CN111597511A - An acceptance judgment method for glass insulator sampling test based on mathematical hypothesis testing - Google Patents

Abstract

The invention provides a method for judging acceptance of glass insulator sampling test based on mathematical hypothesis testing. A series of operations that determine whether or not to accept the batch of products supplied by the sampling inspection test results. The specific steps of the method are as follows: step 1: select relevant parameters for hypothesis testing; step 2: determine the sample size, qualified quality level and preset number of qualified judgments and unqualified judgments of a sampling plan; step 3: calculate statistics The observed value of the test quantity; Step 4: Decide whether to accept or not. The invention improves the sampling and acceptance efficiency of the glass insulator upon arrival, solves the problem of few acceptance methods for the glass insulator, and ensures the rights and interests of both users and suppliers.

Description

An acceptance judgment method for glass insulator sampling test based on mathematical hypothesis testing

technical field

The invention relates to the field of electric power material procurement and acceptance, in particular to a method for judging acceptance of a glass insulator sampling test based on a mathematical hypothesis test.

Background technique

In the process of purchasing power materials and equipment, sampling test is a key link to determine whether the equipment is accepted or not. Insulators play a vital role in the safe production of electricity, and glass insulators are the most widely used materials in the power sector. Sampling tests and acceptance are generally recommended according to GBT1001.1-2003. The nominal medium voltage is higher than 1000V. Overhead line insulators Part 1 Porcelain or glass insulator elements for alternating current systems -- Definitions, test methods and criteria for development. However, when the number of one or more batches of insulators of the same structure produced by the same manufacturer under the same production conditions is large (more than 10,000 pieces) submitted for acceptance, GBT1001.1-2003 recommends that they be divided into batches of 2,000 pieces each. Appropriate batch number consisting of up to 10,000 insulators, randomly selected from the batch according to the negotiated quantity. Such sampling rules and judgment criteria bring more workload to suppliers and users due to quality acceptance management, and are prone to the phenomenon of sample confusion; and due to the large range of sampling negotiation, the risk of quality control is high.

Therefore, it is necessary to take a sampling according to the maximum sampling quantity of four thousandths according to GBT1001.1-2003 for the problems existing in the sampling acceptance test when the quantity of the supply batch is more than 10,000, and discuss the corresponding judgment method.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a method for judging the acceptance of glass insulator sampling test based on mathematical hypothesis testing, which can solve the problem of complicated and chaotic sampling procedures in glass insulators in one stop, so as to meet the requirements of high efficiency and low risk in material sampling inspection, and improve glass insulators. Insulator arrival acceptance control means to further improve the level of power safety production.

The present invention adopts following technical scheme:

A method for judging acceptance of glass insulator sampling test based on mathematical hypothesis testing, comprising the following steps:

Step 1: Select the relevant parameters of the hypothesis test, the relevant parameters of the hypothesis test specifically include the null hypothesis H ₀ , the parameters required for the non-normal population large sample parameter test, the number of one-sided samples q, the number of samples n, and the significance level α , the observed value of the test statistic T, the degree of freedom υ, the one-sided value of the t distribution table when the degree of freedom υ is infinite

Step 2: Determine the number of samples n, the qualified quality level AQL/% and the preset qualified judgment number A _c and the unqualified judgment number _Re of the primary sampling plan;

Step 3: According to the sample number n of the primary sampling plan determined in step 2, the qualified quality level AQL/% and the preset qualified judgment number A _c and the unqualified judgment number _Re , calculate the observed value of the statistical test quantity;

和预设合格判定数及不合格判定数的观测值比较，决定一次抽样后是否接收该批量产品。Step 4: Use the one-sided value obtained by looking up the t distribution table

Compare with the observed value of the preset qualified judgment number and unqualified judgment number to decide whether to accept the batch of products after one sampling.

Further, the formula for calculating the observed value of the statistical test quantity in step 3 is:

The observed value of the test statistic

为单侧样本数q的极大似然估计，

p为单侧概率。where n is the number of samples,

is the maximum likelihood estimate of the one-sided sample size q,

p is the one-sided probability.

Further, in step 3, the qualified quality level AQL value is used as the hypothesis boundary when testing the hypothesis

H ₀ : p≤0.01 H ₁ : p＞0.01 (4)

Overall X～B(1,p) (5)

The sample obeys the B distribution and needs to be changed to N(0,1) distribution, and then look up the table according to the t distribution;

The maximum likelihood estimate of the one-sided sample size q is:

and approximately have

When H ₀ is established, p≤0.01, thus taking the observed value of the test statistic:

So by

The rejected domains that are checked are:

即可得到检验统计量的观测值T，其中显著性水平α为原假设H₀成立，因观测值进入了拒绝域，从而作出拒绝的结论的作第一类错误的概率。substitute

The observation value T of the test statistic can be obtained, in which the significance level α is the probability that the null hypothesis H ₀ is established, and the observation value enters the rejection domain, thus making a rejected conclusion as the probability of type 1 error.

根据步骤三计算获得预设合格判定数的观测值，若预设合格判定数的观测值小于单侧值

则预设合格判定数正确，则接收本批次产品；若预设合格判定数的观测值大于等于单侧值

预设不合格判定数正确，则进入加倍重复试验程序。Further, step 4 is specifically: use the one-sided value obtained by looking up the t distribution table

Calculate and obtain the observed value of the preset qualified judgment number according to step 3, if the observed value of the preset qualified judgment number is less than the one-sided value

If the preset qualified judgment number is correct, the batch of products will be accepted; if the observed value of the preset qualified judgment number is greater than or equal to the one-sided value

If the preset number of unqualified judgments is correct, enter the double-repetition test procedure.

The invention solves the problem that the sampling procedure of glass insulators is complicated and easy to be confused in one stop, improves the sampling inspection and acceptance efficiency of glass insulators upon arrival, solves the problem of few acceptance methods for glass insulators, and ensures the rights and interests of both users and suppliers.

Description of drawings

FIG. 1 is a schematic flow chart of the acceptance judgment method of the glass insulator sampling test based on the mathematical hypothesis test of the present invention.

Detailed ways

The technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention.

1 shows a schematic flowchart of a method for judging acceptance of glass insulator sampling test based on mathematical hypothesis testing of the present invention. The method for judging acceptance of glass insulator sampling test based on mathematical hypothesis testing includes the following steps:

Step 1: Select relevant parameters for hypothesis testing;

所述假设检验的相关参数来源于下列数学原理和公式：In the first step, the relevant parameters of the hypothesis test are specifically the null hypothesis H ₀ , the one-sided sample number q, the sample number n, the significance level α, and the observed value of the test statistic required for the non-normal population large-sample parameter test. One-sided value of t distribution table when T, degree of freedom υ, and degree of freedom υ are infinite

The relevant parameters of the hypothesis test are derived from the following mathematical principles and formulas:

(1) Features of hypothesis testing

Contradictory thinking: In order to judge whether a certain event is true, first put forward a certain hypothesis, and think that this hypothesis is true, this hypothesis is generally called the null hypothesis or null hypothesis, and is often expressed as H ₀ , and then proceed according to this hypothesis. reasoning. Under the condition that this assumption is established, if an unreasonable phenomenon occurs, the assumption is rejected; otherwise, the assumption is accepted, so as to make a judgment on the nature of the event.

(2) Non-normal population large sample parameter test

Overall X～B(1,p) (1)

Maximum likelihood estimate of the one-sided sample size q:

The properties approximated by the large sample normal approximation are:

That is, the expression on the left obeys the 0,1 distribution.

(3) Two types of errors in hypothesis testing

If the null hypothesis H ₀ is established, but because the observed value enters the rejection domain, the conclusion of rejection is made, which is called the first type of error. The first type of error is the error of "taking the true as a false", also known as the "discarding the true" error. According to the definition, the significance level α is exactly the probability of making the first type of error (take α=0.01 in the judgment).

If the null hypothesis H ₀ does not hold, but because the observations are in the receptive field, the conclusion that the hypothesis is accepted is called Type II error. This type of error is the error of "taking false as true", also known as "taking false" error, usually the probability of making the second type of error is represented by β.

One would of course want both α and β to be small, but that's hard to do. Because, in general, when α is small, β is large; when β is small, α is large. Therefore, the usual practice is to increase the sample size appropriately to reduce β under the premise of fixing α.

(4) t distribution table

When the sample obeys the 0, 1 distribution, there is a t value according to the one-sided probability p and the degree of freedom υ.

Table 1 t distribution table

Step 2: Determine the sample size, qualified quality level, and the preset number of qualified and unqualified judgments for the primary sampling plan;

In the second step, the sample size (ie the number of samples n), the qualified quality level AQL/%, the preset qualified judgment number A _c and the unqualified judgment number R _e are determined according to the product batches in Table 2. The batch of products is in units of 10,000, and sampling is performed by 4/1,000.

Table 2 Partial one-shot sampling plan

Step 3: Calculate the observed value of the statistical test quantity;

In the third step, when the number of samples n is 80, the preset number of qualified judgments A _c =2, and the preset number of unqualified judgments _Re =3 as an example, the specific calculation observation value T is:

Taking the sample number n as 80, A _c =2; _Re =3 as an example, the calculation and analysis are as follows:

Test the hypothesis (use the acceptable quality level AQL value as the hypothesis boundary)

H ₀ : p≤0.01 H ₁ : p＞0.01 (4)

Overall X～B(1,p) (5)

Way of thinking: The sample obeys the B distribution, which needs to be changed to N(0,1) distribution, and then look up the table according to the t distribution.

The maximum likelihood estimate of the one-sided sample size q is:

and approximately have

When H ₀ is established, p≤0.01, thus taking the observed value of the test statistic:

So by

The rejected domains that are checked are:

得到检验统计量的观测值T：substitute

Get the observed value T of the test statistic:

If 3 defective products are found, then

Observation T:

Step 4: Decide whether to accept or not.

和预设合格判定数及不合格判定数的观测值比较，决定一次抽样后是否接收该批量产品。具体计算如下：In the step 4, use the one-sided value obtained by looking up the t distribution table

Compare with the observed value of the preset qualified judgment number and unqualified judgment number to decide whether to accept the batch of products after one sampling. The specific calculation is as follows:

Look up the t distribution table to get

t _0.99 = 2.32 (15)

The observed value when the preset number of qualified judgments is 2 is 1.34

Obviously 1.34 < 2.32 (16)

Therefore, H ₀ cannot be rejected, that is, the preset number of qualified judgments is correct, and this batch of products is accepted. The observed value when the preset number of unqualified judgments is 3 is 2.52

Obviously 2.52 > 2.32 (17)

Therefore, H ₀ is rejected, that is, the preset number of unqualified judgments is correct, and the double-repeat test procedure is entered.

Similarly, observations of other sample sizes can be obtained as shown in Table 3

Table 3 Test statistic observations for different sample sizes

Obviously, the observed values of acceptance in Table 3 are all less than 2.32, and the observed values of rejection are greater than 2.32.

The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, All should be included within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (4)

1. a kind of glass insulator sampling test acceptance judgment method based on mathematical hypothesis test is characterized in that comprising the steps: Step 1: Select the relevant parameters of the hypothesis test, the relevant parameters of the hypothesis test specifically include the null hypothesis H ₀ , the parameters required for the non-normal population large sample parameter test, the number of one-sided samples q, the number of samples n, and the significance level α , the observed value of the test statistic T, the degree of freedom υ, the one-sided value of the t distribution table when the degree of freedom υ is infinite

Step 2: Determine the number of samples n, the qualified quality level AQL/% and the preset qualified judgment number A _c and the unqualified judgment number _Re of the primary sampling plan; Step 3: According to the sample number n of the primary sampling plan determined in step 2, the qualified quality level AQL/% and the preset qualified judgment number A _c and the unqualified judgment number _Re , calculate the observed value of the statistical test quantity; Step 4: Use the one-sided value obtained by looking up the t distribution table

Compare with the observed value of the preset qualified judgment number and unqualified judgment number to decide whether to accept the batch of products after one sampling. 2. the glass insulator sampling test acceptance judgment method based on the mathematical hypothesis test as claimed in claim 1, is characterized in that: the formula of the observed value of step 3 calculating statistical test quantity is: The observed value of the test statistic

where n is the number of samples,

is the maximum likelihood estimate of the one-sided sample size q,

p is the one-sided probability. 3. the glass insulator sampling test acceptance judgment method based on mathematical hypothesis test as claimed in claim 1, is characterized in that: in step 3, when testing hypothesis, the qualified quality level AQL value is used as hypothesis boundary H ₀ : p≤0.01 H ₁ : p＞0.01 (4) Overall X～B(1,p) (5) The sample obeys the B distribution and needs to be changed to N(0,1) distribution, and then look up the table according to the t distribution; The maximum likelihood estimate of the one-sided sample size q is:

and approximately have

When H ₀ is established, p≤0.01, thus taking the observed value of the test statistic:

So by

The rejected domains that are checked are:

substitute

The observation value T of the test statistic can be obtained, in which the significance level α is the probability that the null hypothesis H ₀ is established, and the observation value enters the rejection domain, thus making a rejected conclusion as the probability of type 1 error. 4. the glass insulator sampling test acceptance judgment method based on mathematical hypothesis test as claimed in claim 1, is characterized in that: step 4 is specifically: the one-sided value that obtains with looking up t distribution table

Calculate and obtain the observed value of the preset qualified judgment number according to step 3, if the observed value of the preset qualified judgment number is less than the one-sided value

If the preset qualified judgment number is correct, the batch of products will be accepted; if the observed value of the preset qualified judgment number is greater than or equal to the one-sided value

If the preset number of unqualified judgments is correct, enter the double-repetition test procedure.

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