Small-batch product sampling inspection method

Abstract

The invention discloses a small-batch product sampling inspection method. The method comprises the following steps: S1, acquiring quality data of historical products with the same specification as a to-be-detected product; s2, dividing the historical products into a plurality of subgroups with the same production time period according to a production time sequence, performing consistency analysis on the quality data statistical values of the historical products in the plurality of subgroups, and determining a sampling inspection batch according to a consistency analysis result; and S3, carrying out sampling inspection on the to-be-inspected products according to the sampling inspection batch. According to the invention, sample capacity expansion is carried out according to the consistency analysis result of historical product quality, and the expanded sample capacity is ensured to be based on a stable production process, so that the sampling inspection result of small-batch products is more representative; and through statistical process control and process capability inspection, the sampling ability of small-batch products after sample capacity expansion is ensured.

Description

Technical Field

[0001] The invention belongs to the technical field of quality inspection, and in particular relates to a small batch product sampling inspection method. Background Art

[0002] Small batch products cannot be sampled for testing due to their small sample size. They generally need to be fully inspected, which has low testing efficiency and high cost. In order to sample and inspect small batches of products, it is necessary to expand their sample size. The sample size expansion method used in the prior art ignores the inherent fluctuations in the production process. People, machines, materials, methods, and environments are not necessarily in a controlled stable state. Products produced continuously over a period of time may have different quality levels, resulting in the conclusions drawn from sampling and inspecting the expanded batch that cannot represent the quality of small batch products. Summary of the invention

[0003] The purpose of the present invention is to provide a small batch product sampling inspection method to solve the problem that when the sample capacity of a small batch of products is expanded, the inherent fluctuations of the production process are ignored, resulting in the conclusion drawn when the expanded batch is sampled and inspected cannot represent the quality of the small batch products.

[0004] The present invention is achieved through the following technical solutions:

[0005] A small batch product sampling inspection method includes the following steps: S1, obtaining quality data of historical products with the same specifications as the product to be inspected; S2, dividing the historical products into several subgroups with the same production time period according to the production time sequence, performing consistency analysis on the quality data statistical values ​​of the historical products in the several subgroups, and determining the sampling inspection batch according to the consistency analysis results; S3, performing sampling inspection on the product to be inspected according to the sampling inspection batch.

[0006] In some embodiments, the quality data statistics include product failure rates.

[0007] In some embodiments, a consistency analysis is performed on the quality data statistics of historical products in several subgroups, and a sampling inspection batch is determined based on the consistency analysis results, including: sorting the several subgroups according to production time; performing a consistency hypothesis test on the quality data statistics of historical products in multiple consecutive subgroups, finding the largest number of consecutive subgroups that can pass the consistency hypothesis test and using them as the inspection batch, and determining the number of historical products in the inspection batch as the sampling inspection batch.

[0008] In some embodiments, it also includes: judging whether the product to be inspected can be inspected by sampling inspection based on the quality data of historical products in the inspection batch.

[0009] In some embodiments, judging whether the product to be inspected can be inspected by sampling inspection based on the quality data of historical products in the inspection batch includes: judging whether the inspection batch is in a statistical control state; if the inspection batch is in a statistical control state, determining that the product to be inspected can be inspected by sampling inspection.

[0010] In some embodiments, determining whether the inspection batch is in a state of statistical control includes: determining whether the range and mean of the quality data of the historical products in the several subgroups meet the range requirements and the mean requirements respectively; if the range and mean of the quality data of the historical products in the several subgroups meet the range requirements and the mean requirements respectively, then determining that the inspection batch is in a state of statistical control.

[0011] In some embodiments, the range requirement includes: the ranges of the quality data of historical products in several subgroups are all between the upper control limit and the lower control limit of the range, and there are no abnormal patterns or trends; the mean requirement includes: the means of the quality data of historical products in several subgroups are all between the upper control limit and the lower control limit of the mean, and there are no abnormal patterns or trends.

[0012] In some embodiments, judging whether the products to be inspected can be inspected by sampling inspection based on historical product quality data within the inspection batch also includes: judging whether the process capability of the inspection batch meets the requirements; if the process capability of the inspection batch meets the requirements, then judging whether the products to be inspected can be inspected by sampling inspection.

[0013] In some embodiments, determining whether the process capability of the inspection batch meets the requirements includes: obtaining a process capability index based on quality data of historical products in the inspection batch, and determining whether the process capability index meets the requirements.

[0014] In some embodiments, obtaining the process capability index based on the quality data of historical products in the inspection batch includes: determining whether the quality data of the historical products in the inspection batch obeys the normal distribution; if the quality data of the historical products in the inspection batch obeys the normal distribution, directly calculating the process capability index based on the quality data of the historical products in the inspection batch; if the quality data of the historical products in the inspection batch does not obey the normal distribution, converting the quality data of the historical products in the inspection batch into a normal distribution, and calculating the process capability index based on the converted quality data of the historical products in the inspection batch.

[0015] In some embodiments, determining whether the quality data of historical products in the inspection batch obeys a normal distribution includes: performing a normal distribution goodness of fit test on the quality data of historical products in the inspection batch; if the normal distribution goodness of fit test passes, it is determined that the quality data of historical products in the inspection batch obeys a normal distribution.

[0016] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0017] 1. Expand the sample size based on the consistency analysis results of historical product quality, ensure that the expanded sample size is based on a stable production process, and make the results of small-batch product sampling inspection more representative.

[0018] 2. Ensure the sampling feasibility of small batch products after the sample capacity is expanded through statistical process control and process capability testing. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0020] Figure 1 This is a flow chart of Embodiment 1 of the present invention.

[0021] Figure 2 This is a metering coefficient table according to an embodiment of the present invention.

[0022] Figure 3 Embodiment 1 of the present invention Control chart.

[0023] Figure 4 Schematic diagram of process capability index evaluation in Example 1 of the present invention. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0025] Embodiment 1

[0026] like Figure 1 As shown, this embodiment is a small batch product sampling inspection method, including the following process:

[0027] S1. Obtain the quality data of historical products with the same specifications as the product to be tested;

[0028] S21, dividing the historical products into several subgroups with the same production time period according to the production time sequence, performing consistency analysis on the quality data statistics of the historical products in the several subgroups, and determining the sampling inspection batch according to the consistency analysis results;

[0029] S22. Determine whether the product to be inspected can be inspected by sampling inspection based on the quality data of the historical products in the inspection batch.

[0030] S3. Perform sampling inspection on the products to be inspected according to the sampling inspection batch.

[0031] Generally, manufacturers use drawing numbers to determine product specifications, so historical product quality data can be collected according to part drawing numbers. Before collecting historical product quality data, the quality characteristics of the product need to be identified.

[0032] The specific collection period can be determined according to the specific small batch products. In this embodiment, the measuring machine is used to automatically collect measured data of historical products with the same specifications, and the collection period is 1 year.

[0033] Step S21 is specifically as follows: sorting the several subgroups according to production time; performing a consistency hypothesis test on the quality data statistics of historical products in multiple consecutive subgroups, finding out the largest number of consecutive subgroups that can pass the consistency hypothesis test and taking them as the inspection batch, and determining the number of historical products in the inspection batch as the sampling inspection batch.

[0034] The purpose of step S21 is to find the longest time period for stable production. The quality data statistical value can be selected according to the demand, and the unqualified rate of the product is used in this embodiment.

[0035] Assume that the production time period is b days, that is, the products produced in b days are regarded as a subgroup, and there are a subgroups in total. The number of historical products in each subgroup is represented by n 1. 、n 2. ……n a. Indicates that the number of qualified products and unqualified products in each subgroup is calculated, where the number of qualified products in each subgroup is represented by n 11 、n 21 ……n a1 Represented by n as the number of defective products 12 、n 22 ……n a2 The details are shown in the following Table 1.

[0036] Table 1 Historical product quality data statistics

[0037]

[0038]

[0039] where n .1 is the total number of qualified products, n .2 is the total number of defective products, n aIt is the quantity of all historical products produced during the collection period.

[0040] There are many consistency analysis methods, which can be selected according to needs. This embodiment adopts the consistency hypothesis test method, and the specific steps are as follows:

[0041] The quality level consistency test problem of c consecutive subgroups is reduced to the following consistency hypothesis test:

[0042] Null hypothesis H0: p1=p2=……=p c ;

[0043] Alternative hypothesis: H1: p1, p2...p c Not all equal;

[0044] Among them, p1, p2, ..., p c Represents the product failure rate for each consecutive subgroup.

[0045] Calculate the consistency of the unqualified rate of group C products and construct the statistic, i.e., the chi-square value, as follows:

[0046]

[0047] n c represents the total number of historical products of consecutive c subgroups, when n c →∞, Z c The distribution of tends to the chi-square distribution with c-1 degrees of freedom if It means that H0 is accepted at the significance level of α, and the consistency hypothesis test is passed, that is, the quality level of the parts in group c is consistent; if The consistency hypothesis test fails, and the quality levels of the parts in group c are inconsistent. It can be obtained by table lookup. The value of α can be determined according to the required accuracy. If there is no special requirement, 0.05 can be used.

[0048] In order to obtain the sampling inspection batch, it is necessary to find the longest period of stable production, that is, to find the continuous subgroups with the largest number of subgroups that can pass the above consistency hypothesis test, that is, to find the largest c value. max Indicates that the continuous c max All historical products in the subgroup are taken as inspection batches, and the inspection batches (i.e. b*c max Total historical product volume (produced in days) As inspection batch.

[0049] If you cannot find any c value that can pass the consistency hypothesis test, it means that the product quality fluctuates significantly in a short period of time. The product quality should be improved. After the improvement, the above steps should be repeated until a c value that passes the consistency hypothesis test can be found, and then c can be found from it. max and

[0050] If the production environment, such as production equipment, changes occur, the above steps should be repeated to calculate a new sampling inspection batch.

[0051] Before conducting sampling inspection, it is necessary to determine whether small batches of products can be inspected by sampling inspection, that is, to determine the sampling feasibility of small batches of products. If the inspected products reach statistical steady state, that is, they are in a state of statistical control, and the process capability is sufficient, the conclusions obtained by sampling inspection on small batches of products with expanded sample capacity can better represent the quality of the batch of products.

[0052] The specific judgment steps are: first determine whether the historical product quality data in the inspection batch is in a state of statistical control. If it is in a state of statistical control, then use the process capability index to determine whether the process capability is sufficient. If the process capability index meets the requirements, then determine that the product to be inspected can be inspected by sampling inspection.

[0053] For measurement data, when the process contains only normal fluctuations, the quality data X of the process output presents a normal distribution N(μ,б 2 ), where μ is the normal mean and б is the standard deviation. To determine whether the inspection batch is in a statistical control state, the mean and range control can be used, or other control methods can be selected. This embodiment uses the mean and range control, and the specific steps are:

[0054] Determine whether the range and mean of the quality data of the historical products in the several subgroups meet the range requirements and the mean requirements respectively; if the range and mean of the quality data of the historical products in the several subgroups meet the range requirements and the mean requirements respectively, determine that the inspection batch is in a statistical control state.

[0055] The range requirement can be: requiring the range of the quality data of historical products in all subgroups to be between the upper control limit and the lower control limit of the range, and without abnormal patterns or trends;

[0056] The mean requirement can be: requiring that the means of the quality data of historical products in all subgroups are between the upper control limit and the lower control limit of the mean, and there are no abnormal patterns or trends.

[0057] In actual operation, two control charts are needed, one for controlling μ and one for controlling б.

[0058] Mean-range chart Control chart is the most commonly used and basic control chart among measurement control charts, such as Figure 3 As shown, the mean The control chart is used to observe the change of the mean of the normal distribution, and the range R control chart is used to observe the dispersion of the normal distribution, that is, the fluctuation of quality. The control chart combines the two to observe changes in the normal distribution and is suitable for situations where the control object is a measurement value such as length, weight, strength, purity, time and production volume.

[0059] Assume that the number of historical products in the i-th subgroup is m.

[0060] Mean of historical product quality data in the i-th subgroup:

[0061] in Represents the quality data of each historical product in the i-th subgroup.

[0062] The quality data of historical products in the i-th subgroup is extremely poor: R i =x imax -x imin ;

[0063] where x imax and x min Respectively represent the maximum and minimum values ​​of the quality data of the historical products in the i-th subgroup.

[0064] In order to facilitate observation, it is generally necessary to draw the mean The center line of the control chart and the range R chart is the average of the means and the average of the ranges.

[0065] The average of the quality data means of the historical products in all subgroups:

[0066] The average value of the extreme values ​​of the quality data of the historical products in all subgroups:

[0067] Next, you need to set the upper and lower control limits for the mean and range. Distribution and mathematical expectation of R distribution μ R and variance б R are all unknown and need to be estimated using data from a sample group.

[0068] Upper control limit for the mean:

[0069] Lower control limit for the mean:

[0070] Upper control limit for range:

[0071] Lower control limit for range:

[0072] in and Used to estimate The value of

[0073] and To estimate μ R ±3σ R The value of

[0074] A2, D3, and D4 are coefficients related to the number of historical products in the subgroup, which can be obtained by looking up the table, such as Figure 2 shown.

[0075] Finally made Control chart and R control chart, that is, Point each Connect them into a broken line and point out each R on the R control chart. i Connect them into a broken line and draw the center line and upper and lower control limits UCL R , LCL R The center line is usually represented by a solid line, and the upper and lower control lines are usually represented by dotted lines. Control diagram Figure 3 shown.

[0076] You can first check on the R control chart whether the quality data range of the historical products in the sub-groups exceeds the upper and lower control limits of the range, and whether there are any abnormal patterns or trends. When it is determined that the range R is under control, you can move on to Control chart analysis also checks whether the mean of the quality data of historical products in the sub-groups exceeds the upper and lower control limits of the mean, and whether there are any abnormal patterns or trends.

[0077] Abnormal patterns or trends can be determined based on actual production conditions or based on the provisions given in some current production standards.

[0078] For example, the national standard GB / T 4091-2001 stipulates that when the control chart meets the following four conditions, it can be concluded that the process is in statistical control:

[0079] 1. Points walk randomly around the center line;

[0080] 2. The point is within the upper and lower control lines;

[0081] 3. No chain, trend and other patterns;

[0082] 4. The process is stable and predictable.

[0083] When any of the following conditions occur on the control chart, it can be concluded that the process is not in statistical control:

[0084] 1. The point exceeds the upper and lower control lines;

[0085] 2. Chains, trends, cycles, etc. appear;

[0086] 3. The cause can be identified.

[0087] If it is found that the inspection batch is not in a state of statistical control, the cause should be identified in time and the process steady state should be adjusted.

[0088] When a process is in a state of statistical control, we should be concerned about whether the process has the ability to meet technical standards and technical requirements. Therefore, we should also analyze the technical steady state of the process. The technical steady state is affected by the occasional fluctuations. To improve the technical steady state, we need to reduce the occasional fluctuations. The process technical steady state is generally characterized by process capability. The commonly used indicator to measure process capability is the process capability index C. p , which indicates the degree to which the process capability meets the technical standards (product specifications, tolerances). Only when the process capability is sufficient can it be determined whether the product to be inspected can be inspected by sampling inspection, that is, whether the process capability of the inspection batch meets the requirements. If the process capability of the inspection batch meets the requirements, it is determined that the product to be inspected can be inspected by sampling inspection. That is, the process capability index is obtained based on the quality data of historical products in the inspection batch to determine whether the process capability index meets the requirements.

[0089] The premise of using the process capability index is that the quality data of the historical products in the inspection batch conforms to the normal distribution, so it is necessary to first determine whether the quality data of the historical products in the inspection batch obeys the normal distribution. If it obeys the normal distribution, the process capability index is calculated directly; if it does not obey the normal distribution, it is necessary to convert the quality data of the historical products in the inspection batch into a normal distribution, and then calculate the process capability index based on the converted quality data of the historical products in the inspection batch.

[0090] An appropriate method may be selected according to the difficulty of calculation or accuracy requirements to determine whether the historical product quality data within the inspection batch obeys the normal distribution. This embodiment adopts the method of normal distribution goodness of fit test.

[0091] The specific method for normal distribution goodness of fit test is:

[0092] First, make the following assumptions:

[0093] Null hypothesis H0: The population obeys normal distribution;

[0094] Alternative hypothesis H1: The population does not follow a normal distribution;

[0095] Next, the test statistic is calculated. In this embodiment, the Anderson–Darling test statistic is used to measure the gap between the assumed distribution and the actual distribution of the data.

[0096] The calculation formula is as follows:

[0097] Anderson–Darling test statistic:

[0098] Where n is the number of samples, F norm (x) is the theoretical distribution function of normal distribution, F D (x) The distribution function of the sample. Calculate A 2 Then, according to A 2 Calculate the P value.

[0099] When the P value is greater than 0.05, H0 is accepted, that is, the data follows a normal distribution;

[0100] When the P value is less than 0.05, it means that there is sufficient reason to believe that the data does not obey the normal distribution. At this time, the data needs to be normally transformed. The normal transformation can be performed using transformation methods such as Box-Cox.

[0101] Process capability index is expressed as C p It is expressed as follows:

[0102]

[0103] Where USL is the upper specification limit, LSL is the lower specification limit, and σ is the standard deviation of the production process.

[0104] When the distribution range of quality data exceeds the upper and lower limits of the specification, defective products will appear. The defective product rate can be calculated using the following formula;

[0105] Defective product rate: P = P (X<LSL or X> USL)=P(X<LSL)+P(X> USL);

[0106] The relationship between the process capability index and the defective product rate can show the process capability.

[0107] The probability that the distribution range of quality data exceeds the upper specification limit is expressed as P U It means that the probability that the distribution range of quality data exceeds the lower limit of specification is P L Indicates that the defective rate P = P U +P L ;

[0108]

[0109] Where: μ is the mean of the normal distribution function, σ is the standard deviation, is a random variable that follows a standard normal distribution, φ represents The distribution function of the standard normal distribution, φ(X)=P(t <X);T=2(USL-μ)

[0110] Due to symmetry, P L =P(X <LSL)=1-φ(3C P ).

[0111] Therefore, the defective rate P = P U +P L =2-2φ(3C P )=2φ(-3C P ).

[0112] Under the premise of knowing the acceptable quality level AQL, it can be determined that the production process capability to achieve the AQL standard should meet the following conditions:

[0113]

[0114] If the AQL or defective product rate requirements are unknown, in order to ensure stable production quality, the process capability can be evaluated according to Table 2 below.

[0115] Table 2 Process capability evaluation criteria

[0116]

[0117]

[0118] According to the above table, C can be adjusted according to the actual situation of the process. p The value should be selected according to the requirements. For the existing process, the general requirement is C p ≥1.33 (i.e., defective product rate P < 0.0006%); For new processes or existing processes related to safety, strength or key parameters, C is required p ≥1.50, and new processes for safety, strength or key parameters require C p ≥1.67.

[0119] For the sampling inspection method, please refer to the sampling plan in Table 3 below.

[0120] Table 3 Sampling inspection plan

[0121]

[0122]

[0123] An example is provided below.

[0124] The geometric feature data of structural part A produced in small batches in a factory over the past year were collected, and these parts A were divided into 20 subgroups. The significance level α was set to 0.05, and the consistency analysis results are shown in Table 4 below.

[0125] Table 4 Consistency analysis results

[0126]

[0127]

[0128] From the above table, we can see that The maximum value of c is 10, that is, all parts A from the 1st to the 10th are the inspection batch, that is, 875. These 875 parts A are taken as the inspection batch. The control chart does not exceed the control limit, there is no abnormal pattern or trend, and the process capability index C p =1.79≥1.67, the grade is I, which meets the requirements, indicating that small batch production of parts A with the same specifications can be sampled and inspected. The specific process is as follows Figure 4 shown.

[0129] The inspection level for part A is II, which is a general inspection level without special requirements. The acceptable quality level AQL (percentage of defective products) is 1, and the sampling plan type is single sampling.

[0130] The sampling inspection procedure is summarized in Table 5. According to the table, the final sampling plan (n, Ac) is (80, 2). Compared with the full inspection, the inspection cost of this plan is reduced by 91%.

[0131] Table 5 Sampling inspection procedures

[0132]

[0133]

[0134] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification or equivalent change made to the above embodiment based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A small batch product sampling inspection method, characterized in that: The steps include: S1. Obtain the quality data of historical products with the same specifications as the product to be tested; S2. Divide the historical products into several subgroups with the same production time period according to the production time sequence, perform consistency analysis on the quality data statistics of the historical products in the several subgroups, and determine the sampling inspection batch according to the consistency analysis results; S3. Perform sampling inspection on the products to be inspected according to the sampling inspection batch.

2. The small batch product sampling inspection method according to claim 1 is characterized in that: The quality data statistics include product failure rate.

3. The small batch product sampling inspection method according to claim 1 is characterized in that: The consistency analysis is performed on the quality data statistics of the historical products in the several subgroups, and the sampling inspection batch is determined according to the consistency analysis results, which includes: sorting the several subgroups according to the production time; performing a consistency hypothesis test on the quality data statistics of the historical products in multiple consecutive subgroups, finding the largest number of consecutive subgroups that can pass the consistency hypothesis test and taking them as the inspection batch, and determining the number of historical products in the inspection batch as the sampling inspection batch.

4. The small batch product sampling inspection method according to claim 3 is characterized in that: Also includes: Determine whether the product to be inspected can be inspected by sampling inspection based on the quality data of historical products in the inspection batch.

5. The small batch product sampling inspection method according to claim 4 is characterized in that: The determining whether the product to be inspected can be inspected by sampling inspection based on the quality data of historical products in the inspection batch includes: determining whether the inspection batch is in a statistical control state; if the inspection batch is in a statistical control state, determining that the product to be inspected can be inspected by sampling inspection.

6. The small batch product sampling inspection method according to claim 5 is characterized in that: Determining whether the inspection lot is in a statistical control state includes: Determine whether the range and mean of the quality data of the historical products in the several subgroups meet the range requirements and the mean requirements respectively; if the range and mean of the quality data of the historical products in the several subgroups meet the range requirements and the mean requirements respectively, determine that the inspection batch is in a statistical control state.

7. The small batch product sampling inspection method according to claim 6 is characterized in that: The range requirements include: the ranges of the quality data of the historical products in the plurality of subgroups are all between the upper control limit and the lower control limit of the range, and there are no abnormal patterns or trends; The mean requirement includes: the means of the quality data of the historical products in the plurality of subgroups are all between the upper control limit and the lower control limit of the mean, and there are no abnormal patterns or trends.

8. The small batch product sampling inspection method according to claim 4 is characterized in that: The determining whether the product to be inspected can be inspected by sampling inspection based on the historical product quality data in the inspection batch also includes: determining whether the process capability of the inspection batch meets the requirements; if the process capability of the inspection batch meets the requirements, determining that the product to be inspected can be inspected by sampling inspection.

9. The small batch product sampling inspection method according to claim 8, characterized in that: The determining whether the process capability of the inspection batch meets the requirements includes: obtaining a process capability index according to quality data of historical products in the inspection batch, and determining whether the process capability index meets the requirements.

10. The small batch product sampling inspection method according to claim 9, characterized in that: The step of obtaining the process capability index based on the quality data of the historical products in the inspection batch includes: judging whether the quality data of the historical products in the inspection batch obeys a normal distribution; if the quality data of the historical products in the inspection batch obeys a normal distribution, directly calculating the process capability index based on the quality data of the historical products in the inspection batch; if the quality data of the historical products in the inspection batch does not obey a normal distribution, converting the quality data of the historical products in the inspection batch into a normal distribution, and calculating the process capability index based on the quality data of the historical products in the inspection batch after the conversion.

11. The small batch product sampling inspection method according to claim 10, characterized in that: The determining whether the quality data of the historical products in the inspection batch obeys the normal distribution includes: performing a normal distribution goodness of fit test on the quality data of the historical products in the inspection batch; if the normal distribution goodness of fit test passes, it is determined that the quality data of the historical products in the inspection batch obeys the normal distribution.

Images