO 2859 the AQL will be specified in the contract or specifications. Different AQL’s may be designated for groups of defects considered collectively or for individual defects. A common practice is to designate different values of AQL for major, minor, critical and/or total defects. Due to the differences in the specified AQL values, it is possible that one sample size may be indicated in the sampling procedures of ISO 2859 for major defects, and another sample size for minor defects or total defects. Whenever two or more sample sizes are indicated by the Tables (for a given sample size code letter but for different values of AQL), the correct procedure is to select the largest indicated sample at random from the lot, then select the smaller sample sizes at random from the larger sample.

6.6.5 CHINA GATEWAY Standard Inspection Criteria: Acceptance Quality Limit

AQL
Critical Defectives	Major Defectives	Minor Defectives
None	1.0	2.5
Note: The above AQL’s are applied by COSMO SERVICES unless specified otherwise by the Inspection Protocol or client specification. Refer to section 5.1 of this document for additional information

Steps for Calculating Sampling Parameters

STEP	CALCULATION – EXAMPLE
1. Determine Lot/Batch Size 3000 items (client supplied)
2. Determine Sampling Plan Single (client supplied)
3. Determine Severity Normal (client supplied)
4. Determine Inspection Level II (client supplied)
5. Find Sample Size Code Letter (Table I*) K
6. Find Sample Size (Table II-A**) 125 items
7. Determine AQL’s 2.5 for Major, 4.0 for Minor (client supplied)
8. Find Accept/Reject #’s for Major Defectives 7/8
9. Find Accept/Reject #’s for Minor Defectives 10/11
* – Refer to section 5.9.1.1 ** – Refer to section 5.9.1.2

6.8 PRO RATA Sampling

6.8.1 Pro Rata (or “pro rating”) sampling is the selection of samples to be inspected from populations of products that consist of a varied assortment. Pro Rata Sampling can be done based on the following: Style, Size, Color, Production Status – “packed / not packed”, etc.

6.8.2 The individual samples to be inspected will be “pro-rated” (distributed) based on the ratio of the total quantity versus the individual quantities. An example based on size assortment follows:

DETAILS
Lot/batch Size	2500 pcs in 3 PO’s
Sampling Plan	Single
Inspection Severity	Normal
Inspection Level	II
Sample Size	125 items
Individual Quantities	300 pcs – Siemssen (SIE)
	1500 units Easylink (EL)
	500 units – Honeywell (HW)

RESULTS
SIZE	INDIVIDUAL QUANTITY	MULTIPLY	SAMPLE SIZE	DIVIDE	LOT/BATCH SIZE	SAMPLE SIZE
SIE	300	X	125	/	2500	15
EL	1500	X	125	/	2500	75
HW	500	X	125	/	2500	25
TOTAL	2500	X	125	/	2500	125

6.9 Sampling of Products Supplied in Sets or Packs

6.9.1 Products supplied in sets/packs containing several individual products packaged together for sale will be sampled as if each set or pack is a single sample.

6.9.2 Individual products from within each selected set/pack will be inspected for defects and the results will be reported based on each set/pack.

6.10 ISO 2859 Sampling Tables

6.10.1 Several tables commonly used for the sampling and inspection of consumer products exist, for additional tables and information please refer directly to ISO 2859.

6.11 Cosmo Services AQL SUMMARY TABLE (ISO 2859. Table II-A)

Sampling Plan >	Single
Inspection Procedure >	Normal
Inspection Level >	II

Cosmo Services	INSPECTION PROCEDURE CS 001	Edition: 01	Page: 1/9
	STATISTICAL SAMPLING & AQL

LOT SIZE	SAMPLE SIZE		0.65			1			1.5			2.5			4
LOT SIZE	SAMPLE SIZE	Ac		Re	Ac		Re	Ac		Re	Ac		Re	Ac		Re
151 – 280	32		↑			↑		1		2	2		3	3		4
281 – 500	50		↓		1		2	2		3	3		4	5		6
510 – 1200	80	1		2	2		3	3		4	5		6	7		8
1201 – 3200	125	2		3	3		4	5		6	7		8	10		11
3201 – 10000	200	3		4	5		6	7		8	10		11	14		15
10001 – 35000	315	5		6	7		8	10		11	14		15	21		11
35001 – 150000	500	7		8	10		11	14		15	21		22
150001 – 500000	800	10		11	14		15	21		22		↑

6.11.1 There can be situations where an inspector must inspect a different sample size for Critical defects than for Major defects than for Minor defects within the same lot size. The inspector should select the largest sample size required and then perform the entire inspection on these samples recording the defects for each type of defect on the individual sample sizes required.

6.11.1.1Examples based on General Level 2:

Lot size = 280 pcs
Code letter	AQL	Sample Size	Acc/ Rej	Defect Counting
K	AQL 1.0	50	1/2	from 1 to 50
	AQL 2.5	32	2/3	from 1 to 32
Select a sample size of 50. Sample size for counting critical defects is 50. Sample size for counting major defects is 50. Sample size for counting minor defects is 32. No need to count minor defects from samples 33 to 50.

Lot size = 80 pcs
Code letter	AQL	Sample Size	Acc/ Rej	Defect Counting
E	AQL 1.5	8	0/1	from 1 to 8
	AQL 2.5	20	1/2	from 1 to 20
Select a sample size of 20. Sample size for counting critical defects is 20. Sample size for counting major defects is 8. Sample size for counting minor defects is 20 No need to count major defects from samples 9-20

6.12Double Sampling Plans

6.12.1Upon specific request from a client, Double Sampling may be used based on the following procedure. • Determine the applicable Double Sampling Plan to be used in ISO 2859. • Select (at random) the number of sample units equal to the first sample size given by the plan.

•If the number of defectives found in the first sample is equal to or less than the first acceptance number, the lot is considered ACCEPTABLE.

• If the number of defectives found in the first sample is equal to or greater than the first rejection number, the lot is considered NOT ACCEPTABLE.

• If the lot is considered ACCEPTABLE OR NOT ACCEPTABLE, the inspection is finished.

• If the number of defectives found in the first sample is between the first acceptance and rejection numbers, a second sample must be inspected.

• Select (at random) the number of sample units equal to the second sample size given by the plan.

• The number of defectives found in the first and second samples shall be added together.
• If the cumulative number of defectives is equal to or less than the second acceptance number, the lot is considered ACCEPTABLE.

• If the cumulative number of defectives is equal to or greater than the second rejection number, the lot is considered NOT ACCEPTABLE.

• Refer to the table below for details.

Sampling Plan >	Double
Inspection Procedure >	Normal
Inspection Level >	II

LOT SIZE	SAMPLE SIZE	n1		0.65			1			1.5			2.5			4
LOT SIZE	SAMPLE SIZE	n1+n2	Ac		Re	Ac		Re	Ac		Re	Ac		Re	Ac		Re
151 – 280	First	20					↓		0		2	0		3	1		4
151 – 280	Second	40					↓		1		2	3		4	4		5
281 – 500	First	32				0		2	0		4	1		4	2		5
281 – 500	Second	64				1		2	3		4	4		5	6		7
510 – 1200	First	50	0		2	0		3	1		4	2		5	3		7
510 – 1200	Second	100	1		2	3		4	4		5	6		7	8		9
1201 – 3200	First	80	0		3	1		4	2		5	3		7	5		9
1201 – 3200	Second	160	3		4	4		5	6		7	8		9	12		13
3201 – 10000	First	125	1		4	2		5	3		7	5		9	7		11
3201 – 10000	Second	250	4		5	6		7	8		9	12		13	18		19
10001 – 35000	First	200	2		5	3		7	5		9	7		11	11		16
10001 – 35000	Second	400	6		7	8		9	12		13	18		19	26		27
35001 – 150000	First	315	3		7	5		9	7		11	11		16
35001 – 150000	Second	630	8		9	12		13	18		19	26		27
150001 – 500000	First	500	5		9	7		11	11		16		↑
150001 – 500000	Second	1000	12		13	18		19	26		27

AC = ACCEPTANCE NUMBER
RE = REJECTION NUMBER

6.12.2. Example for Double Sampling

Sampling Plan >	Double
Inspection Procedure >	Normal
Inspection Level >	II
AQL >	Major = 1.0, Minor = 2.5
Lot or Batch Size >	3,600 pieces

Major Defectives:

Select 125 samples for inspection (first sample).

• If the number of major defectives found in the first sample is equal to or less than 5, the lot is considered ACCEPTABLE and the inspection is finished for Major Defectives.

• If the number of major defectives found in the first sample is equal to or greater than 9, the lot is considered NOT ACCEPTABLE and the inspection is finished for Major Defectives.

• If the number of major defectives found in the first sample is 6, 7 or 8, a second sample must be inspected.

• Select 125 samples for inspection (2nd sample).

• The number of major defectives found in the first and second samples shall be added together (cumulative number of defectives).

•· If the cumulative number of major defectives is equal to or less than 12, the lot is considered ACCEPTABLE.

• If the cumulative number of defectives is equal to or greater than 13, the lot is considered NOT ACCEPTABLE

Minor Defectives :

• Inspect the same 125 samples inspected above for Minor Defectives, substituting the Accept/Reject criteria listed under AQL 4.0.

• If the number of minor defectives found in the first sample is equal to or less than 7, the lot is considered ACCEPTABLE and the inspection is finished for Minor Defectives.

• If the number of minor defectives found in the first sample is equal to or greater than 11, the lot is considered NOT ACCEPTABLE and the inspection is finished for Minor Defectives.

• If the number of minor defectives found in the first sample is 8, 9 or 10, a second sample must be inspected.

• Select 125 samples for inspection (2nd sample).

• The number of minor defectives found in the first and second samples shall be added together (cumulative number of defectives).

• If the cumulative number of minor defectives is equal to or less than 18, the lot is considered ACCEPTABLE.

• If the cumulative number of minor defectives is equal to or greater than 19, the lot is considered NOT ACCEPTABLE