CN110866691A - Staged and layered sampling method for isolated batch intelligent electric energy meters - Google Patents
Staged and layered sampling method for isolated batch intelligent electric energy meters Download PDFInfo
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Abstract
The invention relates to a staged and layered sampling method for an isolated batch of intelligent electric energy meters, which comprises the steps of obtaining the total amount of the isolated batch of intelligent electric energy meters, and performing staged sampling on the intelligent electric energy meters according to a time sequence, wherein the staged sampling comprises a first stage sampling, a second stage sampling and a third stage sampling which are performed in sequence, the first stage sampling is used for performing one-time sampling acceptance on the isolated batch of intelligent electric energy meters on the basis of a probability theory, the second stage sampling and the third stage sampling are used for performing layered sampling on the isolated batch of intelligent electric energy meters, and the third stage sampling is used for sampling on the basis of the result of the second stage sampling. Compared with the prior art, the method and the device are suitable for the characteristics of isolated intelligent electric energy meters, accurately reflect the real state of the running intelligent electric energy meters, have small sample amount, and have the advantages of time saving, economic cost saving and high reliability of sampling results.
Description
Technical Field
The invention relates to the field of intelligent electric energy meters, in particular to a staged and layered sampling method for isolated intelligent electric energy meters.
Background
With the factors of comprehensive construction of the intelligent power grid, transformation and upgrading of the rural power grid and the like, the market development of the intelligent electric meter is vigorous, and the full coverage of the intelligent electric meter is basically realized. The application of the metering equipment has the characteristics of large quantity, multiple types, intellectualization and complex operating environment. At present, the number of the electric meters hung on the national grid is nearly 2.2 million, the number of the electric meters hung on the south grid is nearly 5000 ten thousand, and the market scale of the intelligent electric meter and the electricity utilization management system of the two power grids in the future is about 160 million yuan per year. Whether the running state of the metering equipment with huge number is stable and reliable directly relates to the vital interests of common people and the harmony and stability of the society. The trend of strengthening the health state monitoring, life cycle management and operation intensive management of the intelligent electric energy meter is inevitable. With the proposal of the state exchange strategy of the electric energy meter, the operation management mode of the electric energy meter is changed into a fixed period rotation mode, and scientific evaluation decision is carried out according to the operation quality level, so that sufficient technical means are required to analyze the reliability level of the electric energy meter.
The intelligent electric energy meter has the same service life as other products, and if the intelligent electric energy meter is used for a long time, the metering stability of the intelligent electric energy meter is possibly changed, so that the metering performance requirement during the first detection cannot be met. In order to ensure the metering accuracy, according to the verification regulation of the electric energy meter, the operation management mode of the electric energy meter is an expiration rotation system. However, once the electric energy meter has a fault in the grid operation, no active and effective means for monitoring the quality measures of the electric energy meter in the grid operation except for the complaints of residents exists. On the other hand, when the rotation period is reached, the electric energy meter needs to be replaced no matter what the actual metering performance of the electric energy meter in the house of the user is, and then the electric energy meter enters a scrapping process. However, with the improvement of the technical level of the electric energy meter and the improvement of the monitoring level of the operation level of the electric energy meter, the defects of the 'one-time cutting' method in the aspects of causing waste of manpower and material resources, being not beneficial to energy conservation and environmental protection and the like are more and more obvious. Therefore, the operation quality level of the electric energy meter running on the network is required to be mastered, and the most accurate mode is full quality verification. However, with the popularization of one meter per household and the full coverage of the intelligent electric energy meters, the number of the intelligent electric energy meters in operation is huge, and a full verification method is not advisable.
The scheme is a sampling method based on probability statistics, and the working condition of the whole batch of tables is judged through proper sampling inspection, so that the discarding of a large amount of still usable weekly inspection instruments is avoided, and the inspection workload can be reduced.
The scheme of Q/GDW 206 plus 2008 'electric energy meter sampling technical specification' is convenient to retrieve, clear in judgment result and strong in operability, and because the scheme mainly aims to judge whether the product batch is qualified or not, the risk point of a user is not clear enough. The standard normative citation document GB/T15239-.
On one hand, in order to ensure the quality level of the operation of the intelligent electric energy meter, the sampling reliability at the acceptance stage of the intelligent electric energy meter needs to be ensured, and on the other hand, in the operation process of the intelligent electric energy meter, if an independent and single sampling method is adopted, the sampling result reliability is low.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a staged and layered sampling method of the isolated batch intelligent electric energy meter, which is suitable for the characteristics of the isolated batch intelligent electric energy meter, can accurately reflect the real state of the running intelligent electric energy meter, is time-saving and economical and has high reliability of sampling results.
The purpose of the invention can be realized by the following technical scheme:
the method comprises the steps of obtaining the total amount of the isolated intelligent electric energy meters in batches, and carrying out staged sampling on the intelligent electric energy meters according to a time sequence, wherein the staged sampling comprises a first-stage sampling, a second-stage sampling and a third-stage sampling which are sequentially carried out, the first-stage sampling is used for carrying out one-time sampling acceptance on the isolated intelligent electric energy meters in batches on the basis of a probability theory, the second-stage sampling and the third-stage sampling are used for carrying out layered sampling on the isolated intelligent electric energy meters in batches, and the third-stage sampling is used for carrying out sampling on the basis of the result of the second-stage sampling.
In order to sample the running intelligent electric energy meter according to the sampling principle of 'economy, reasonability, simplicity, feasibility and point-surface combination', a layered sampling method is adopted. The limited sampling samples can truly reflect the operation conditions of the intelligent electric energy meter under different manufacturers and different operation environment conditions. The layered sampling can fully ensure the consistency of the sample structure and the total body, namely, all units in the total body are merged into a plurality of sets which are not crossed and repeated, namely layers, and then the samples are extracted by taking the layers as the units.
In order to judge the quality difference between the electric energy meters produced by different manufacturers and combine the characteristics of the electric energy meters, the method is suitable for selecting a sampling mode combining stage sampling and layered sampling, and mainly considers the factors as follows:
1) the operation of the electric energy meter is a continuous process, the result of one sampling cannot reflect the whole appearance, and the sampling frequency is too high, so that the cost is increased. And setting the full life cycle of the electric energy meter to be 5 years by combining the characteristics of the bathtub curve, and respectively sampling the electric energy meter in the second year and the fourth year of operation, wherein the second year is the early expiration date in the bathtub curve, and the fourth year is the accidental expiration date.
2) The running electric energy meters have the characteristics of large quantity and wide distribution, and the detection of the electric energy meters is destructive and only can adopt a sampling detection mode.
3) The electric energy meters are usually produced in whole batches, and are less influenced by human and objective factors in the production and installation processes, so that the quality conditions of the products in the same batch are always consistent, and samples randomly drawn from the batches can represent the actual quality level of the products in the batch to a certain extent.
4) Considering the difference between the electric energy meters produced by different manufacturers, the quality conditions of the electric energy meters produced by the same manufacturer tend to be consistent, so that the manufacturers have operability as a layering mode.
Further, the hierarchical sampling specifically includes that the isolated intelligent electric energy meters are hierarchically sampled based on manufacturers, models, specifications and/or purchasing years.
Further, the first stage sampling specifically includes the steps of:
a parameter acquisition step: acquiring the receiving quality limit, the limit quality and the batch of the intelligent electric energy meters for the sampling inspection of the isolated batches, and setting the risk of a producer and the risk of a user;
a sample quantity equation establishing step: establishing a sample size solving equation based on the receiving upper limit, the limit quality, the risk of a production party, the risk of a user party and a pre-established batch receiving probability mathematical model of the isolated batch intelligent electric energy meter for the sampling inspection according to the sampling characteristic curve;
and (3) solving a sample quantity equation: solving a sample quantity equation to obtain a sample quantity and a receiving judgment number;
a sample size testing step: the sample size and the receiving judgment number are adjusted according to the GB/T2828.2 standard;
sampling: and sampling and checking the intelligent electric energy meter based on the sample amount and the receiving judgment number.
Further, in the step of establishing the sample volume equation, the batch reception probability mathematical model is specifically,
when the ratio of the batch to the sample size is larger than a preset first threshold value and the reject ratio is within (0, 1), adopting a batch receiving probability equation based on binomial distribution;
when the ratio of the batch size to the sample size is smaller than a preset first threshold value and the reject ratio is smaller than 0.1, adopting a batch receiving probability equation based on Poisson distribution;
in other cases, a batch receiving probability equation based on super-geometric distribution is adopted.
Further, in the step of solving the sample amount equation, the sample amount equation is solved by using a binomial equation or chi-square distribution. Considering that the sample size and the receiving judgment number are required to be integer solutions, the sample size equation has no precise solution and only can approximate the solution, and therefore the approximate solution is directly obtained by adopting chi-square distribution.
Further, in the second-stage sampling and the third-stage sampling, a sample amount is obtained according to a pre-established electric energy meter sampling sample amount calculation model, and the intelligent electric energy meter to be sampled is subjected to layered sampling based on the sample amount to obtain a sampling result.
Further, it is obtained based on American national Standard ANSIC 12.1-1995.
Furthermore, in the second-stage sampling, hierarchical sampling is performed by adopting an equal proportion distribution method, and in the third-stage sampling, hierarchical sampling is performed by adopting an unequal proportion distribution method. In the second stage, the sample size distribution is mainly based on equal proportion distribution, the sample capacity selected from each layer is in direct proportion to the total size of the layer, and when the difference between the layers is great and the homogeneity exists in the layers, the sample variance is reduced; the third stage performs unequal proportion distribution according to the variance size, and can improve the precision or reduce the inspection cost by increasing the sampling ratio in the layer with higher variance or lower cost.
Furthermore, in the second-stage sampling, the method also comprises the step of obtaining the qualified level and the error level of each layer of intelligent electric energy meter based on the sampling result, and obtaining the comprehensive score. The qualification level of the electric energy meter reflects the qualification rate of the running electric energy meter, and is divided into a pressure test, a creeping test, a word moving test, a starting test, other tests and visual inspection. And carrying out weight assignment on each test qualification rate of the product according to past experience. The error is an important parameter comprehensively reflecting the quality characteristics of the electric energy meter, and the quality level of the electric energy meter produced by each manufacturer can be judged through comparison.
Furthermore, in the third stage of sampling, a Raman distribution method is adopted for hierarchical sampling.
Compared with the prior art, the invention has the following advantages:
(1) the invention relates to a staged and layered sampling method of an isolated batch of intelligent electric energy meters, which comprises the following steps of controlling the quality of the isolated batch of intelligent electric energy meters in three stages, and carrying out once sampling acceptance on the isolated batch of intelligent electric energy meters in the first stage based on probability theory, so that the method is suitable for the characteristic that the batch of the isolated batch of intelligent electric energy meters is only one batch; in the third stage sampling, adaptive sampling adjustment is carried out according to the result of the second stage sampling, and the reliability of the random sampling result is ensured; sampling of each stage is carried out on the intelligent electric energy meter according to batches or layers, and the quality conditions of the same batch of products are always consistent, so that the time and the economy are saved, and the reliability of random sampling results is ensured.
(2) The invention relates to a staged and layered sampling method of an isolated batch intelligent electric energy meter, wherein in the first stage of sampling, aiming at single batch production of isolated batches or products manufactured in small batches or with large quality fluctuation, or one batch or a few batches of products purchased from manufacturers/suppliers in continuous and stable production, the sampling is carried out once based on the characteristics of probability theory and sampling characteristic curve, the sampling scheme is simple, and the consumed manpower and material resources are few.
(3) The invention discloses a staged and layered sampling method of an isolated batch of intelligent electric energy meters, which is characterized in that sampling and sample size inspection are carried out in the first-stage sampling according to CB/T13262 and GB/T2828.2 standards, and the standards are suitable for sampling of isolated batches, thereby meeting the inspection and acceptance requirements of the intelligent electric energy meters.
(4) According to the staged and layered sampling method for the isolated batch intelligent electric energy meter, in the first-stage sampling, batch receiving probability equations based on binomial distribution, Poisson distribution and super-geometric distribution are respectively constructed through the batch size, the operation complexity is reduced, two solving methods of binomial formulas and chi-square distribution are provided, and the reliability of the obtained sample size result is guaranteed by matching with the GB/T2828.2 standard.
(5) The invention relates to a staged and layered sampling method of an isolated batch of intelligent electric energy meters, which is characterized in that in the second stage sampling and the third stage sampling, the isolated batch of intelligent electric energy meters are subjected to layered sampling based on manufacturers, models, specifications and/or purchasing years, so that the quality conditions of each layer of intelligent electric energy meters tend to be consistent, for example, the quality conditions of the electric energy meters produced by various manufacturers tend to be consistent while the quality conditions of the electric energy meters produced by the same manufacturer tend to be consistent, therefore, the manufacturers are used as layers, and the quality conditions of the intelligent electric energy meters tend to be consistent.
(6) In the third stage of sampling, the comprehensive score of each layer of intelligent electric energy meter is obtained based on the second stage of sampling, the hierarchical sampling is carried out by adopting the internal man distribution method, the difference among the intelligent electric energy meters of each layer and the reject ratio of the intelligent electric energy meters after running for several years are fully considered, the adaptive sampling adjustment is carried out, and the reliability of the sampling result is ensured on the basis of saving time and economic cost.
(7) The invention discloses a staged and layered sampling method of an isolated batch intelligent electric energy meter, which adopts random sampling in three-stage sampling, wherein the electric energy meter is usually produced in whole batch and is less influenced by human and objective factors in the production and installation processes, so that the quality conditions of the same batch of products are always consistent, and the samples randomly extracted from the electric energy meter can represent the actual quality level of the batch of products to a certain extent.
(8) The invention discloses a staged and layered sampling method of an isolated batch of intelligent electric energy meters, which considers that the operation of the electric energy meters is a continuous process, the result of one-time sampling cannot reflect the whole appearance, and the sampling frequency is too high, thus increasing the cost.
Drawings
FIG. 1 is a schematic flow chart of a staged and stratified sampling method for an isolated batch of intelligent electric energy meters according to the present invention;
FIG. 2 is a schematic diagram of a sampling characteristic;
FIG. 3 is a flow chart of the second stage sampling and the third stage sampling of the staged and hierarchical sampling method of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
Example 1
As shown in fig. 1, the embodiment is a staged and layered sampling method for an isolated batch of intelligent electric energy meters, and the method specifically includes acquiring the total amount of the isolated batch of intelligent electric energy meters, and performing staged sampling on the intelligent electric energy meters according to a time sequence, wherein the staged sampling includes a first-stage sampling, a second-stage sampling and a third-stage sampling which are performed in sequence, the first-stage sampling performs one-time sampling acceptance on the isolated batch of intelligent electric energy meters based on a probability theory, the second-stage sampling and the third-stage sampling both perform layered sampling on the isolated batch of intelligent electric energy meters, and the third-stage sampling performs sampling based on a result of the second-stage sampling.
The following is a detailed description of the sampling of each stage:
1. first stage sampling
The first stage sampling specifically comprises the following steps:
a parameter acquisition step: acquiring the receiving quality limit, the limit quality and the batch of the intelligent electric energy meters for the sampling inspection of the isolated batches, and setting the risk of a producer and the risk of a user;
a sample quantity equation establishing step: establishing a sample size solving equation based on the receiving upper limit, the limit quality, the risk of a production party, the risk of a user party and a pre-established batch receiving probability mathematical model of the isolated batch intelligent electric energy meter for the sampling inspection according to the sampling characteristic curve;
and (3) solving a sample quantity equation: solving a sample quantity equation to obtain a sample quantity and a receiving judgment number;
a sample size testing step: the sample size and the receiving judgment number are adjusted according to the GB/T2828.2 standard;
sampling: and sampling and checking the intelligent electric energy meter based on the sample amount and the receiving judgment number.
1.1 batch receiving probability mathematical model
In counting sampling tests, the number of rejects in a sample is a discrete random variable that conforms to a hyper-geometric distribution.
1.1.1, super-geometric distribution
In the non-return sampling test, the probability of the occurrence of the failure in the sample is subjected to super-geometric distribution. Assuming that the batch in a batch of products is N, where the total number of rejects is D, the total number of passes in the batch is N-D, and thus the probability Pa (p) of having exactly D rejects in a sample of size N drawn by the random number is
Wherein, for any positive integer m, n has
1.1.2, binomial distribution
The calculation of pa (p) by the hypergeometric distribution formula is theoretically accurate, but the calculation is very complicated. When N is more than or equal to N, the sample without putting back can be approximately regarded as the sample with putting back; that is, when N ≧ N, Pa (p) can be calculated by substituting a binomial distribution formula for the hypergeometric distribution formula, i.e.
In actual production, when production is in a normal state, the number D of unqualified products in a batch of products is quite small, which is equivalent to the batch N and can be ignored; when N is 10N or more, that is, N is large, d is D, N and can be ignored for N. So that the following approximate calculation can be made:
therefore, when N is more than or equal to 10N, the approximate calculation can be carried out by using a binomial distribution formula, namely:
wherein:
referred to as reject rate.
1.1.3 Poisson distribution
When n is large, the calculation of the binomial distribution is also rather cumbersome, as known from the "poisson theorem" in probability theory: if λ np is taken, then for any fixed non-negative integer d:
thus for any X >0, there is a positive integer M, when n > M there is:
therefore, within a certain error (X), when n is large enough, the probability of the binomial distribution can be approximately calculated by using the Poisson distribution. Practice proves that when N is less than or equal to 10N and p is less than or equal to 0.1, the probability calculation can be carried out by using Poisson distribution to approximately replace binomial distribution in counting sampling inspection, namely
The batch acceptance means that the number of detected unqualified products is less than or equal to the qualification judgment number, namely d is less than or equal to Ac, then the probability of batch acceptance is P { d is less than or equal to Ac }, and the property of the discrete random variable is known as follows:
when N is more than or equal to 10N and 0< p <1, the approximate calculation of the binomial distribution is used:
when N is less than or equal to 10N and p is less than or equal to 0.1, the Poisson distribution is approximately calculated to obtain:
from the above demonstration, for the counting-once-sampling scheme, the batch acceptance probability can be calculated according to the above formula when the batch reject rate is known. A similar calculation method is also available for calculating the multi-sampling scheme.
1.2 sampling characteristic curve
The receive quality limit (AQL) refers to the process average upper quality limit of consecutive submitted batches deemed acceptable in a sample check, referred to as an acceptable quality level. The receive quality limit (AQL) provides a guide to the quality level of the product desired by the user, and if the process quality of the product received by the user is not higher than the receive quality limit (AQL), then the product will be received with a high probability, and typically this indicator is used in the producer quality control process.
The Limit Quality (LQ) indicates that the selected solution can only be accepted with a low probability (typically 10%) when the process quality (the number of rejects per hundred units of product) in the batch reaches the Limit Quality (LQ). This may help the user to effectively control the risk. Since the closer the values of LQ and AQL are, the larger the sample size and the higher the inspection cost, the Limit Quality (LQ) should be reasonably determined as needed.
As shown in fig. 2, the curve obtained by using p as the abscissa and Pa (p) as the ordinate is an OC (sampling characteristic) curve, and if the production-side risk quality level Pa (p0) and the use-side risk quality level Pa (p1) are given, the reception quality limit is p0, and the limit quality is p1, the production-side risk α and the use-side risk β are:
1.3 sample size equation solving and verifying steps
In the embodiment, the sample size is calculated by taking N as 500 in the sampling scheme of the intelligent electric energy meter.
Since the values of α and β are usually specified by the relevant national standards, the sample size n and the reception determination number Ac can be solved simultaneously according to equations (1) and (2) or (3) as long as Pa (p0) and Pa (p1) are obtained through negotiation between the producer and the consumer.
In this embodiment, after negotiation, the power company and the user determine that P0 is 0.11%, P1 is 6.0%, and if N is 500, the sampling scheme is determined according to the standard rule of "count standard one-time sampling inspection degree and table" of rejection rate of CB/T13262, α is 5%, and β is 10%.
After the sample amount n and the acceptance determination number Ac are obtained, a sample amount checking step is performed at the same time, and the final sample amount n and the acceptance determination number Ac are obtained.
Considering that the LQ priority value sequences specified in GB/T2828.2 are 0.5, 0.8, 1.25, 2.00, 3.15, 5.00, 8.00, 12.5 … … and the selected Limit Quality (LQ) of the current sample is between 5.00 and 8.00, the sampling scheme of the intelligent electric energy meter is shown in table 1.1.
TABLE 1.1 Intelligent electric energy Meter sampling scheme
Note: if the batch size is less than 81%, then 100% inspection is performed, if the batch size exceeds 35000, the batch size is preferably divided into a plurality of batches
Solution: because the batch size is large, a binomial formula can be used for calculating the receiving probability and solving. To solve the problem:
when Ac is 0, the formula (4) is changed to
Solved n-46.6 and n-37.2
When Ac is 1, the formula (4) is changed to
The iterative method is utilized to obtain n ≈ 321 and n ≈ 63
Since these two n values are too different, it is impossible to obtain a solution by taking Ac ═ 1. So the requested scheme is either (47/0) or (37/0).
Calculation method two
The title is that N is 500, p0 is 0.0011, p1 is 0.06, α is 0.05, β is 0.10, and the formula 3 and the formula 1 can be combined into a cubic range:
this is an transcendental equation and requires that n and Ac be integer solutions, so there is no exact solution, only an approximate solution. According to probability, this equation can be solved approximately with a chi-square distribution, and the system of equations becomes:
therefore, Ac and n can be solved to obtain a scheme, and the scheme can be determined according to the corresponding relation between the judgment number Ac and p1/p0 for simplifying calculation and table look-up, as shown in Table 1.2
TABLE 1.2 comparison of Ac with p1/p0
Dividing the two formulas of formula (5) to obtain
Assuming that Ac is 0, 1, 2, 3 … with the 3.9, the decimal place is obtained according to the charpy square quantile table
When Ac is equal to 0, the voltage of Ac,
when Ac is equal to 1, the total of the three,
when Ac is 2
It can be seen that when Ac is 0, the result calculated using the chi-square quantile table is 44.71; when Ac is 1, the result is 10.94; when Ac is 2, the result is 6.51, and of these three results, the result 44.71 when Ac is 0 is closer to the result of p1/p0 being 54.54 in formula 7.10, and the result is more in line with the design requirement, so Ac is 0.
At this time, when Ac is 0, according to formula 5:
Since n must be a positive integer, n-38 or n-47 is taken. The solution obtained by this method is approximately the same as the solution obtained by the first calculation method, and this method is feasible.
Because n and c must be positive integers, two exactly identical solutions are generally not found, and a solution with a smaller sample size or a compromise may be considered, as in this example, a solution (40/0) may be taken between the sampling solution (50/0) and the solution (32/0) of Table 1. substituting the sampling solution (40/0) into equation 1, equation 7, then calculating a producer risk α of 4.31% and a consumer risk β of 8.42%.
Therefore, according to the scheme (40/0), the sample size is 40, the receiving judgment number is 0, 40 electric energy meters are randomly extracted from the isolated batch of 500 intelligent electric energy meters for detection, if one or more unqualified electric energy meters are detected, the batch of intelligent electric energy meters is unqualified, and otherwise, the batch of intelligent electric energy meters is qualified.
2. Second stage sampling and third stage sampling
And the second-stage sampling and the third-stage sampling are performed on the intelligent electric energy meter in a layered mode, and the third-stage sampling is performed according to the result of the second-stage sampling.
The hierarchical sampling specifically includes hierarchical sampling of the running intelligent electric energy meter based on the manufacturer, the model, the specification and/or the purchasing year, and in this embodiment, hierarchical sampling is performed based on the manufacturer. In the second-stage sampling and the third-stage sampling, the sample size is obtained according to a pre-established electric energy meter sample size calculation model, and the intelligent electric energy meter to be sampled is subjected to layered sampling based on the sample size to obtain a sampling result.
And sampling in the second stage in the second year of the operation of the intelligent electric energy meter, and sampling in the third stage in the fourth year of the operation of the intelligent electric energy meter. In the second stage of sampling, an equal proportion distribution method is adopted for layered sampling, and based on the sampling result, the qualification level and the error level of each layer of intelligent electric energy meter are obtained, and the comprehensive score is obtained; in the third stage of sampling, hierarchical sampling is carried out by adopting an unequal proportion distribution method, and hierarchical sampling is carried out by adopting an internal Manchester distribution method.
The following is a detailed description:
2.1 construction of the model
By referring to American national standard ANSIC12.1-1995, a power meter sample quantity calculation model is obtained according to two conditions of the intelligent power meter failure rate P:
when P < ═ LQ, there are:
Or
(considering relative error limits)
When P > LQ, consider to carry out the full inspection acceptance to the electric energy meter.
Wherein LQ is the limit quality, which means that when the reject ratio of a certain batch of products reaches a certain value, the batch of products are rejected with high probability by a sampling scheme, P represents the estimated value of the reject ratio of the intelligent electric energy meter, N represents the total amount, t represents the reliability, which is the double side α quantiles of standard normal distribution, d and r represent the precision, which are represented by absolute error limit and relative error limit, and N represents the sample size.
2.2 solving of the model
In the sample quantity calculation model, except that the overall N is easy to know and the relevant standard of the critical value t is specified, the overall fraction defective P, the limit quality LQ, the absolute error limit d and the relative error limit r are all waiting coefficients and need to be determined in advance.
(1) Determination of the overall reject ratio P
Since the true value of P is not available before the sampling test is performed, the estimated value of P can be obtained by two ways, namely, estimation according to small-scale pre-sampling and estimation by using the previous test result. U.S. standard ANSIC12.1-1995 uses the cumulative mean failure rate y% calculated from the last (or cumulative) spot test results as an estimate of P.
(2) Determination of the limiting mass LQ
The relevant cost detected by the intelligent electric energy meter, including the error loss cost, the meter replacement cost and the detection cost of the intelligent electric energy meter, can be obtained after analysis, and 6% is taken as the value of LQ.
(3) Determination of the absolute error limit d and the relative error limit r
Since the absolute error and the relative error are two expressions of the sampling precision requirement, the sampling precision is related to the sampling cost on one hand, and is also closely related to the cost of benefit loss caused by the sampling error on the other hand.
2.3 distribution of layers at stages of sample size
(1) Distribution of sample size in the second stage layers
For the combination of the layered sampling and the staged sampling, the whole life cycle of the electric energy meter is divided into two stages, and then the layered sampling is adopted for each stage. For the hierarchical sampling, when the total sample size is constant, the problem of how much sample size should be allocated to each layer needs to be studied, because the variance of the estimation quantity is related to not only the variance of each layer but also the sample size allocated to each layer when the overall estimation is carried out.
In the second stage, the sample size distribution is mainly based on equal proportion distribution, the sample capacity selected from each layer is in direct proportion to the total size of the layer, and when the difference between the layers is great and the homogeneity exists in the layers, the sample variance is reduced; the third stage performs unequal proportion distribution according to the variance size, and can improve the precision or reduce the inspection cost by increasing the sampling ratio in the layer with higher variance or lower cost.
The equal proportion distribution method refers to the sample capacity n extracted from each layer when all units of the sample are distributed in each layerkAccounts for all the units NhIs equal, equivalent to the proportion of the sample volume N to the total volume N, i.e.:
The proportion of the sample size of each layer to the total sample size is as follows:
for stratified sampling, this time the overall mean
The unbiased estimate of (c) is:
(2) distribution of sample size in third stage of each layer
And the sample size is distributed in each layer in the third stage in an unequal proportion mode mainly according to the variance. Common unequal proportion distribution modes include optimal distribution and Raman distribution.
a. Optimal allocation
In the hierarchical random sampling, how to distribute the sample size to each layer enables the variance of the estimated quantity to be minimum under the condition of the total cost to be given, or the total cost to be minimum under the condition of the given estimated quantity variance, and the sample size distribution which can meet the sample size is the optimal distribution.
The linear function of the sampling cost is:
wherein c is the total cost, c0For a base cost, chThe cost per unit sample in the h-th layer.
The optimal allocation mode is as follows:
b. neumann distribution
During the electric energy meter sampling inspection process, the inspection cost of the electric energy meters in different layers is basically the same, namely chC, the optimal allocation is simplified as:
wherein N is the sample size, NhIs the total number of h-th layers, ShIs the comprehensive score of the first sampling inspection of the h-th layer, nhIs the number of samples of the h-th layer.
2.4, indoor inspection and data analysis
(1) The qualification level of the electric energy meter reflects the qualification rate of the running electric energy meter, and is divided into a pressure test, a diving test, a character moving test, a starting test, other tests and visual inspection. The qualification rates of the products in the prior tests are weighted according to the past experience, and the weights are shown in the table 2.1
TABLE 2.1 Experimental weight assignment schematic
And then calculating to obtain the qualified level Z of each manufacturer by a weighting method, namely
Z＝qWithstand voltage×f1+qDiving motion×f2+qStarting up×f3+qWalk word×f4+qDirect viewing×f5+qOthers×f6
Wherein Z is the qualification level, qWithstand voltageFor the qualification rate of the withstand voltage test, f1As a weight of withstand voltage test, qDiving motionFor the shunt test qualification rate, f2As shunt test weights, qStarting upTo start the test pass rate, f3To initiate trial weights, qWalk wordFor pass rate of the test of writing, f4For test weights of wording, qDirect viewingFor visual test of pass rate, f5For visual testing of the weights, qOthersFor other test yields, f6Other trial weights. Other tests include component testing, parameter setting testing, communication response delay testing, and the like.
The closer Z is to 1, the higher the qualification level of the manufacturer. By comparing the sizes of the manufacturers Z, the high or low degree of the cold can be evaluated.
(2) The error is an important parameter comprehensively reflecting the quality characteristics of the electric energy meter, and the quality level of the electric energy meter produced by each factory can be judged through comparison. Considering the inconsistency of the error conditions of the electric energy meters under different powers, respectively selects
Lower sum of
The total 8 detection points (the detection points can be increased or decreased according to actual conditions) are used for analyzing errors among household electrical energy meters of different factories and household electrical appliances. The detection points are shown in Table 2.2.
TABLE 2.2 error detection points
The standard deviation coefficient is a statistic for measuring the variation degree of each observed value. Due to the different levels between different manufacturers, it is appropriate to use the standard deviation coefficients for comparison. The coefficient of standard deviation is the ratio of the standard deviation to the mean, i.e.
CV＝σ/χ
In the formula, CV is an error level, sigma is a standard deviation of errors of all detection points of the intelligent electric energy meter, and χ is an average value of the errors of all the detection points of the intelligent electric energy meter.
The method comprises the steps of firstly calculating the average value of the error values of the electric energy meters produced by each manufacturer under each detection point, then giving different weights to each detection point according to actual requirements, calculating the weighted average value of the error values of the electric energy meters of each manufacturer and the standard deviation of the error values, and finally calculating the standard deviation coefficient of the error values of the electric energy meters of each manufacturer. The larger the standard deviation coefficient is, the larger the quality fluctuation of the electric energy meter of the manufacturer is, and the worse the quality stability is.
As shown in fig. 3, the sampling inspection scheme of the intelligent electric energy meter is as follows:
(1) determining a period of inspection;
(2) determining a sampling method and the total amount according to a related sampling statistical theory and by combining limiting conditions such as precision, cost and the like;
(3) layering the electric energy meter to be sampled and inspected according to manufacturer, model, specification, purchasing year and the like;
(4) determining the quantity of electric energy meters to be sampled and inspected for each group of sampling population, namely determining the distribution of the sample quantity in each layer;
(5) sampling in stages, namely if the whole life cycle of the electric energy meter is 5 years, the first inspection is carried out in the 1 st year; in the 2 nd year, sampling in equal proportion according to the proportion of the electric energy meter unit; in the 3 rd year, the electric energy meter operates; in the 4 th year, unequal proportion sampling is carried out by using the result of sampling in the second year;
(6) sampling each group of intelligent electric energy meters according to the determined sample amount, and then carrying out performance detection on each sampled electric energy meter according to a verification standard;
(7) and deducing the population according to the detection result of the sample, and judging whether the population is qualified or not.
2.5 detailed description of the invention
2.5.1 Total sample size
The sampling detection method proposed by the research is verified by taking a three-phase electric energy meter installed in 2010 of a certain city as an example. The distribution of the electric energy meters of each manufacturer is shown in table 2.3
TABLE 2.3 installation of three-phase electric energy meter for 2010 manufacturer in a certain city
2.5.2 second-time electric energy meter sampling inspection sample size confirmation
According to the estimation of the detection cost and the loss cost of the intelligent electric energy meter and by referring to the sampling inspection method in appendix A of national standard JB/T5007-2002 'reliability requirement and assessment method for intelligent electric energy meters', the limit quality LQ is determined to be 6%. According to past experience, the reject ratio of a three-phase electronic electric energy meter in a certain market is between 0.1% and 0.3%, so that the sampling average damage rate P set by the example is 0.3%, and the operating electric energy meter in the area is determined to be detected in a sampling inspection mode because P < LQ.
Taking the confidence level 1-a as 0.95, namely t as 1.96; the accuracy requirement controls the absolute error d to be 0.004: calculating the total number of samples to be extracted by using a sample size model:
the sampling ratio in each layer is:
therefore, the distribution of the sample size from each manufacturer is shown in Table 2.4
TABLE 2.4 sample size distribution from the first run of each manufacturer
The qualification rate of each indoor test is shown in table 2.5.
TABLE 2.5 qualified horizontal distribution of the manufacturers
All the test items were 0.15 except for the visual inspection weighted 0.25, Z for the acceptable level aloneA＝0.9990，ZB0.9991, manufacturer B is superior to manufacturer a.
Table 2.6 mean value of electric energy meter of each manufacturer at each detection point
Calculated from table 2.6: the standard deviation of manufacturer A is 0.0739, and the standard deviation coefficient is 0.49205;
the manufacturer B standard deviation was 0.0846, and the coefficient of standard deviation was 0.74178.
And (4) giving scores to the electric energy meters of the two manufacturers by comprehensively considering the qualified level and the error level, wherein the specific standard is referred to as table 2.7.
TABLE 2.7 Standard of acceptable and error level division
| Item scoring | Qualification level | Level of error |
| 5 | (99.9％，100％] | (0，0.46) |
| 4 | (99.8％，99.9％] | (0.47，0.62) |
| 3 | (99.7％，99.8％] | (0.63，0.78) |
| 2 | (99.6％，99.7％] | (0.79，0.93) |
| 1 | (-∞，99.6％] | (0.93，+∞) |
The qualification level is weighted to 0.4 and the error level is weighted to 0.6 according to experience, so the comprehensive scores of the two manufacturers are as follows:
SA＝4×0.4+4×0.6＝4.0
SB＝5×0.4+3×0.6＝3.8
2.5.3, determination of sample size of sampling test of third electric energy meter
And performing a third sampling inspection in the fourth year of the operation of the electric energy meter, and determining the sample amount of each layer in a Raman distribution mode. The total amount N from the three-phase electric energy meter is 65000. Determining the average sample damage rate according to the first sample inspection result as follows:
and (3) determining the limit quality LQ to be 6% by referring to a sampling inspection method of national standard JB/T50070-2002 appendix A. And determining that P is less than LQ according to the result of the first sampling, and detecting the operating electric energy meter of the region in a sampling inspection mode.
Taking the confidence level 1-a as 0.95, namely t as 1.96; the precision requires that the absolute error d is controlled to be 0.004; calculating the total number of samples to be extracted by using a sample size model:
according to the formula of endoman assignment:
the distribution of sample size between layers is shown in table 2.8.
TABLE 2.8 sample size distribution from the second run of each manufacturer
After sampling at each stage, detecting the extracted intelligent electric energy meter, and if the detected unqualified number d is less than or equal to the receiving number Ac, judging that the batch is qualified; if the number d of the unqualified products at the detection position is larger than or equal to the rejection number Re, the batch is judged to be unqualified, and the acceptance number Ac and the rejection number Re are preset.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (10)
1. The method is characterized by specifically obtaining the total amount of isolated intelligent electric energy meters in batches and carrying out staged sampling on the intelligent electric energy meters according to a time sequence, wherein the staged sampling comprises a first stage sampling, a second stage sampling and a third stage sampling which are sequentially carried out, the first stage sampling is used for carrying out one-time sampling acceptance on the isolated intelligent electric energy meters in batches based on a probability theory, the second stage sampling and the third stage sampling are used for carrying out layered sampling on the isolated intelligent electric energy meters in batches, and the third stage sampling is used for carrying out sampling based on the result of the second stage sampling.
2. The staged and stratified sampling method for isolated batch of intelligent electric energy meters as claimed in claim 1, wherein the stratified sampling is carried out on the isolated batch of intelligent electric energy meters based on manufacturers, models, specifications and/or purchasing years.
3. The staged and stratified sampling method for isolated batch of intelligent electric energy meters as claimed in claim 1, wherein said first stage sampling specifically comprises the steps of:
a parameter acquisition step: acquiring the receiving quality limit, the limit quality and the batch of the intelligent electric energy meters for the sampling inspection of the isolated batches, and setting the risk of a producer and the risk of a user;
a sample quantity equation establishing step: establishing a sample size solving equation based on the receiving upper limit, the limit quality, the risk of a production party, the risk of a user party and a pre-established batch receiving probability mathematical model of the isolated batch intelligent electric energy meter for the sampling inspection according to the sampling characteristic curve;
and (3) solving a sample quantity equation: solving a sample quantity equation to obtain a sample quantity and a receiving judgment number;
a sample size testing step: the sample size and the receiving judgment number are adjusted according to the GB/T2828.2 standard;
sampling: and sampling and checking the intelligent electric energy meter based on the sample amount and the receiving judgment number.
4. The sampling test method for the isolated batch of intelligent electric energy meters according to claim 3, wherein in the sample size equation establishing step, the batch receiving probability mathematical model is specifically,
when the ratio of the batch size to the sample size is larger than a preset first threshold value and the reject ratio is within (0, 1), adopting a batch receiving probability equation based on binomial distribution;
when the ratio of the batch size to the sample size is smaller than a preset first threshold value and the reject ratio is smaller than 0.1, adopting a batch receiving probability equation based on Poisson distribution;
in other cases, a batch receiving probability equation based on super-geometric distribution is adopted.
5. The sampling detection method for the isolated batch of intelligent electric energy meters according to claim 3, wherein in the step of solving the sample size equation, the sample size equation is solved by a binomial equation or a chi-square distribution.
6. The staged and layered sampling method for the isolated batch of intelligent electric energy meters as claimed in claim 1, wherein in the second stage sampling and the third stage sampling, the sample size is obtained according to a pre-established electric energy meter sampling detection sample size calculation model, and based on the sample size, the intelligent electric energy meters to be sampled are hierarchically sampled to obtain the sampling result.
7. The staged and stratified sampling method for an isolated batch of intelligent electric energy meters as claimed in claim 6, wherein the electric energy meter sampling test sample size calculation model is obtained based on the American national Standard ANSIC 12.1-1995.
8. The staged and stratified sampling method for an isolated batch of intelligent electric energy meters as claimed in claim 1, wherein in the second stage sampling, stratified sampling is performed by using an equal proportion distribution method, and in the third stage sampling, stratified sampling is performed by using an unequal proportion distribution method.
9. The staged and stratified sampling method for isolated batches of intelligent electric energy meters as claimed in claim 1, wherein the second stage of sampling further comprises obtaining the qualification level and the error level of each intelligent electric energy meter layer based on the sampling result, and obtaining the comprehensive score.
10. The staged and stratified sampling method for an isolated batch of intelligent electric energy meters as claimed in claim 9, wherein in the third stage of sampling, stratified sampling is performed by using a Raman distribution method.
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