A Success-Failure Group Sequential Test Method

Abstract

The present invention provides a success-failure group sequential test method, including: inputting production-related parameters and user-related parameters; based on the production-related parameters and the user-related parameters, calculating the maximum number of test samples N and its receiving number Ac, and grouping the samples of the batch of products to be tested; testing each group of samples of the products to be tested one by one, and after each group of product samples is tested, judging whether the test results can be obtained, if so, terminating the test; if not, adding the next group of product samples to continue the test until the test results are obtained, and the test results refer to whether the samples of the batch of products to be tested are qualified or unqualified. The present invention can provide a corresponding group sequential test scheme when any production-related parameters and user-related parameters and the number of samples of the products to be tested are large, thereby improving the accuracy of product testing.

Description

Technical Field

[0001] The present invention relates to the field of product inspection, and more specifically, to a success-failure type grouping sequential test method. Background Art

[0002] In the process of product reliability verification, several product samples are selected from the batch of products for testing, and the success or failure of the sample test is used as the test result. Finally, based on the test results of the sample products, a conclusion is given as to whether the batch of products is qualified: when the product is deemed qualified, the user will accept the batch of products; when the product is deemed unqualified, the user will reject the batch of products. The so-called sequential sampling means that one or a group of products are selected from the batch each time, and after inspection, acceptance or rejection or inspection of another group of products is made according to a certain rule. The results of a certain inspection test are recorded as (n,m), where n is the total number of samples participating in the test and m is the number of samples that failed the test. When n is large, in order to obtain the test conclusion in a shorter time, a grouped sequential test mode in which a group of products are tested simultaneously each time will be adopted.

[0003] Since there is always a possibility that the sample quality deviates from the overall quality of the product in a sampling test, there are inevitably two risks: the risk of false sampling and the risk of discarding the true one. The risk of false sampling is borne by the user, also known as the user's risk, which means that the sampling inspection conclusion is "the quality of this batch of products is qualified and acceptable", but in actual use it is found that the quality of this batch of products is lower than the minimum quality level acceptable to the user. 1 ,q 1 The corresponding products are referred to as defective products in this article (actually, the lower limit of qualified products); the risk of rejection is borne by the manufacturer, also known as the manufacturer's risk, which means that the sampling inspection conclusion is "the quality of this batch of products is unqualified and rejected", but in fact the quality of this batch of products is generally qualified, and the good product rate in this batch of products is higher than the manufacturer's expectations. The quality level of good products is recorded as q 0 The probability of two risks occurring is usually used to quantitatively describe the possibility. If the product quality is described from the perspective of reliability, the quality level is recorded as q; if the product quality is described from the perspective of unreliability, the quality level is recorded as p, and p+q=1. 0 and p 0 Describe the quality of good products from the perspectives of reliability and unreliability, and p 0 +q 0 =1;q 1 and p 1 Describe the quality of poor products from the perspectives of reliability and unreliability, and p 1 +q 1 =1, and q 0 >q 1 .

[0004] At present, there are standardized design methods for sequential sampling plans. The core of the sequential sampling plan design methods in these international standards, national standards and military standards lies in the likelihood ratio defined in them.

[0005] On this basis, through a series of approximate calculations, a receiving line L is obtained on the n~m plane with n as the horizontal coordinate and m as the vertical coordinate. 0 :m=-h 0 +sn and a rejection line L 1 :m=h 1 +sn. When the test result (n,m) is on the receiving line L 0 When the test result (n, m) is below the rejection line L, the test is terminated and the batch of products is accepted; when the test result (n, m) is above the rejection line L 1 When the test result (n, m) is above the acceptance line L, the test is terminated and the batch of products is rejected. 0 and rejection line L 1 To prevent the test results (n, m) from being on the receiving line L for a long time 0 and rejection line L 1 Two cutoff parameters are specified: n t and m t , and agreed that: when n = n t When m≤m t If the batch is deemed qualified, it is accepted; otherwise, the batch is deemed unqualified and rejected. t The physical meaning of is the maximum number of test samples, m t is with n t The corresponding maximum acceptable number of test failure samples.

[0006] After comparison, it was found that: in the test requirement q 0 , D, α, β are the same If the national standard fixed number sampling plan is adopted, the number of test samples n c and the maximum number of test failure samples A c Although the physical meaning of t 、m t Same, but n c 、n t The two are not equal, and n c Generally much smaller than n t .

[0007] For sequential sampling test, the national standard only gives the case when α=β and q 0 , D, α, β when the cut-off test parameters n are typical values t 、m t , without the cut-off test parameter n t 、m tAlthough the national standard has published the calculation method of fixed number sampling test n c , A c method, but if n c , A c To replace n t 、m t If the user risk exceeds the threshold, the national standard only lists the typical sequential test schemes for the four cases of D = 1.5, 1.75, 2, and 3, and α = β and α = 0.05, 0.1, 0.2, and 0.3. Therefore, in actual inspection work, once q 0 , D, α, β are not in the test plan table published by the national standard, unless q 0 , D, α, β are modified to the typical values ​​of the national standard, otherwise we can only settle for the next best option and use a constant test with a larger number of test samples. 0 , D, α, β, hinders the widespread implementation of sequential sampling experiments in practical work. Summary of the invention

[0008] Regarding the lack of atypical q in the national standard 0 , D, α, β corresponding to the sequential sampling test plan, provides a success-failure grouping sequential test method, including:

[0009] Input the relevant parameters of the producer and the user;

[0010] Based on the manufacturer-related parameters and the user-related parameters, calculate the maximum number of test samples N and the number of acceptances Ac, and group the samples of the product batch to be tested;

[0011] Each group of product samples to be tested is tested one by one. After each group of product samples is tested, it is determined whether the test results can be obtained. If they can be obtained, the test is terminated; if not, the next group of product samples is added and the test is continued until the test results are obtained. The test results refer to whether the product samples in the batch to be tested are qualified or unqualified.

[0012] The success-failure group sequential test method provided by the present invention is not based on the likelihood ratio and can be used in any setting of q 0 , D, α, β, when the number of test samples is expected to be large, the corresponding grouped sequential test plan is given. For products of various quality levels, the product pass rate performance of this plan is equivalent to that of the national standard test plan, but the required sample of participating products is significantly less than that of the national standard constant test, which is equivalent to the national standard sequential test. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1A flow chart of a success-failure group sequential test method provided by the present invention;

[0014] Figure 2-1 It is a schematic diagram comparing the product acceptance probability of the sequential test method of the present invention and the national standard sequential test method;

[0015] Figure 2-2 A schematic diagram showing the comparison of the number of test samples required for the sequential test method of the present invention and the national standard sequential test method;

[0016] Figure 3-1 It is a schematic diagram comparing the product acceptance probability of the sequential test method of the present invention and the national standard constant test method;

[0017] Figure 3-2 It is a schematic diagram comparing the number of test samples required for the sequential test method of the present invention and the national standard constant test method. DETAILED DESCRIPTION

[0018] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0019] Regarding the lack of atypical q in the national standard 0 , D, α, β corresponding to the sequential sampling test plan, the present invention provides a success-failure grouping sequential test plan design method, the method is not based on the likelihood ratio On this basis, you can set q at any 0 , D, α, β, when the number of test samples is expected to be large, the corresponding grouped sequential test plan is given. For products of various quality levels, the product pass rate performance of this plan is equivalent to that of the national standard test plan, but the required sample of participating products is significantly less than that of the national standard constant test, which is equivalent to the national standard sequential test.

[0020] See also Figure 1 The present invention provides a success-failure group sequential test method, the specific steps of which include:

[0021] 1. Enter the relevant parameters of the producer and the user.

[0022] Among them, the relevant parameters of the input manufacturer are: the manufacturer's risk threshold α and the good product quality level q 0 ; Input the relevant parameters of the user: the user risk threshold β and the poor quality level q 1 Let p 0 =1-q 0 , p 1 =1-q 1 .

[0023] 2. Based on the manufacturer-related parameters and the user-related parameters, calculate the maximum number of test samples N and the number of acceptances Ac, as well as group the samples of the test batch products.

[0024] As an embodiment, the calculation of the maximum number of test samples N and the number of received samples Ac based on the relevant parameters of the production party and the relevant parameters of the user party includes: initializing the total number of samples of the batch of products to be tested n and the number of failed samples m; based on the initialization of the total number of samples of the batch of products to be tested n, the number of failed samples m and the quality level of good products q 0 and the quality level of inferior products q 1 , calculate the producer risk probability Pa and the user risk probability Pb; by continuously updating m=m+1 and n=n+1 until Pa<α and Pb<β, the maximum number of test samples N=n, and the number of acceptances Ac=m.

[0025] Specifically, the specific steps of calculating the maximum number of test samples N and its acceptance number Ac include:

[0026] (2.1) Initialize the total number of samples of the batch to be tested n = 1, the number of failed samples m = 0, and set 1.2p 1 n rounds up to an integer and is recorded as t, let the discriminant number m t Equal to the smaller number between n and t, that is, m t =min(n-1,t);

[0027] (2.2) Calculate the risk probability of the producer and user risk probability Among them, p 0 =1-q 0 , p 1 =1-q 1 , B(·) is the beta function,

[0028] (2.3) If Pa<α and Pb<β, let N=n, Ac=m, and the calculation of N and Ac is completed; otherwise, execute (2.4);

[0029] (2.4) Update m, let m = m + 1, if m ≤ m t , execute (2.2); if m>m t , then let n=n+1, m=0, update m t , m t The update algorithm of is obtained according to the calculation method of (2.1);

[0030] (2.5) Execute (2.2).

[0031] Calculate the maximum number of test samples N and its acceptance number Ac, group the samples of the product batch to be tested, where the total number of samples of the product batch to be tested is N, calculate the number of groups z, and divide all the samples of the product to be tested into (1+z) groups as equally as possible. The specific grouping steps include:

[0032] (3.1) Initialize the number of groups z = 2;

[0033] (3.2) Calculation of Pt 1 , Pt 2 ,make

[0034] (3.3) If and At the same time, it is established, ended, and Pt is obtained 1 , Pt 2 and the number of groups z; otherwise, set z = z + 1 and execute (3.2);

[0035] Among them, n Z1 and n Z2 Take an integer, n Z1 and n Z2 The value principle is to make Around 0.01, when α≥0.1, the value n Z1 Make When β≥0.1, the value of n Z2 Make

[0036] Through steps 1 and 2, the total number of test samples N, the acceptance number Ac, and the risk probability criterion Pt can be obtained. 1 , Pt 2 and the number of groups z.

[0037] According to the number of groups z, the number of samples in each group in the total number of samples N is determined, and a total of (1+z) groups are divided, and the number of samples in each group is as equal as possible. Let n 1 equal Round up the value of 2 =N-zn 1 The number of samples in group 1 to group z is n. 1 , the number of samples in group 1+z is n 2 .

[0038] 3. Test each group of product samples to be tested one by one. After each group of product samples is tested, determine whether the test results can be obtained. If they can be obtained, terminate the test; if not, add the next group of product samples and continue the test until the test results are obtained. The test results refer to whether the product samples in the batch to be tested are qualified or unqualified.

[0039] It is understandable that after the batch product samples are grouped, a group sequential test is carried out, and the test steps specifically include:

[0040] (4.1) After grouping, each group of product samples to be tested is numbered, and the serial number of each group is recorded as i, 1≤i≤1+z. Let the initial value of i be 1, and randomly select n from the batch of product samples. 1 Products form Group 1;

[0041] (4.2) Starting from group 1, the test is started group by group, and all samples in the same group are tested at the same time;

[0042] (4.3) After the test of group i is completed, the number of samples that fail during the test from group 1 to the current group i is recorded as m, and the number of test samples is recorded as n;

[0043] (4.4) If i≤z holds, then calculate the risk probabilities Pa and Pb, where:

[0044]

[0045]

[0046] where n=in 1 ;

[0047] (4.5) Based on Pa and Pt 1 The size relationship between Pb and Pt 2 , judge whether the test result can be obtained. If so, terminate the test; if not, i=i+1, execute (4.3) until the test result can be obtained.

[0048] Among them, step (4.5) is based on Pa and Pt 1 The size relationship between Pb and Pt 2 The size relationship between the two is used to determine whether the test results can be obtained, including:

[0049] (d.1) If Pa <Pt 1 If the above condition is established, the batch of products will be rejected and the test will be terminated.

[0050] (d.2) If Pb <Pt 2 If the above conditions are met, the batch of products will be accepted and the test will be terminated.

[0051] (d.3) If Pa <Pt 1 and Pb <Pt 2 If none of them holds, let i=i+1, execute (4.3), and proceed to the next set of experiments.

[0052] The above step (4.4) also includes:

[0053] If i=1+z, the test is terminated after the 1+zth group of tests are completed, the total number of sample failures m during the entire test period is counted, and it is determined whether m≤Ac is true; if m≤Ac is true, the batch of product samples is accepted, otherwise the batch of product samples is rejected. At this time, the total number of product samples participating in the test n=zn 1 +n 2 .

[0054] The group sequential test method provided by the present invention is described below with a specific example.

[0055] Now we need to conduct a success-failure sequential sampling test on a batch of products, and give a conclusion of whether each sample is qualified or unqualified after the test. 0 =0.999, the risk threshold of the manufacturer α = 0.1; the poor quality level of the user's concern q 1 =0.998, user risk threshold β =0.1. Applying the method of the present invention, a group sequential test plan is designed, which includes the following steps:

[0056] (1) Initialization: From the known information, we can get: α = 0.1, β = 0.1, q 0 =0.999,q 1 =0.998, p 0 =0.001, p 1 =0.002.

[0057] (2) Calculate the total number of samples N and the number of receptions Ac.

[0058] After calculation, when N=10061 and Ac=14, Pa=0.087 and Pb=0.099, at which time Pa<α and Pb<β both hold true.

[0059] (3) Initialize the number of groups z = 2, let n Z1 =15 and n Z2 =15, And judge and Are they both true? If not, update z = z + 1. When z = 16, Pt 1 =0.0066, Pt 2 =0.0066, satisfying and All the requirements are met, save the current z, Pt 1 , Pt 2 .

[0060] (4) The test plan is designed and the test plan content is output: the total number of samples N = 10061, the number of received samples Ac = 14, the number of groups z = 16, and the risk probability criterion Pt 1 =0.0066, Pt 2 =0.0066.

[0061] The specific implementation steps of the test method for the test product samples are as follows:

[0062] (a) Determine the sample size for each group.

[0063] Let the number of samples in each group be as equal as possible, and divide them into 1+z groups in total. 1 =592, let n 2 = 589. The number of samples in group 1 to group z is n 1 , the number of samples in group 1+z is n 2 .

[0064] (b) After the i-th group completes the test, the number of samples that fail during the test from the first group to the current i-th group is recorded as m, and the number of test samples is recorded as n.

[0065] (c) If i≤z holds, then calculate the risk probabilities Pa and Pb.

[0066]

[0067]

[0068] where n=in 1 , and make the following judgments in turn.

[0069] (c.1) If Pa <Pt 1 If the above condition is established, the batch of products will be rejected and the test will be terminated.

[0070] (c.2) If p b <Pt 2 If the test is established, the batch of products will be accepted and the test will be terminated.

[0071] (c.3) If Pa <Pt 1 and Pb <Pt 2 If none of them holds, set i=i+1, execute (b), and proceed to the next set of experiments.

[0072] (d) If i=1+z, the test is terminated after the 1+zth group of tests are completed, the total number of sample failures m during the entire test period is counted, and it is determined whether m≤Ac is established. If m≤Ac is established, the batch of products is accepted, otherwise it is rejected.

[0073] The effectiveness of the method of the present invention can be verified by simulation and compared with the test of relevant national standards.

[0074] When 0 When , D, α, and β take typical values, the test scheme of the method of the present invention and the success-failure sequential test scheme of the national standard GB5080.5-1985 are simulated in a simulation manner. 0 , D, α, and β are within the range of the success-failure sequential test plan recommended by the national standard GB5080.5-1985. Figure 2-1 and Figure 2-2 The simulation comparison results of the above example are shown in Figure 2. Among them, the national standard success-failure sequential test scheme has a cutoff parameter N of 16563, an acceptance number Ac of 21, and the same grouping method as the example is used to divide the test into 17 groups approximately equally. Figure 2-1 and Figure 2-2 It shows that for good quality q 0 and difference product q 1 The product acceptance probability of the test scheme of the present invention is the same as that of the national standard sequential scheme, and the risk probability of both sides of the scheme does not exceed the threshold. For products of various quality levels, the number of test samples required is equivalent to that of the national standard scheme as a whole, and the number of test samples in some product quality ranges is even less than that of the national standard grouped sequential scheme.

[0075] When 0 When , D, α, and β are atypical values, the test scheme of the method of the present invention and the constant test scheme of the national standard GB5080.5-1985 are simulated in a simulation manner. For example, when the thresholds of the above example are changed to α = 0.15 and β = 0.1, and other parameters remain unchanged, the sequential grouping test scheme of the method of the present invention is: the total number of samples N = 8297, the number of acceptances Ac = 11, the number of groups z = 17, and the risk probability criterion Pt 1 =0.0095, Pt 2 =0.0062. The national standard constant test plan is: total sample size N = 8297, acceptance number Ac = 11. Figure 3-1 and Figure 2-1 This is the comparison result of the above example. Figure 3-1 and Figure 3-2 It shows that for products of various quality levels, the product acceptance rate of the test scheme of the method of the present invention is extremely consistent with the product acceptance rate of the relevant national standards, and the risk probability of both sides of the scheme does not exceed the threshold, but the number of test samples required is significantly less than that of the constant test scheme of the national standard.

[0076] The success-failure group sequential test method provided by the embodiment of the present invention is not based on the likelihood ratio and can be used in any setting of q 0, D, α, β, when the number of test samples is expected to be large, the corresponding grouped sequential test plan is given. For products of various quality levels, the product pass rate performance of this plan is equivalent to that of the national standard test plan, but the required sample of participating products is significantly less than that of the national standard constant test, which is equivalent to the national standard sequential test.

[0077] It should be noted that in the above embodiments, the description of each embodiment has its own emphasis, and for parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0078] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0079] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A success-failure group sequential test method, characterized in that: include: Input the relevant parameters of the producer and the user; Based on the manufacturer-related parameters and the user-related parameters, calculate the maximum number of test samples N and its acceptance number Ac, as well as the grouping of the test batch product samples; Each group of product samples to be tested is tested one by one. After each group of product samples is tested, it is determined whether the test results can be obtained. If they can be obtained, the test is terminated; if they cannot be obtained, the next group of product samples is added to continue the test until the test results are obtained. The test results refer to whether the product samples in the batch to be tested are qualified or unqualified; The grouping of the samples of the batch of products to be tested includes: (3.1) Initialize the number of groups z=2; (3.2) Calculation , ,make , ; (3.3) If and At the same time, it ends; otherwise, Then, execute (3.2); in, and Take the integer, and The value principle is to make , Around 0.01, when When Make ,when When Make ; The total number of samples of the batch of products to be tested is N The grouping of the test batch product samples includes: The samples of the tested batch of products are divided into 1+z groups, among which the number of samples of the first z groups is , equal The rounded-up value of the last group of product samples to be tested is , ; Each group of product samples to be tested is tested one by one. After each group of product samples is tested, it is determined whether the test results can be obtained. If so, the test is terminated; if not, the next group of product samples is added to continue the test until the test results are obtained. The test results refer to whether the product samples in the batch to be tested are qualified or unqualified, including: (4.1) After grouping, number each group of product samples to be tested, and record the serial number of each group as , ,make The initial value is 1, and the sample is randomly selected from the batch of products. Products form Group 1; (4.2) Starting from group 1, the test is started group by group, and all samples in the same group are tested at the same time; (4.3) In the After the experiment of each group is over, statistics are collected from the first group to the current group. The number of samples that failed during the test is recorded as m , the number of test samples is recorded as n ; (4.4) If If established, then calculate the risk probability , ,in: ； ； In the formula ; (4.5) Based on Pa and The size relationship between Pb and The size relationship is used to determine whether the test results can be obtained. If so, the test is terminated; if not, , execute (4.3) until the test results can be obtained.

2. The group sequential test method according to claim 1, characterized in that: The producer-related parameters include producer risk threshold and quality level of finished products The user-related parameters include the user risk threshold and poor quality level .

3. The group sequential test method according to claim 2, characterized in that: The maximum number of test samples is calculated based on the production-related parameters and the user-related parameters. N And its receiving number Ac, including: Initialize the total number of samples of the batch of products to be tested n and the number of failed samples m ; Based on the total number of samples of the initial batch of products to be tested n , the number of failed samples m And the quality level of good products and poor quality level , calculate the producer risk probability Pa and the user risk probability Pb; By constantly updating m = m +1 and n = n +1 until and , then the maximum number of test samples N = n , receiving number Ac= m .

4. The group sequential test method according to claim 3, characterized in that: The maximum number of test samples is calculated based on the production-related parameters and the user-related parameters. N And its receiving number Ac, including: (2.1) Initialize the total number of samples of the batch of products to be tested , the number of failed samples ,Will Round up to an integer and record it as t , let the discriminant number ; (2.2) Calculate the risk probability of the producer and user risk probability ;in, , , is the beta function, ; (2.3) If and , then let , , N , Ac is calculated; otherwise, execute (2.4); (2.4) Update ,make ,like m ≤ , execute (2.2); if , then let , ,renew ; (2.5) Execute (2.2).

5. The group sequential test method according to claim 1, characterized in that: Said (4.5) includes: (d.1) If If the above is established, the batch of products will be rejected and the test will be terminated; (d.2) If If established, the batch of products will be accepted and the test will be terminated; (d.3) If and If neither is true, then , execute (4.3) and continue to the next set of experiments.

6. The group sequential test method according to claim 1, characterized in that: Said (4.4) also includes: like Established, then after completing After the group test, terminate the test and count the total number of sample failures during the entire test period , and judge Is it established? If the test is successful, the batch of product samples will be accepted, otherwise the batch of product samples will be rejected. At this time, the total number of product samples participating in the test .

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