Iec 62058-11-2008.Pdf

Sources of data

NOTE 1 A characteristic can be inherent or assigned

NOTE 2 A characteristic can be qualitative or quantitative

(reference) totality of items under consideration [ISO 3534-2, 1.2.1 modified]

3.1.3 lot definite part of a population constituted under essentially the same conditions as the population with respect to the sampling purpose

NOTE The sampling purpose can, for example, be to determine lot acceptability, or to estimate the mean value of a particular characteristic

3.1.4 isolated lot lot separated from the sequence of lots in which it was formed and not forming part of a current sequence

3.1.5 re-submitted lot lot which previously has been designated as not acceptable and which is submitted again for inspection after having been further treated, tested, sorted, reprocessed, etc

3.1.6 item entity anything that can be described and considered separately; for the purposes of this standard, an electricity meter [ISO 3534-2, 1.2.11 modified]

3.1.7 nonconforming item item with one or more nonconformities [ISO 3534-2, 1.2.12]

3.1.8 defective item item with one or more defects [ISO 3534-2, 1.2.13]

LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU.

3.1.9 sampling unit unit one of the individual parts into which a population is divided [ISO 3534-2, 1.2.14 modified]

3.1.10 nonconforming unit unit with one or more nonconformities [ISO 3534-2, 1.2.15]

3.1.11 sample subset of a population made up of one or more sampling units [ISO 3534-2, 1.2.17 modified]

3.1.12 sample size number of sampling units in a sample

NOTE In a multistage sample, the sample size is the total number of sampling units at the conclusion of the final stage of sampling

Types of sampling

3.2.1 sampling act of drawing or constituting a sample [ISO 3534-2, 1.3.1]

Simple random sampling is a method in which a sample of $ n $ units is selected from a population, ensuring that every possible combination of $ n $ units has an equal chance of being chosen.

3.2.3 acceptance sampling sampling after which decisions are made to accept or not to accept a lot based on sample results

Specifications, values and test results

3.3.1 specification limit limiting value stated for a characteristic [ISO 3534-2, 3.1.3]

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U specification limit that defines the upper limiting value [ISO 3534-2, 3.1.4]

L specification limit that defines the lower limiting value [ISO 3534-2, 3.1.5]

3.3.4 single specification limit specification limit where the decision criteria is applied only to one limit [ISO 3534-2, 3.1.7]

3.3.5 combined double specification limit specification limit where the decision criteria is applied collectively to the upper and lower limits

3.3.6 combined control requirement when nonconformity beyond both the upper and the lower specification of a quality characteristic belongs to the same class, to which a single AQL is applied

3.3.7 nonconformity non-fulfilment of a requirement

NOTE See notes to “defect”

3.3.8 defect non-fulfilment of a requirement related to an intended or specified use

The distinction between "defect" and "nonconformity" is crucial due to its legal implications, especially regarding product liability Therefore, the term "defect" must be used with great care.

NOTE 2 The intended use by the customer can be affected by the nature of the information, such as operating or maintenance instructions, provided by the customer

Types of inspection

3.4.1 conformity evaluation systematic examination of the extent to which an item/entity fulfils specified requirements [ISO 3534-2, 4.1.1]

3.4.2 inspection conformity evaluation by observation and judgement accompanied as appropriate by measurement, testing or gauging

Inspection by attributes involves assessing items based on the presence or absence of specific characteristics This method requires counting how many items possess these characteristics and how many do not, as well as tracking the frequency of such occurrences within the group being evaluated.

Inspection can be categorized into two types: inspection for nonconforming items, which involves determining whether an item meets standards, and inspection for number of nonconformities, which focuses on counting the specific defects present in each unit.

3.4.4 inspection by variables inspection by measuring the magnitude(s) of the characteristic(s) of an item [ISO 3534-2, 4.1.4]

100 % inspection inspection of selected characteristic(s) of every item in the group under consideration [ISO 3534-2, 4.1.5]

3.4.6 sampling inspection inspection of selected items in the group under consideration [ISO 3534-2, 4.1.6]

3.4.7 acceptance sampling inspection acceptance inspection where the acceptability is determined by means of sampling inspection [ISO 3534-2, 4.1.8]

3.4.8 normal inspection inspection which is used when there is no reason to think that the quality level achieved by the process differs from a specified level

Reduced inspection refers to a less stringent evaluation process compared to normal inspection This approach is adopted when the inspection results from a predetermined number of lots demonstrate that the quality level achieved by the process exceeds the specified standards.

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3.4.10 switching score indicator that is used under normal inspection to determine whether the current inspection results are sufficient to allow for a switch to reduced inspection

Tightened inspection refers to a more rigorous evaluation process than standard inspection This heightened scrutiny is implemented when the inspection results of a specified number of lots reveal that the quality level achieved by the process falls below the established standards.

3.4.12 isolated lot inspection inspection of a unique lot or one separated from the sequence of lots in which it was produced or collected [ISO 3534-2, 4.1.14]

3.4.13 lot-by-lot inspection inspection of a product submitted in a series of lots [ISO 3534-2, 4.1.15]

3.4.14 original inspection inspection of a lot, or other amount, not previously inspected

Re-inspection of a lot that was previously deemed unacceptable is distinct from initial evaluations, especially when the lot has undergone additional sorting or reprocessing.

3.4.15 acceptance inspection inspection to determine whether a lot or other amount is acceptable [ISO 3534-2, 4.1.17]

Types of acceptance sampling inspection

3.5.1 single acceptance sampling inspection acceptance sampling inspection in which the decision, according to a defined rule, is based on the inspection results obtained from a single sample of predetermined size, n [ISO 3534-2, 4.2.2]

3.5.2 double acceptance sampling inspection multiple acceptance sampling inspection in which at most two samples are taken

NOTE The decisions are made according to defined rules

Skip-lot acceptance sampling inspection is a method where certain lots in a series are accepted without inspection, provided that the sampling results from a specified number of immediately preceding lots meet predetermined criteria.

Acceptance sampling inspection by variables involves statistically determining the acceptability of a process based on measurements of specific quality characteristics from a sample taken from a lot.

NOTE Lots taken from an acceptable process are assumed to be acceptable

Acceptance sampling inspection by attributes involves observing the presence or absence of specific characteristics in each item of a sample This method is used to statistically determine the acceptability of a lot or process, as outlined in ISO 3534-2, section 4.2.12.

Acceptance sampling inspection system aspects

3.6.1 acceptance sampling inspection system collection of acceptance sampling plans or acceptance sampling schemes together with criteria by which appropriate plans or schemes may be chosen

3.6.2 acceptance sampling scheme combination of acceptance sampling plans with switching rules for changing from one plan to another

3.6.3 acceptance sampling plan plan which states the sample size(s) to be used and the associated criteria for lot acceptance [ISO 3534-2, 4.3.3]

3.6.4 switching rule instruction within an acceptance sampling scheme for changing from one acceptance sampling plan to another of greater or lesser severity of sampling based on demonstrated quality history

NOTE Normal, tightened, reduced inspection or discontinuation of inspection are examples of severity of sampling

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3.6.5 inspection level index of the relative amount of inspection of an acceptance sampling scheme, chosen in advance, and relating the sample size to the lot size

NOTE 1 A lower/higher inspection level can be selected if experience shows that a less/more discriminating operating characteristic curve will be appropriate

NOTE 2 The term should not be confused with severity of sampling which concerns switching rules, which operate automatically

The severity of sampling refers to the degree of discrimination in an acceptance sampling scheme when transitioning from a normal to a reduced or tightened acceptance sampling plan This adjustment is necessary when there are changes in the quality of the submitted product or service, whether it improves or deteriorates.

NOTE The term should not be confused with inspection level (4.3.5) which is independent of switching rules (4.3.4)

3.6.7 acceptance sampling procedure operational requirements and/or instructions related to the use of a particular acceptance sampling plan

NOTE This covers the planned method of selection, withdrawal and preparation of sample(s) from a lot to yield knowledge of the characteristic(s) of the lot

3.6.8 curtailed inspection acceptance sampling procedure which contains a provision for stopping inspection when it becomes apparent that adequate data have been collected for a decision

3.6.9 sigma method acceptance sampling inspection by variables using the presumed value of the process standard deviation

3.6.10 s method acceptance sampling inspection by variables using the sample standard deviation [ISO 3534-2, 4.3.10]

Acceptance criteria

The smallest number of nonconformities or nonconforming items identified in a sample through acceptance sampling by attributes determines whether a lot is rejected, as specified in the acceptance sampling plan.

Acceptance sampling by attributes allows for the identification of the largest number of nonconforming items in a sample, which determines whether a lot can be accepted based on the established acceptance sampling plan.

The acceptability constant $ k $ is a variable that depends on the predetermined acceptance quality limit and the sample size utilized in the criteria for lot acceptance within an acceptance sampling plan based on variables.

NOTE Other acceptability constants are p * and M , where p * is the maximum acceptable estimate of the process fraction nonconforming M (= 100 p *) is an alternative notation in use

The Maximum Sample Standard Deviation (MSSD) represents the largest sample standard deviation achievable for a specific sample size, code letter, and acceptance quality limit This metric is crucial for meeting acceptance criteria under double specification limits, particularly when the variability of the process is not known.

NOTE The MSSD depends on whether the double specification limits are combined, separate or complex and on the inspection severity (i.e normal, tightened or reduced)

The Maximum Process Standard Deviation (MPSD) represents the highest allowable process standard deviation for a specific sample size, code letter, and Acceptable Quality Level (AQL) It ensures compliance with acceptance criteria for double specification limits across all inspection severities, including normal, tightened, and reduced, when the variability of the process is known.

NOTE The MPSD depends on whether the double specification limits are combined, separate or complex, but does not depend on the inspection severity

Q function of the specification limit, the sample mean and the sample or process standard deviation, used in assessing the acceptability of a lot

NOTE For the case of a single specification limit, the lot may be sentenced on the result of comparing quality characteristic, Q, with the acceptability constant, k

Q U function of the upper specification limit, the sample mean, and the sample or process

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NOTE For a single, upper specification limit, the lot is sentenced on the result of comparing the upper quality characteristic, Q U , with the acceptability constant, k

Q L function of the lower specification limit, the sample mean, and the sample or process standard deviation

NOTE For a single, lower specification limit, the lot is sentenced on the result of comparing the lower quality characteristic, Q L , with the acceptability constant, k

Types of operating characteristic curves

3.8.1 operating characteristic curve curve showing the relationship between probability of acceptance of product and the incoming quality level for a given acceptance sampling plan

3.8.2 isolated lot operating characteristic curve type A curve operating characteristic curve applicable to isolated or individual lots, where the quality level relates to the lot

3.8.3 lot sequence operating characteristic curve type B curve operating characteristic curve applicable to a continuing series of lots from a given source, where the quality level relates to the process

Terms relating to operating characteristics

P a probability that, when using a given acceptance sampling plan, a lot will be accepted when the lot or process is of a specific quality level

CR β probability of acceptance when the quality level has a value stated by the acceptance sampling plan as unsatisfactory

NOTE Quality level could relate to fraction nonconforming and be unsatisfactory to the LQL

3.9.3 probability of non-acceptance probability that, when using a given acceptance sampling plan, a lot will not be accepted when the lot or process is of a specified quality level

PR α probability of non-acceptance when the quality level has a value stated by the plan as acceptable

NOTE 1 Quality level could relate to fraction nonconforming and be acceptable to AQL

NOTE 2 Interpretation of the producer’s risk requires knowledge of the stated quality level

3.9.5 consumer’s risk point CRP point on the operating characteristic curve corresponding to a predetermined low probability of acceptance

The low probability of acceptance, known as "consumer's risk," defines the lot quality associated with this risk, referred to as "consumer's risk quality" (CRQ).

NOTE 2 The type of operating characteristic curve needs to be specified

3.9.6 producer’s risk point PRP point on the operating characteristic curve corresponding to a predetermined high probability of acceptance

NOTE Interpretation of the producer’s risk point requires knowledge of the stated quality level

3.9.7 slope of operating characteristic curve slope of the line joining the producer’s risk point and the consumer’s risk point on an operating characteristic curve

NOTE The nearer to vertical the slope of the line, the greater is the discriminatory power of the acceptance sampling plan

Q CR quality level of a lot or process which, in the acceptance sampling plan, corresponds to a specified consumer’s risk

NOTE The specified consumer’s risk is usually 10 %

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Q PR quality level of a lot or process which, in the acceptance sampling plan, corresponds to a specified producer’s risk

NOTE 1 The type of operating characteristic curve needs to be specified

NOTE 2 The specified producer’s risk is usually 5 %

3.9.10 discrimination ratio ratio of quality levels consumer’s risk quality and producer’s risk quality [ISO 3534-2, 4.6.12]

LQ quality level, when a lot is considered in isolation, which, for the purposes of acceptance sampling inspection, is limited to a low probability of acceptance

3.9.12 limiting quality level LQL quality level which, for the purposes of acceptance sampling inspection, is the limit of an unsatisfactory process average when a continuing series of lots is considered

3.9.13 acceptance quality limit AQL worst tolerable quality level

NOTE 1 This concept only applies when an acceptance sampling scheme with rules for switching and for discontinuation, such as ISO 2859-1 and ISO 3951, is used

While lots with quality at the acceptance quality limit can be accepted with a high probability, this does not imply that such a quality level is desirable.

Acceptance sampling schemes, like those outlined in ISO 2859-1, are structured to motivate suppliers to maintain process averages that consistently exceed the acceptance quality limit If suppliers do not meet these standards, they risk being moved from normal inspection to tightened inspection, making lot acceptance more challenging Once placed under tightened inspection, without corrective actions to enhance the process, suppliers are likely to face a rule that mandates the discontinuation of sampling inspection until improvements are made.

NOTE 4 The use of the abbreviation AQL to mean “acceptable quality level” is no longer recommended

3.9.14 quality level quality expressed as a rate of nonconforming units or rate of number of nonconformities [ISO 3534-2, 4.6.16]

Outgoing quality concepts

3.10.1 average outgoing quality AOQ expected average quality level of outgoing product for a given value of incoming product quality

The average outgoing quality is determined by evaluating all accepted lots along with all non-accepted lots, which are inspected thoroughly at 100% Any nonconforming items are replaced with conforming items during this process.

In certain situations, new concepts and terminology may be applied when nonconforming items are replaced with conforming units during the 100% inspection of rejected lots.

NOTE 3 An approximation often used is: “Average outgoing quality = incoming process quality x probability of acceptance” This formula is exact for accept-zero plans and overestimates otherwise

The Average Outgoing Quality Limit (AOQL) represents the maximum average outgoing quality (AOQ) achievable across all potential incoming product quality levels for a specific acceptance sampling plan This applies to the rectification of all non-accepted lots unless stated otherwise, as defined in ISO 3534-2, section 4.7.2.

Other terms

To calculate the percentage of nonconforming items in a sample, use the formula: $\frac{100 \times d}{n}$, where $d$ represents the number of nonconforming items and $n$ is the total sample size.

(in a population or lot) one hundred times the number of nonconforming items in the population or lot divided by the population or lot size, viz:

100 where p is the proportion of nonconforming items;

D is the number of nonconforming items in the population or lot;

N is the population or lot size

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3.11.3 process fraction nonconforming rate at which nonconforming items are generated by a process, expressed as a proportion [ISO 3951-1, 3.5]

The concept of a responsible authority is essential for ensuring the neutrality of this standard, particularly for specification purposes, regardless of whether it is being utilized by the first, second, or third party.

NOTE The responsible authority may be: a) the quality department within a supplier's organization (first party); b) the purchaser or procurement organization (second party); c) an independent verification or certification authority (third party)

Symbols

Ac acceptance number β consumer’s risk d number of nonconforming items (or nonconformities) found in a sample from a lot

In quality control, the number of nonconforming items in a lot is denoted as D The factor $ f_s $ connects the maximum sample standard deviation to the difference between the upper (U) and lower (L) limits, while the factor $ f_\sigma $ relates the maximum process standard deviation to the same difference The acceptability constant is represented by k, and the process mean, which is a key population parameter, is denoted by $ \mu $ Additionally, the sample size is indicated by n.

In statistical quality control, the probability of acceptance is denoted as \$P\$, while \$\hat{p}\$ represents the estimated fraction of nonconforming items in a process The estimate of the fraction nonconforming below the lower specification limit is indicated by \$\hat{p}_L\$, and \$\hat{p}_U\$ signifies the estimate of the fraction nonconforming above the upper specification limit Additionally, \$p^*\$ refers to the maximum acceptable value for the estimate of the process fraction that is nonconforming.

Re rejection number s sample standard deviation of the measured values of the quality characteristics (also an estimation of the standard deviation of the process)

= n x x s n j j s max maximum sample standard deviation (MSSD) σ standard deviation of a process that is under statistical control σ max maximum process standard deviation (MPSD)

U specification limit, upper x j measured value of the quality characteristic for the j th item of the sample x arithmetic mean of the measured values of the quality characteristics in the sample, i.e n x x

Acronyms

AOQ average outgoing quality AOQL average outgoing quality limit AQL acceptance quality limit

CRP consumer’s risk point CRQ consumer’s risk quality

LQL limiting quality level MPSD maximum process standard deviation MSSD maximum sample standard deviation

PRP producer’s risk point PRQ producer’s risk quality

NOTE This clause is based on ISO/TR 8550-1, ISO/TR 8550-2 and ISO/TR 8550-3.

The objectives of acceptance inspection

When meters are supplied, both manufacturers and customers utilize acceptance sampling procedures to ensure product quality Manufacturers aim to uphold their reputation and minimize warranty claims while controlling production costs Conversely, customers seek cost-effective evidence that the received product meets specifications In many cases, effective sampling methods provide significant advantages over 100% inspection in achieving these objectives.

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Various sampling systems, schemes, and plans are available for electricity metering equipment, as outlined in relevant ISO standards selected by IEC TC 13.

NOTE 1 If necessary, other sampling systems, schemes and plans may be selected from the relevant ISO standards

The selection of a sampling system or plan is influenced by various conditions and circumstances It is crucial for both the manufacturer and the customer to clearly understand and agree on the product requirements, as well as the criteria for its release and acceptance, which includes any acceptance sampling methods that will be implemented.

Unacceptable lots create challenges for both manufacturers and customers, leading to increased costs for rework, scrap, and inspections, as well as potential damage to the manufacturer's reputation and loss of sales Customers face burdens from delivery delays and re-inspection expenses Therefore, it is crucial for manufacturers to ensure that lots have a high acceptance probability of 95% or more Effective quality control in the production and delivery processes is essential to achieve this goal, and acceptance sampling inspection schemes are designed to encourage the production of lots that meet acceptable quality standards.

The main goal of acceptance sampling schemes is to maintain control over production processes to achieve an acceptable average quality, rather than merely sorting acceptable from non-acceptable lots While all acceptance sampling plans exhibit some level of discrimination, it is crucial that the process average quality, measured by the percentage of nonconforming items or the number of nonconformities, remains below half of the acceptance quality limit This ensures a high probability of acceptance.

NOTE 2 ISO/TR 8550-1 Clause 4 describes some abuses and uses of acceptance sampling.

Acceptance sampling plans, schemes and systems

An acceptance sampling plan outlines the rules for inspecting a lot to determine its acceptability It specifies the number of items to be randomly sampled from the lot for evaluation against product specifications Based on the inspection results, the lot is classified as either 'acceptable' or 'not acceptable' according to the criteria established in the acceptance sampling plan.

In lengthy inspections of lots, a sampling scheme may require transitioning between different sampling plans based on current and past results These schemes can also lead to halting inspections if product quality is consistently subpar In such cases, customers might switch to an alternative supplier or implement 100% screening until the original supplier enhances their production process to meet acceptable quality standards.

A collection of sampling plans and related sampling schemes constitute a sampling system

The system is generally indexed in some way, for example by lot size, inspection level and acceptance quality limit.

Practical and economic advantages of using standard sampling plans

For effective specification writing, it is essential to implement statistically sound sampling procedures This standard connects sample size to lot size, recognizing the economies of scale associated with larger lots.

This standard not only governs the sample selection methods but also outlines the necessary requirements for managing nonconformities identified during inspections and the handling of lots that are resubmitted following initial nonconformance.

Licensed to MECON Limited for internal use in Ranchi and Bangalore, the supplied sampling systems feature built-in switching rules These rules allow for adjustments in the sampling plan, transitioning between 'normal,' 'tightened,' or 'reduced' inspection based on the quality's deterioration or improvement.

Sampling carries inherent risks, prompting all stakeholders to seek ways to minimize their exposure These risks are theoretically linked to the sampling plan and the agreed quality level, independent of the specific industry or product In practice, however, these risks can be mitigated through effective production process control and enhancements in quality levels.

While risks cannot be completely eliminated, modern statistical techniques allow for precise calculation and economic assessment of these risks Therefore, it is advantageous for all stakeholders to establish statistically sound acceptance criteria in product and process specifications, and to utilize widely applicable basic reference standards for sampling whenever possible.

Acceptance sampling is driven by economic factors, as inspecting a sample from a lot incurs a relatively small cost to ensure the desired quality in the accepted lots This quality is maintained through two key pressures.

• the purely statistical pressure of different probabilities of acceptance of good and bad quality lots; and

• when sequences of lots are purchased, the commercial pressure of frequent non- acceptance of lots and the switch to tightened inspection or discontinuation of inspection when quality is poor

Acceptance sampling inspection involves clearly defining the criteria for evaluating individual items in a lot, including acceptance criteria, expected quality levels, and the effectiveness of sampling plans It is crucial to establish rules for handling rejected lots and to design sampling schemes that can be easily implemented in purchasing contracts The sampling plans outlined in this standard facilitate efficient execution of these requirements.

Agreement between the parties

The parties involved in the process are the manufacturer, the customer and, as the case may be, a responsible authority

Before selecting an acceptance method, a sampling system, scheme or plan, the parties should agree on the following:

The meters must adhere to specific specifications to ensure clarity in agreements between parties regarding conforming and nonconforming items These requirements are outlined in the IEC 62058 series, which details acceptance inspection criteria for various types of meters.

The acceptance of a product can be determined either by evaluating individual items or by assessing inspection lots collectively When the number of items is limited, acceptance of individual items is preferred, as it eliminates the need for sampling.

• when the acceptance is to be on a lot basis, the agreement between supplier and recipient needs to include:

• the criteria for item conformance;

• the criteria for lot acceptance;

• the criteria for non-acceptance of the lot; and

• the acceptance sampling system, scheme or plan to be used

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The latter should be based on risk factors that are mutually acceptable to both producer and customer

Having agreed on the acceptance sampling system, scheme or plan to use, the supplier knows, for various quality levels, the probability that his supply lots will be accepted

Likewise, the customer understands the protection provided by the sampling system, scheme or plan against acceptance of a poor quality product.

Selection of sampling schemes and sampling plans

This standard specifies the following methods for sampling inspection:

• lot-by-lot inspection by attributes;

• inspection of isolated lots by attributes;

• lot-by-lot inspection by variables

The selection process is shown on Figure 1

In addition, 100 % inspection may be used for small lots or when sampling inspection has to be discontinued

Continuing series of lots and long runs?

Lot-by-lot inspection by Attributes Variables

Isolated lot inspection by attributes

Figure 1 – Selection procedure of sampling schemes and plans

Considerations influencing a selection

Long and short production runs

The procedures outlined in Clauses 7, 9, and 10 are designed for application primarily on extended series of lots, ensuring that the switching rules can be effectively implemented This necessitates a 'long' production run.

Clause 8 comprises limiting quality (LQ) plans that can be used when the switching rules of Clause 7 are not applicable These are primarily intended for use with single lots or lots of an

‘isolated nature’ By implication, this embraces a ‘short’ series of inspection lots or a ‘short’ production run

In order for a production run to qualify as ‘long’, one criterion is clearly that the switching rules have a reasonable chance of coming into effect if “the quality is unsatisfactory”

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When no other guidelines are available, a maximum of 10 consecutive inspection lots is classified as a 'short run,' necessitating the use of the plans outlined in Clause 8 It is important to note that lots should not be divided arbitrarily to fabricate a 'long run.'

The practical factor to consider is whether there is evidence that a stable process average has been established and still exists.

Lot-by-lot inspection

Lot-by-lot inspection is the inspection of product submitted in a series of lots

When offering a sequence of lots for acceptance during production, prior inspection results can inform the quality of subsequent lots It is crucial to submit and inspect the lots in the order they are manufactured, ensuring prompt inspections Insights gained from earlier lots may reveal potential process deterioration, allowing for a switching procedure that implements a more rigorous sampling method if needed This approach ultimately safeguards consumers against poor quality in the long run.

Poor quality products lead to more lots being returned to manufacturers due to stricter sampling practices This increased scrutiny raises the risk of acceptable lots being deemed unacceptable Identifying potential declines in product quality serves as a prompt for necessary corrective actions.

If the quality is very much better than that agreed upon, the customer may, with the permission of the responsible authority, elect to adopt reduced or skip-lot sampling.

Isolated lot inspection

Acceptance inspection can be conducted on a single lot, a few isolated lots, or stored lots after production has concluded In such cases, there is limited opportunity for switching rules to be applied, which means they do not affect the quality being presented.

Understanding whether a delivered lot is part of a larger group of similar lots sent to other customers is crucial, especially when the material originates from a controlled process.

Attributes versus variables

Acceptance sampling standards generally describe procedures for inspection by attributes or for inspection by variables, so a key decision to make is which of these to use

Inspection by attributes involves evaluating an item or its characteristics and categorizing it as either "conforming" or "nonconforming." Lot acceptance criteria rely on the count of nonconforming items identified in a random sample This method is applicable when the characteristic being inspected cannot be measured on a continuous scale, or when it can be measured continuously but the normality of the value distribution cannot be assumed.

Inspection by variables involves selecting a random sample of items to measure specific characteristics, providing detailed information on whether these characteristics fall within defined limits and their actual values Acceptance of a lot is determined by calculating the average and variability of the measurements This method is applicable only when production is continuous and the normality of the variable distribution is assumed For further details on normality, refer to ISO/TR 8550-3, Clause 3.

The variables method typically requires a smaller sample size than the attributes method to achieve the same level of protection against incorrect decisions, provided certain assumptions hold true Additionally, it offers greater insight into whether quality is negatively impacted by process mean, process variability, or a combination of both factors.

The attributes method is advantageous due to its robustness, as it does not rely on specific distributional assumptions and is easier to implement The justification for larger sample sizes and the associated costs of attribute sampling methods lies in these benefits Additionally, inspection personnel may find an attribute scheme more comprehensible and acceptable To circumvent the assumption of normality and the challenges of verifying this with short runs or isolated lots, it is advisable to use attribute sampling, even if it requires converting measurements into attributes.

Single and double sampling

For most single sampling plans, it is possible to find double sampling plans with an operating characteristic curve (see 5.9) close to that of a single sampling plan

Choice between single sampling and double sampling depends on the balance between administrative difficulties taking a second sample and the advantages to be gained from the reduction of inspection costs

In this standard, double sampling plans have been selected only for inspection by attributes

When the process standard deviation, σ, is unknown, it can be estimated using the sample standard deviation, s Acceptance sampling methods that utilize s are known as the “s” method, while those that rely on σ are referred to as the “σ” method.

The “σ” method reduces uncertainty in the quality statistic, leading to a significantly lower sample size requirement, especially for large lots.

NOTE The process standard deviation, although never known exactly, might on occasion be known accurately enough for practical purposes

Nonconformity and nonconforming items

In 100% inspection and attribute-based evaluation, any deviation from specified product characteristics, attributes, or performance requirements is classified as a nonconformity A nonconforming item may exhibit multiple nonconformities; however, this designation does not automatically indicate that the product is unsuitable for its intended use.

The quality of a given quantity of meters is expressed in percent nonconforming.

Classification of nonconformities

This standard makes a distinction between critical and non-critical nonconformities

For different types of meters, the classification of various nonconformities as critical and non- critical is specified in the relevant standards specifying particular requirements for acceptance testing

For non-critical nonconformities, inspection by attributes using single or double sampling

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For critical nonconformities, it would be desirable to establish that there are no nonconforming items in the lot, but this is possible only with 100 % inspection

Single sampling plans with an acceptance number of zero have been chosen for attribute inspection to facilitate sampling inspection As the sample size increases, the Acceptable Quality Level (AQL) decreases.

Operating characteristic (OC) curve

NOTE This subclause is based on 8.3 of ISO/TR 8550-1

The operating characteristic (OC) curve illustrates the expected performance of a specific sampling plan regarding the acceptance and rejection of lots.

‘efficiency curve’ An OC curve refers to a particular sampling plan Each possible plan has its own curve

In sampling inspection by attributes during a long production run with a stable process, the Operating Characteristic (OC) curves indicate the proportion of lots of a specific quality that will be accepted For isolated or individual lots, these OC curves represent the probability of acceptance for a lot with a certain quality level.

In variable sampling inspection, Operating Characteristic (OC) curves indicate the average percentage of accepted lots but do not provide the acceptance probabilities for specific lots Consequently, a lot that is rejected could potentially contain no nonconforming items, while a lot with a high rate of nonconformity might have a lower actual rejection probability than what the OC curve suggests for the overall process.

The OC curves of the sampling plans selected for the purposes of this standard are given in 7.6, 8.5 and 10.14 respectively.

Producer’s risks (PR) and consumer’s risk (CR)

Sampling poses risks for both producers and consumers, as it only represents a small portion of an entire inspection lot There are instances where a 'good' lot may be rejected because the randomly selected sample fails to accurately reflect the lot's true quality This potential for rejection is referred to as the 'producer's risk' (PR).

Conversely, a ‘poor quality’ lot might pass inspection because of the limited data available in the sample This eventuality is known as the ‘consumer’s risk’ (CR)

The producer would require a high probability of acceptance if the quality were good, while the customer would want a low probability of acceptance if the quality were poor

The selected sampling plans for this standard, specifically sections 7.10 and 10.15, present the Consumer’s Risk Quality (CRQ) values corresponding to specific Consumer Risk (CR) levels, applicable to both lot-by-lot inspection by attributes and inspection by variables.

Similarly, 7.11 and 10.16 show the values of the producer’s risk

The OC curves and the tables also show the effect of moving to tightened inspection: the producer’s risk increases and the consumer’s risk decreases

Methods of reducing the risks for both parties are:

• to improve the quality of production; and

• to increase the lot size

AQL, PRQ, LQ and CRQ

The AQL and PRQ are interchangeable terms in this standard, both representing acceptable quality levels for sampling inspection The key distinction lies in the PRQ being linked to a defined small PR, while the AQL indicates a quality level associated with an unspecified small PR.

The LQ and CRQ serve as equivalent indices, similar to the AQL and PRQ, indicating a level of 'objectionable' quality that is unlikely to be accepted during sampling.

The AQL and LQ values are used for indexing the sampling plans

ISO 2859-1, ISO 2859-3 and ISO 3951-2 standards define a preferred series of AQL values

For non-critical nonconformities, this standard specifies AQL = 1,0 %

Limitation: The designation of an AQL shall not imply that the supplier has the right to supply knowingly any nonconforming items of product

Similarly, ISO 2859-2 defines a preferred series of LQ values For non-critical nonconformities, this standard specifies LQ = 5,0 %

NOTE Other standard levels for AQL and LQ may be agreed on between the parties involved The appropriate sampling plans can be found in the relevant ISO standards.

Switching rules for normal, tightened and reduced inspection

An ideal sampling plan would allow for the acceptance of lots with quality exceeding the Acceptable Quality Level (AQL) and the rejection of those falling below it However, this perfect scenario is unattainable To satisfy both producers and customers, a compromise in the sampling process is necessary.

The device integrates standard inspections with enhanced inspections, establishing clear guidelines for transitioning between the two types of inspections as needed.

Normal inspection is initiated at the beginning of the inspection process If sampling results suggest that the process average may fall below the Acceptable Quality Level (AQL), tightened inspection is implemented Conversely, if quality appears to improve and is likely above the AQL, normal inspection resumes However, if tightened inspection fails to prompt the producer to enhance the production process, sampling inspection will be halted.

Tightened inspection and the discontinuation rule are integral and therefore obligatory procedures of this International Standard if the protection implied by the AQL is to be maintained

Sometimes there is evidence that the product quality is consistently better than the AQL

In cases where there is confidence in the ongoing quality of production, reduced inspection sampling plans or skip-lot sampling plans may be implemented However, the adoption of these practices is optional and subject to the discretion of the responsible authority.

Details of the operation of the switching rules are given in 7.5 and 10.10 and are shown diagrammatically in Figure 2

2 of 5 or fewer consecutive lots not accepted

5 lots not accepted while on tightened inspection

- 10 successive lots accepted under normal inspection, and

- sampling scheme specific conditions met, and

- reduced inspection is approved by the responsible authority

Figure 2 – Outline of switching rules

Inspection level

The inspection level serves as an indicator of the extent of inspection within a sampling scheme, linking the sample size to the lot size and determining the level of discrimination achieved.

‘good’ and ‘poor’ quality ISO 2859-1 and ISO 3951-2 provide seven inspection levels

Generally, inspection level II shall be used

Inspection level III may be used to meet the requirements for selectivity at smaller lot sizes

The inspection level that has been specified shall be kept unchanged when switching between normal, tightened and reduced inspection.

Sample size code letter

Sampling plans are identified by sample size code letters

Understanding the requirements for the selectivity of operating characteristic curves allows for the appropriate selection of the sample size code letter, which in turn helps determine the inspection level and the lot size.

Inspection is carried out using lot-by-lot inspection by attributes, AQL = 1,0, single sampling plans

The agreement stipulates that a quality level with 1% nonconforming items will yield a minimum acceptance probability of 95%, while a quality level with 7% nonconforming items will result in an acceptance probability of less than 10% According to the OC curves in Figure 3 and Table 9, the first sample size code letter that satisfies these criteria is J Additionally, Table 2 indicates that for inspection level II, the lot size ranges from 501 to 1,200 or higher, and for inspection level III, it ranges from 281 to 500 or higher.

Place of inspection

Lot-by-lot inspection is crucial for providing feedback to the manufacturing process Consequently, inspections should take place at the manufacturer's location, utilizing test benches that are distinct from those used for adjustments.

In the case of isolated lot inspection, the inspection shall be carried out by mutual agreement:

• on the manufacturer's premises, but on test benches other than those on which the adjustments were made; or

• on the customer's test benches; or

• on other agreed test benches.

Submission of product for acceptance inspection

The product will be organized into distinct lots, with each lot ideally containing items of the same type that are produced under consistent conditions and within a similar timeframe.

The manufacturer must designate or obtain approval for the formation, size, and identification of each lot from the customer or responsible authority Additionally, the manufacturer is responsible for providing sufficient storage space, necessary equipment for proper lot identification and presentation, and trained personnel for handling products and drawing samples.

Drawing of samples

In acceptance sampling, the quality of a lot is determined by the sample taken, making it essential for the sample to accurately represent the entire lot A random sample is crucial to avoid bias and ensure reliable quality assessment.

The selection of a random sample can be made using Table A.1 and the manufacturing numbers of the meters making up the lot

A sample of 8 items will be selected from a total of 5,000 articles, each labeled with a unique number from 1 to 5,000 The selected articles for the sample are numbered 110, 4,148, 2,403, 1,828, 2,267, 2,985, 4,313, and 4.

691 (the numbers 5 327, 5 373, 9 244, etc., being ignored as corresponding articles would not be found in the lot)

The following should be noted with regard to the use of a table of random sampling numbers:

Starting at the top of the first column is not always the correct approach for drawing samples Instead, it is more effective to begin at a random point and navigate through the table, either moving up or down the columns or across the rows.

When dealing with lot sizes of 1,000 or fewer, it is sufficient to read only the first three digits, such as 11, 532, or 537, rather than interpreting the numbers as four figures.

Sometimes two figures are enough, sometimes more than four are required As many or as few as desired may be combined.

Acceptability of lots

Acceptability of lots shall be determined by the use of a sampling plan or plans

The parties shall agree how lots that are not accepted will be disposed of Such lots may be scrapped, sorted (with or without nonconforming items being replaced), reworked, etc

If a lot is accepted, the right to reject any nonconforming items during inspection is reserved, regardless of whether they were part of a sample Required meters will be opened and examined, and nonconforming items may be reworked or replaced with conforming items for re-inspection, subject to mutual agreement between the parties.

All items in a lot must be re-examined or retested before resubmission, ensuring customer satisfaction with the removal or replacement of nonconforming items The parties involved will determine if re-inspection covers all characteristics or just those that led to initial non-acceptance For lot-by-lot inspection, an agreement is needed on whether to apply normal or tightened inspection procedures.

Application of the method

This method shall be applied:

• for small lots, for which sampling plans are either not available, or insufficiently discriminatory;

• for critical nonconformities, if sampling inspection using accept zero plans is not approved by the responsible authority;

• when the results of sampling inspection indicate that the required process quality is not reached See 7.5.6 and 10.11;

• when the parties agree to use 100 % inspection

6.2 Lot sizes and acceptance numbers

100 % inspection is done by attributes The lot sizes and acceptance numbers are shown in Table 1

Table 1 – Acceptance number Ac for 100 % inspection

Nonconformity Lot size N Acceptance number Ac for every single attribute

NOTE For a quantity equal to the middle of each respective lot size range, these acceptance numbers correspond to 1% percent nonconforming

In addition to 5.18, the following applies

The lot is accepted if:

• there are no items found with any critical nonconformity (Ac = 0);

• the number of meters found with a non-critical nonconformity is equal to or less than the acceptance number Ac; and

• the cumulated number of non-critical nonconformities is not more than twice the acceptance number Ac

Otherwise, the lot shall be considered unacceptable

100 meters are tested The results are the following:

• no meters with critical nonconformities are found;

• one meter is found exhibiting a non-critical nonconformity This meter exhibits two non- critical nonconformities

If this meter had had three non-critical nonconformities, the lot would have to be rejected

7 Lot-by-lot inspection by attributes

Sampling schemes for lot-by-lot inspection by attributes described here are based on ISO 2859-1

These schemes are designed for a continuous series of lots, ensuring that the switching rules outlined in section 7.5 can be effectively implemented.

• a protection to the consumer (by means of a switch to tightened inspection or discontinuation of sampling inspection) should a deterioration in quality be detected;

• an incentive (at the discretion of the responsible authority) to reduce inspection costs (by means of a switch to reduced inspection) should consistently good quality be achieved

Reduced inspection may be replaced by skip-lot sampling when the requirements of Clause 9 are fulfilled

For isolated lot inspection, see Clause 8

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Samples may be drawn after the lot has been produced, or during production of the lot In either case, the samples shall be selected according to 5.17

When double sampling is used, the second sample shall be selected from the remainder of the same lot.

Inspection level

Generally, inspection level II shall be used Inspection level III provides greater discrimination and double sampling plans are available with smaller lots.

Sampling plans

Obtaining a sampling plan

The sampling plans shall be obtained from Table 2, single sampling or from Table 7, double sampling respectively

NOTE If justified and agreed by the responsible authority, other sampling plans may be selected from ISO 2859-1

In the absence of a sampling plan for a specific sample size code letter, users are guided to refer to an alternative code letter The sample size to be utilized will correspond to this new code letter rather than the original one.

When multiple plan types, whether single or double, are offered for a specific sample size, either code letter can be utilized The choice of plan type typically depends on comparing the administrative complexity with the average sample sizes of the available options.

Single sampling plans

Table 2 contains single sampling plans for non-critical nonconformities with AQL = 1,0, indexed by the sample size code letter, for normal, tightened and reduced inspection

Table 2 – Single sampling plans for normal, tightened and reduced inspection, AQL = 1,0

Lot sizes for inspection levels Normal inspection Tightened inspection Reduced inspection

Sample size n normal and tightened

Ac Re Ac Re Sample size n Ac Re

The values utilized are sourced from Tables 1, 2-A, 2-B, and 2-C of ISO 2859-1 With the approval of the responsible authority, larger lot sizes may be implemented, and the appropriate sampling plans can be chosen from the referenced tables.

The sample sizes are the same for normal and tightened inspection

Re = Rejection number ỉ Sampling plan not available Use the first sampling plan below the arrow × Sampling plan not available Use the first sampling plan above the arrow

The lot size is 80, with an agreed inspection level of II and a sample size code letter of E A sampling plan is provided for both normal and reduced inspections, while tightened inspection refers users to code letter F, outlining the corresponding sampling scheme.

Table 3 – Example with lot size = 80, inspection level II

Normal inspection Tightened inspection Reduced inspection

In this case, the acceptance number is the same for all three plans Tightening is achieved by increasing the sample size For reduced inspection, the sample size is decreased

The lot size is set at 400, with an agreed inspection level of II and a sample size code letter of H A sampling plan is provided for normal inspection, while tightened and reduced inspection refer to code letter J, which outlines the corresponding sampling scheme.

Table 4 – Example with lot size = 400, inspection level II

Again, the acceptance number is the same for all three plans Tightening is achieved by increasing the sample size For reduced inspection, the sample size is decreased

The lot size is 800, with an agreed inspection level of III and a sample size code letter of K A comprehensive sampling plan is provided for normal, tightened, and reduced inspections, all utilizing the same code letter, resulting in a consistent sampling scheme.

Table 5 – Example with lot size = 800, inspection level III

For tightened inspection, the sample size is kept the same, but the acceptance number is decreased For reduced inspection, both the sample size and the acceptance number are decreased

For critical nonconformities, sampling plans with acceptance number 0 have been selected

The sampling plans are shown in Table 6

Table 6 – Single sampling plans for critical nonconformities Ac = 0

Lot sizes for inspection levels Normal inspection Tightened inspection Reduced inspection

Sample size code letter Sample size n AQL Sample size n

NOTE 1 The values are taken from Tables 1, 2-A, 2-B and 2-C of ISO 2859-1 If agreed by the responsible authority, higher lot sizes may be applied The corresponding sampling plans can be selected from the tables referenced

NOTE 2 For inspection to AQL = 1,0 the plans corresponding to sample size code letter F and G for normal inspection are not available, but they are available with Ac = 0

For normal inspection, the sample sizes align with those used for non-critical nonconformities In cases of tightened inspection, the sample size is increased, while for reduced inspection, it is decreased by one step.

The AQL value decreases from 1.0 for sample size code letter E as the sample size increases, ultimately reaching a significantly low value at higher sample sizes.

Therefore, these accept zero plans may be used with low sample sizes only upon agreement of the responsible authority Otherwise, 100 % inspection shall be performed.

Double sampling plans

Table 7 contains double sampling plans for non-critical nonconformities with AQL = 1,0, indexed by the sample size code letter, for normal, tightened and reduced inspection

Table 7 – Double sampling plans for normal, tightened and reduced inspection,

Lot sizes for inspection levels

The sample size code letter is crucial for determining the normal and tightened cumulative sample size Proper inspection of the sample size ensures accurate data collection and analysis.

II III Ac Re Ac Re Ac Re

NOTE 1 The values are taken from Tables 1, 3-A, 3-B and 3-C of ISO 2859-1 If agreed by the responsible authority, higher lot sizes may be applied The corresponding sampling plans can be selected from the tables referenced

NOTE 2 Sampling plans below code letter H are not available

NOTE 3 The sample sizes are the same for normal and tightened inspection

Re = Rejection number ỉ Sampling plan not available Use the first sampling plan below the arrow.

Determination of acceptability

In addition to 5.18, the following applies:

The sample size for inspection must match the predetermined plan A lot is deemed acceptable if the number of nonconforming items in the sample is less than or equal to the acceptance number Conversely, if the number of nonconforming items meets or exceeds the rejection number, the lot is classified as unacceptable.

The acceptance number indicates the maximum allowable nonconforming items in a sample If multiple characteristics are inspected, some items may show several nonconformities A lot is deemed acceptable if the number of nonconforming items is less than the acceptance number Conversely, if the nonconformities are found on different items and exceed the acceptance number, the lot is considered unacceptable.

A lot of 400 units is tested for three non-critical characteristics, using inspection level II The sampling plan, from Table 2, is as follows:

• sample size code letter is H;

A lot is accepted if only one nonconforming item is found, regardless of whether it has two or three nonconformities Conversely, if two items are discovered, each with one nonconformity, the lot will be rejected.

The initial sample size for inspection must match the predetermined plan If the count of nonconforming items in this first sample is less than or equal to the acceptance threshold, the lot is deemed acceptable Conversely, if the number of nonconforming items meets or exceeds the rejection threshold, the lot is classified as unacceptable.

When the count of nonconforming items in the initial sample falls between the specified acceptance and rejection thresholds, a second sample of the predetermined size must be inspected The total number of nonconforming items from both the first and second samples will be combined for evaluation.

A lot is deemed acceptable if the total number of nonconforming items is less than or equal to the second acceptance number Conversely, if the cumulative count of nonconforming items meets or exceeds the second rejection number, the lot is classified as unacceptable.

During the inspection of a sample, the necessary action regarding acceptance or rejection may become clear before all items are examined If the inspection is concluded once a definitive decision can be made, it is referred to as a curtailed inspection.

Although there are obvious costs savings to be gained, this practice would lead to loss of information regarding the process average

Therefore, curtailed inspection in single sampling is not allowed

In double sampling, the process average can be estimated using the percentage of nonconforming items from the initial sample of each lot or by calculating the overall percentage of nonconforming items across multiple initial samples Typically, when implementing double sampling plans, the second sample is often reduced, as its data is not used for estimating the process average.

Normal, tightened and reduced inspection (see also 5.12)

Procedures specified

Standard multivariate “s” method procedures for independent quality

Normality and outliers

Records

Switching between the “s” and “σ” methods

Tiêu đề	Acceptance Inspection Methods for Electricity Metering Equipment
Chuyên ngành	Electrical Engineering
Thể loại	Standard
Năm xuất bản	2008
Thành phố	Geneva

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Số trang	168
Dung lượng	1,65 MB