Abnormal value screening and control limit determining method for finite univariate reliability data based on normal quantile

Abstract

The invention belongs to the technical field of data analysis and statistical process control, and discloses an abnormal value screening and control limit determining method for finite single variable reliability data based on a normal quantile, which specifically comprises the following steps: acquiring a finite single variable reliability data set to be analyzed; sorting the finite single variable reliability data sets, and calculating an empirical cumulative distribution function value of each data point based on the sorted finite single variable reliability data sets; calculating a standard normal distribution quantile corresponding to each empirical cumulative distribution function value; and establishing a function relation model between a standard normal distribution quantile and an observed value of the sorted finite univariate reliability data set, substituting a target cumulative distribution function value into the function relation model, and carrying out extrapolation calculation to obtain an extreme quantile, so that normal, non-normal and even multi-modal distribution data can be effectively processed.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of data analysis and statistical process control, and particularly relates to a method for outlier screening and control limit determination of limited single variable reliability data based on normal quantile. BACKGROUND

[0002] In statistical data analysis, outliers are data points that deviate significantly from the overall distribution of the data set, usually representing unusually high or low values that are inconsistent with the general pattern. The existence of outliers may be caused by inherent variability, measurement errors, or may indicate novel or rare phenomena. Outliers are encountered in various types of data, including single variable, multivariate, time series, and spatial data sets. In the research and manufacturing process of integrated circuits, the analysis of reliability test data is crucial. Accurate identification of outliers and setting of control limits for statistical process control charts is a key step in monitoring process stability and ensuring product quality.

[0003] Currently, commonly used outlier detection methods such as Z-score method and interquartile range method are usually based on the assumption that the data follows a normal distribution. However, the reliability data collected in actual industrial environments often has characteristics such as limited sample size, high cost, and complex distribution form (such as non-normal, skewed, and multimodal), which severely limits the applicability and accuracy of traditional methods.

[0004] For non-normal distribution data, theoretically, a parameterized method can be used, i.e., first fitting the data to a specific known distribution, and then calculating the control limit based on the parameters of the distribution. However, this method requires the use of professional statistical software and the user to have corresponding statistical modeling knowledge, which is difficult to popularize in most manufacturing enterprises' engineering practice. In addition, for complex distribution forms such as multimodal, it is difficult to effectively model even with advanced statistical tools. Therefore, there is an urgent need for a simple, practical, and complex distribution assumption-free method that can be implemented on widely used general tools to effectively screen outliers and determine control limits for limited single variable reliability data.

[0005] The above content is only used to assist in understanding the technical solutions of the present application and does not represent an acknowledgement of the above content as prior art. SUMMARY

[0006] The main purpose of the present application is to provide a method for outlier screening and control limit determination of limited single variable reliability data based on normal quantile, aiming to solve the problem that the existing method needs to rely on professional statistical software and requires the user to have corresponding statistical modeling knowledge, which is difficult to popularize in most manufacturing enterprises engineering practice. In addition, for complex distribution forms such as multimodal, it is difficult to effectively model even using advanced statistical tools, and there is an urgent need for a simple, practical, and complex distribution assumption-free method that can be implemented on a general tool widely used by engineers to effectively screen outliers and determine control limits for limited single variable reliability data.

[0007] To achieve the above purpose, the present application provides a method for outlier screening and control limit determination of limited single variable reliability data based on normal quantile, comprising the following steps: Obtain the limited single variable reliability data set to be analyzed; Sort the limited single variable reliability data set, and calculate the empirical cumulative distribution function value of each data point based on the sorted limited single variable reliability data set; Calculate the standard normal distribution quantile corresponding to each empirical cumulative distribution function value; Establish a functional relationship model between the standard normal distribution quantile and the observation value of the sorted limited single variable reliability data set, wherein the functional relationship model is constructed in any of the following ways: Regression analysis is performed on all data points; Or select at least two representative data points, and establish a linear proportional relationship based on the coordinate values of the representative data points; Or regression analysis is performed on part of the data points at the high end and / or low end of the data; Substitute the target cumulative distribution function value into the functional relationship model to extrapolate and calculate the extreme quantile, which is used as the outlier screening and control limit.

[0008] In some embodiments, the empirical cumulative distribution function value F(t) is calculated by the formula F(t) = i / (N + 1), where i is the ranking of each data point in the sorted limited single variable reliability data set, and N is the total sample size of the sorted limited single variable reliability data set.

[0009] In some embodiments, the regression analysis is linear regression or nonlinear regression, and the nonlinear regression is quadratic polynomial regression.

[0010] In some embodiments, the linear proportional relationship is: Quantile (F3) = Quantile (F1) + k × [Quantile (F2) - Quantile (F1)]; Wherein, k is a proportional coefficient, F1 and F2 are empirical cumulative distribution function values of two selected representative points, and F3 is a target cumulative distribution function value to be solved.

[0011] In some embodiments, the regression analysis of the partial data points at the high end and / or the low end of the data is respectively used for the prediction of the high-end extreme quantile, and the last M data points after sorting are used for fitting, and the prediction of the low-end extreme quantile, and the first K data points after sorting are used for fitting, wherein M and K are positive integers set according to the sample size and the accuracy requirement.

[0012] In some embodiments, the regression analysis of all data points in the function relationship model is used for data that is normally distributed, the selection of at least two representative data points in the function relationship model is used for the establishment of a linear proportional relationship based on the coordinate values of the representative data points, and the regression analysis of the partial data points at the high end and / or the low end of the data in the function relationship model is used for data that is not normally distributed.

[0013] In some embodiments, the target cumulative distribution function value includes a target high-end cumulative distribution function value and a target low-end cumulative distribution function value.

[0014] In addition, in order to achieve the above-mentioned purpose, the application further provides an abnormal value screening and control limit determination device for limited single variable reliability data based on normal quantile, which comprises: An acquisition module is configured to acquire a limited single variable reliability data set to be analyzed; A calculation module is configured to sort the limited single variable reliability data set, and calculate an empirical cumulative distribution function value of each data point based on the sorted limited single variable reliability data set; The calculation module is configured to calculate a standard normal distribution quantile corresponding to each empirical cumulative distribution function value; A construction module is configured to establish a function relationship model between the standard normal distribution quantile and the observation value of the sorted limited single variable reliability data set, wherein the construction of the function relationship model is in any one of the following modes: Regression analysis of all data points; Or selection of at least two representative data points, and establishment of a linear proportional relationship based on the coordinate values of the representative data points; Or regression analysis of the partial data points at the high end and / or the low end of the data; The calculation module is configured to substitute a target cumulative distribution function value into the function relationship model, and to calculate an extreme quantile by extrapolation, which is used as an abnormal value screening and control limit.

[0015] Further, to achieve the above object, the present application also provides an apparatus for outlier screening and control limit determination of limited univariate reliability data based on normal quantile, which comprises a memory, a processor and an outlier screening and control limit determination program of limited univariate reliability data based on normal quantile stored in the memory and executable on the processor, and the program is configured to implement the steps of the method for outlier screening and control limit determination of limited univariate reliability data based on normal quantile.

[0016] Further, to achieve the above object, the present application also provides a storage medium, which stores an outlier screening and control limit determination program of limited univariate reliability data based on normal quantile, and the program is executable on a processor to implement the steps of the method for outlier screening and control limit determination of limited univariate reliability data based on normal quantile.

[0017] In the present application, a limited univariate reliability data set to be analyzed is obtained, the limited univariate reliability data set is sorted, and the empirical cumulative distribution function value of each data point is calculated based on the sorted limited univariate reliability data set; the standard normal distribution quantile corresponding to each empirical cumulative distribution function value is calculated; a functional relationship model between the standard normal distribution quantile and the observed value of the sorted limited univariate reliability data set is established, the target cumulative distribution function value is substituted into the functional relationship model, and the extreme quantile is calculated by extrapolation, and the above method can effectively process data of normal, non-normal and even multi-modal distribution. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 Flowchart of the first embodiment of the method for outlier screening and control limit determination of limited univariate reliability data based on normal quantile of the present application; Figure 2 Probability graph of 400 normal distribution data points drawn by Excel in the method for outlier screening and control limit determination of limited univariate reliability data based on normal quantile of the present application; Figure 3 Schematic diagram of NORM.S.INV(F(t)) and the observed value of the Gamma distribution data set in the method for outlier screening and control limit determination of limited univariate reliability data based on normal quantile of the present application; Figure 4The structure block diagram of the first embodiment of the abnormal value screening and control limit determination device for the normal quantile-based finite single variable reliability data of the application.

[0019] The implementation, functional features and advantages of the application will be further explained with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION

[0020] It should be understood that the specific embodiments described herein are merely illustrative of the application and are not intended to limit the application.

[0021] The embodiment of the application provides an abnormal value screening and control limit determination method for normal quantile-based finite single variable reliability data. Figure 1 , Figure 1 The flowchart of the first embodiment of the abnormal value screening and control limit determination method for normal quantile-based finite single variable reliability data of the application.

[0022] In the embodiment, the abnormal value screening and control limit determination method for normal quantile-based finite single variable reliability data comprises the following steps. Step S10: acquiring a finite single variable reliability data set to be analyzed.

[0023] In the embodiment, the execution subject of the embodiment is an abnormal value screening and control limit determination device for normal quantile-based finite single variable reliability data, wherein the abnormal value screening and control limit determination device for normal quantile-based finite single variable reliability data has functions of data processing, data communication and program running, and can be a computer terminal device or other network device, and of course can also be other devices with similar functions, and the embodiment does not limit this.

[0024] In statistical data analysis, outliers are data points that deviate significantly from the overall distribution of the dataset, often representing unusually high or low values that do not align with the general pattern. The presence of outliers can be caused by inherent variability, measurement errors, or can indicate novel or rare phenomena. Outliers are encountered in various types of data, including univariate, multivariate, time series, and spatial datasets. In the research and manufacturing process of integrated circuits, the analysis of reliability test data is crucial. Accurate identification of outliers and setting of control limits for statistical process control charts is a key step in monitoring process stability and ensuring product quality. Currently, commonly used outlier detection methods such as Z-score method and interquartile range method are usually based on the assumption that the data follows a normal distribution. However, the reliability data collected in actual industrial environments often has characteristics such as limited sample size, high cost, and complex distribution form (such as non-normal, skewed, and multimodal), which severely limits the applicability and accuracy of traditional methods. For non-normal distributed data, theoretically, parameterized methods can be used, i.e., first fitting the data to a specific known distribution, and then calculating the control limit based on the parameters of the distribution. However, this method requires the use of professional statistical software and the user to have corresponding statistical modeling knowledge, which is difficult to popularize in most manufacturing enterprises' engineering practice. In addition, for complex distribution forms such as multimodal, it is difficult to effectively model even with advanced statistical tools. Therefore, there is an urgent need for a simple, practical, and distribution-free method that can be implemented on widely used general tools by engineers to effectively screen outliers and determine control limits for limited univariate reliability data.

[0025] To solve the above technical problems, in the embodiment, a limited univariate reliability dataset to be analyzed is obtained; the limited univariate reliability dataset is sorted in an Excel environment, and the empirical cumulative distribution function value of each data point is calculated based on the sorted limited univariate reliability dataset; the standard normal distribution quantile corresponding to each empirical cumulative distribution function value is calculated in Excel; a functional relationship model between the standard normal distribution quantile and the observation value of the sorted limited univariate reliability dataset is established; the target cumulative distribution function value is substituted into the functional relationship model, and the extreme quantile is calculated by extrapolation. The above method can effectively handle data with normal, non-normal, and even multimodal distributions without using complex and expensive professional statistical software, significantly reducing the technical threshold and implementation cost of statistical process control. Specifically, the method can be implemented as follows.

[0026] It should be noted that the method proposed in the embodiment has the following core innovations: 1. No distribution assumption: By using the empirical cumulative distribution function (CDF) combined with linear extrapolation technology, the extreme quantiles (such as 0.00135 and 0.99865 quantile points) are directly estimated without relying on data distribution assumptions or complex parameter fitting.

[0027] 2. Excel standardization: Only need to sort data, calculate empirical CDF (formula: ) and call built-in function NORM.S.INV() to complete normal quantile conversion and linear regression extrapolation, reducing the dependence on statistical software.

[0028] 3. Small sample adaptability: For limited sample size scenarios, such as 741 (i.e. 1 / 0.00135), the extrapolation model is constructed by selecting high and low end data points (such as the first / last 10 points), solving the problem of invalidation of traditional quantile method. The accuracy of the forecast is related to the size of the limited sample. The larger the sample, the smaller the error.

[0029] 4. Multi-modal compatibility: Can handle complex distribution patterns (such as gamma distribution, multi-modal data), with an error of ≤8.8% under actual gamma data, meeting the industrial precision requirements.

[0030] This method significantly simplifies the outlier screening and SPC control limit setting process of reliability data (such as electromigration failure time and leakage current data in IC manufacturing).

[0031] In a specific implementation, in the embodiment, a limited univariate reliability data set to be analyzed needs to be obtained first. When the sample size of the data set is large enough, it becomes feasible to directly identify the quantile corresponding to the extreme low and high cumulative distribution function (CDF) values. For example, if the sample size N exceeds the threshold value 1 / N0, the quantile at 1 / N0 can be easily observed or solved using simple interpolation. Specifically, for the CDF values of 0.00135 and 0.99865 (usually used for screening limit determination), if the sample size is equal to 1 / 0.00135≈741, the minimum and maximum data points can be used as the estimates of the quantile (0.00135) and the quantile (0.99865), respectively. However, when the sample size is less than 741, alternative methods are needed to predict these extreme quantiles. To illustrate this point, a sample of 400 normally distributed data points is used to estimate the quantile (0.00135) and the quantile (0.99865). For this sample, the empirical CDF of the minimum value is approximately 1 / (400+1)=0.002494, and the empirical CDF of the maximum value is approximately 400 / 401=0.997506. That is, in actual applications, the limited univariate reliability data set to be analyzed can be a sample of 400 normally distributed data points.

[0032] Step S20: Sort the limited univariate reliability data set, and calculate the empirical cumulative distribution function value of each data point based on the sorted limited univariate reliability data set.

[0033] In a specific implementation, no complex statistical software is required in the embodiment, and Excel can be used, so the limited single-variable reliability data set needs to be sorted in the Excel environment in the embodiment, the sorting can be in ascending order, and then the empirical cumulative distribution function of each data point is calculated by using the data set after sorting.

[0034] It should be noted that the empirical CDF value F(t) and the corresponding NORM.S.INV(F(t)) value are shown in Table 1 (the first 20 data points) and Table 2 (the last 20 data points).

[0035] Table 1:

[0036] Table 2:

[0037] The empirical cumulative distribution function value F(t) is calculated by the formula F(t) = i / (N + 1), where i is the ranking of each data point in the sorted limited single-variable reliability data set, and N is the total sample size of the sorted limited single-variable reliability data set.

[0038] Further, the probability graph of 400 normal distribution data points drawn by Excel can be specifically referred to as shown in Figure 2

[0039] Step S30: Calculate the standard normal distribution quantile corresponding to each empirical cumulative distribution function value.

[0040] Step S40: Establish a function relationship model between the standard normal distribution quantile and the observation value of the sorted limited single-variable reliability data set.

[0041] Step S50: Substitute the target cumulative distribution function value into the function relationship model to extrapolate and calculate the extreme quantile.

[0042] In a specific implementation, after fitting based on the probability graph of the normal distribution data points in the above steps, Y = NORM.S.INV(F(t)) = 0.02718 + 0.966287t is obtained, where NORM.S.INV(F(t)) is the standard normal distribution quantile, and after rearrangement, the following can be obtained . Where t can be regarded as an estimated quantile corresponding to F(t).

[0043] ​It should be noted that the function relationship model in the embodiment is constructed in any one of the following ways: regression analysis is performed on all data points; at least two representative data points are selected, and a linear proportional relationship is established based on the coordinate values of the representative data points; or regression analysis is performed on part of the data points at the high end and / or low end of the data, respectively. The regression analysis on all data points is used for data that is normally distributed, the selection of at least two representative data points and the establishment of a linear proportional relationship based on the coordinate values of the representative data points is a non-distributed method, and the regression analysis on part of the data points at the high end and / or low end of the data is used for data that is not normally distributed.

[0044] The above method is regression analysis on all data points. For this method, the target cumulative distribution function values include the target high-end cumulative distribution function value and the target low-end cumulative distribution function value. Based on the above formula, that is, F(t) = 0.99865 and F(t) = 0.00135, finally, for F(t) = 0.99865, NORM.S.INV(0.99865) ≈ 3.000, it is obtained that:

[0045] For F(t) = 0.00135, NORM.S.INV(0.00135) ≈ -3.000, it is obtained that:

[0046] The t calculated above is the final extreme quantile, which is used as an abnormal value screening and control limit.

[0047] In an embodiment, a linear extrapolation method can also be used in the embodiment, in which two points are selected from the low end and the high end to define a linear relationship, as shown in Table 3, in which two points are selected from the low end and the high end (selected from Table 1 and Table 2).

[0048] Table 3:

[0049] In this way, the linear proportional relationship is: quantile(F3) = quantile(F1) + k * [quantile(F2) - quantile(F1)], that is, Quantile(F3) = Quantile(F1) + k * (Quantile(F2) - Quantile(F1)). Assuming linearity, the relationship between the quantile and its corresponding NORM. In the embodiment, the NORM.S.INV value can be expressed as:

[0050] For the estimated quantile (0.99865): F1=0.49875, F2=0.997506, and F3=0.99865.

[0051] Calculate k1: k1=( ) / ( )

[0052] Thus: Quantile(0.99865)=-0.0661+1.06836x(2.8735+0.0661)=3.07442.

[0053] The estimated quantile (0.00135): F1=0.49875, F2=0.002494, and F3=0.00135.

[0054] Calculate k2: k2= =1.06851 Thus: Quantile(0.00135)=-0.0661+1.06851x(-3.0288+0.0661)=-3.2318.

[0055] The above Quantile(0.99865) and Quantile(0.00135) are the final extreme quantiles, which are used as the outlier screening and control limits.

[0056] In an embodiment, the final quantiles can also be determined by performing regression analysis on the partial data points at the high end and / or low end of the data, respectively. Assuming that the data set is not normally distributed, the empirical CDF values and their corresponding NORM.S.INV(F(t)) values (Table 4 and Table 5) can be obtained, and NORM.S.INV(F(t)) and its observed values are plotted in Figure 3 Table 4 shows the first 15 ordered empirical F(t) and NORM.S.INV(F(t)). Table 5 shows the last 15 ordered empirical F(t) and NORM.S.INV(F(t)).

[0057] Table 4:

[0058] Table 5:

[0059] The regression analysis of the data points at the high end and / or low end of the data is performed for the prediction of the high-end extreme quantile, using the last M data points after sorting for fitting, and for the prediction of the low-end extreme quantile, using the first K data points after sorting for fitting, where M and K are positive integers set according to the sample size and accuracy requirements. Referring to Tables 4 and 5, the lowest ranked data point (1597.77) corresponds to an empirical CDF of 0.00249, which is higher than 0.00135, and the highest ranked data point (47628.95) corresponds to an empirical CDF of 0.9975, which is lower than 0.99865. Therefore, extrapolation is needed to estimate the required quantile.

[0060] In estimating the quantile (0.99865), linear regression is performed in Excel using the top 10 data points, resulting in the following formula: NORM.S.INV(F) = 0.39225 + 4.67x10-05*t.

[0061] Substituting NORM.S.INV(0.99865) = 3.0000, the extrapolated quantile is:

[0062] In estimating the quantile (0.00135), the lowest 10 data points are used to fit a quadratic curve in Excel, described as follows:

[0063] Substituting NORM.S.INV(0.00135) = -3.0000, the quadratic equation gives: t(F = 0.00135) ≈ 965 The t calculated above is the final extreme quantile, which is used as the control limit for outlier screening and control.

[0064] The target CDF values mentioned above, i.e., the target high-end cumulative distribution function value 0.99865 and the target low-end cumulative distribution function value 0.00135, are only for illustration and can be adjusted based on engineering requirements, including but not limited to 0.00135, 0.99865 quantile points, which are not limited in this embodiment.

[0065] The quantiles in the above steps are applicable to outlier identification in reliability test data; control limit setting for single-value control charts in statistical process control (SPC). The entire method can be automatically executed: integrated into yield analysis software through scripts, macros, or plug-ins.

[0066] In this embodiment, a finite univariate reliability dataset to be analyzed is obtained; the finite univariate reliability dataset is sorted, and the empirical cumulative distribution function value of each data point is calculated based on the sorted finite univariate reliability dataset; the standard normal distribution quantile corresponding to each empirical cumulative distribution function value is calculated; a functional relationship model between the standard normal distribution quantile and the observed values ​​of the sorted finite univariate reliability dataset is established, and the target cumulative distribution function value is substituted into the functional relationship model to extrapolate and obtain the extreme quantile. The above method can effectively handle data with normal, non-normal, and even multimodal distributions.

[0067] Furthermore, this embodiment of the invention also proposes a storage medium storing an outlier screening and control limit determination program for finite univariate reliability data based on normal quantiles. When the outlier screening and control limit determination program for finite univariate reliability data based on normal quantiles is executed by a processor, it implements the steps of the outlier screening and control limit determination method for finite univariate reliability data based on normal quantiles as described above.

[0068] Reference Figure 4 , Figure 4 This is a structural block diagram of the first embodiment of the outlier screening and control limit determination device for finite univariate reliability data based on normal quantiles of the present invention.

[0069] like Figure 4 As shown in the embodiment of the present invention, the outlier screening and control limit determination device for finite univariate reliability data based on normal quantiles includes: Module 10 is used to acquire the finite univariate reliability dataset to be analyzed; The calculation module 20 is used to sort the finite univariate reliability dataset and calculate the empirical cumulative distribution function value of each data point based on the sorted finite univariate reliability dataset. The calculation module 20 is used to calculate the standard normal distribution quantile corresponding to each empirical cumulative distribution function value; Module 30 is used to establish a functional relationship model between the standard normal distribution quantiles and the observations of the sorted finite univariate reliability dataset, wherein the method for constructing the functional relationship model includes any of the following: Perform regression analysis on all data points; Alternatively, select at least two representative data points and establish a linear proportional relationship based on the coordinate values ​​of the representative data points; Alternatively, regression analysis can be performed separately on some data points at the high and / or low ends of the data. The computing module 20 is configured to substitute the target cumulative distribution function value into the function relationship model to extrapolate and calculate an extreme quantile, and the extreme quantile is used as an abnormal value screening and control limit.

[0070] In the embodiment, a limited single-variable reliability data set to be analyzed is obtained; the limited single-variable reliability data set is sorted, and an empirical cumulative distribution function value of each data point is calculated based on the sorted limited single-variable reliability data set; a standard normal distribution quantile corresponding to each empirical cumulative distribution function value is calculated; a function relationship model between the standard normal distribution quantile and an observation value of the sorted limited single-variable reliability data set is established, a target cumulative distribution function value is substituted into the function relationship model, and an extreme quantile is calculated by extrapolation, and the above method can effectively process data of normal distribution, non-normal distribution, or even multimodal distribution.

[0071] In some embodiments, the empirical cumulative distribution function value F(t) is calculated by the formula F(t) = i / (N + 1), where i is the ranking of each data point in the sorted limited single-variable reliability data set, and N is the total sample size of the sorted limited single-variable reliability data set.

[0072] In some embodiments, the regression analysis is linear regression or nonlinear regression, and the nonlinear regression is quadratic polynomial regression.

[0073] In some embodiments, the linear proportional relationship is: Quantile (F3) = Quantile (F1) + k × [Quantile (F2) - Quantile (F1)]; where k is a proportional coefficient, F1 and F2 are empirical cumulative distribution function values of two selected representative points, and F3 is a target cumulative distribution function value to be solved.

[0074] In some embodiments, the regression analysis on the partial data points at the high end and / or low end of the data is a prediction of the high-end extreme quantile, and the last M data points after sorting are used for fitting, and the regression analysis on the partial data points at the high end and / or low end of the data is a prediction of the low-end extreme quantile, and the first K data points after sorting are used for fitting, where M and K are positive integers set according to the sample size and accuracy requirements.

[0075] In some embodiments, the regression analysis on all data points in the function relationship model is used for data of normal distribution, the selection of at least two representative data points in the function relationship model is a distribution-free method, and the establishment of a linear proportional relationship based on the coordinate values of the representative data points is a distribution-free method, and the regression analysis on the partial data points at the high end and / or low end of the data is used for data of non-normal distribution.

[0076] In some embodiments, the target cumulative distribution function value includes a target high-end cumulative distribution function value and a target low-end cumulative distribution function value.

[0077] The embodiment of the present application further provides an abnormal value screening and control limit determination device based on normal quantile limited univariate reliability data, which comprises a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory are in communication with each other through the communication bus, the memory is used for storing an abnormal value screening and control limit determination program based on normal quantile limited univariate reliability data, and the processor is used for executing the program stored in the memory to realize the abnormal value screening and control limit determination method based on normal quantile limited univariate reliability data.

[0078] The communication bus of the abnormal value screening and control limit determination device based on normal quantile limited univariate reliability data can be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus.

[0079] The communication interface is used for communication between the abnormal value screening and control limit determination device based on normal quantile limited univariate reliability data and other devices.

[0080] The memory can comprise a random access memory (RAM) and can also comprise a non-volatile memory (NVM), for example at least one disk memory. Optionally, the memory can also be at least one storage device located away from the aforementioned processor.

[0081] The processor described above can be a general processor, including a central processing unit (CPU), a network processor (NP), etc.; or can be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, a discrete gate or transistor logic device, a discrete hardware component.

[0082] In the above embodiments, the implementation can be wholly or partially achieved by software, hardware, firmware or any combination thereof. When implemented by software, the implementation can be wholly or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the processes or functions described in the embodiments of the present application are wholly or partially generated. The computer can be a general purpose computer, a special purpose computer, a computer network or other programmable apparatus. The computer instructions can be stored in a computer readable storage medium or transferred from one computer readable storage medium to another computer readable storage medium, for example, the computer instructions can be transferred from one website, computer, server or data center to another website, computer, server or data center through a wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) manner. The computer readable storage medium can be any available medium accessible by a computer or a data storage device such as a server, data center, etc. integrated with one or more available media. The available medium can be a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid state disk (SSD)), etc.

[0083] It is to be noted that the terms such as first and second, etc. are used herein merely to differentiate one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Also, the terms "comprising", "containing" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus including a list of elements does not only include those elements, but also includes other elements not expressly listed or inherent to such process, method, article or apparatus. Without more limitations, the element defined by the phrase "comprising a" does not exclude the presence of additional identical elements in the process, method, article or apparatus including the element.

[0084] Each of the embodiments in the specification is described in a relevant manner, and the same or similar parts between the embodiments can be referred to each other. Each of the embodiments focuses on the difference from other embodiments. In particular, for the system embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the part of the description of the method embodiments.

[0085] The above embodiments are only used to illustrate the technical solutions of the present application, but not limit the present application; although the present application is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features can be replaced by equivalent features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

[0086] It should be understood that the above is only for illustration, and does not constitute any limitation on the technical solutions of the present application. In specific applications, those skilled in the art can set up according to the needs, and the present application does not limit this.

[0087] It should be noted that the above-described workflow is only illustrative and does not limit the scope of protection of the present application. In actual application, those skilled in the art can select part or all of them to achieve the purpose of the embodiment scheme according to the actual needs, which is not limited here.

[0088] In addition, technical details not described in detail in the embodiment can be referred to the method for determining abnormal value screening and control limit of finite single variable reliability data based on normal quantile provided by any embodiment of the present application, which will not be repeated here.

[0089] Moreover, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of "including" "comprising" "having" "containing" or "decomprising" "containing" or "decomprising" or any other variation thereof, is intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements is not required to comprise only those elements on the list. Any process, method, article, or apparatus that comprises a list of elements is intended to comprise at least those elements in the list, but not excluding additional elements of which the process, method, article, or apparatus inherently possesses.

[0090] The above-mentioned embodiment numbers of the present application are only for description, and do not represent the advantages or disadvantages of the embodiments.

[0091] From the above description of the embodiments, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be realized by means of software and necessary general hardware platforms, and of course can also be realized by hardware, but in many cases the former is a better embodiment. Based on this understanding, the technical solutions of the present application or the part that contributes to the prior art can be embodied in the form of a software product, which is stored in a storage medium (such as a read-only memory (ROM) / RAM, a magnetic disk, an optical disk) and includes a plurality of instructions for making a terminal device (which can be a mobile phone, a computer, a server, or a network device) execute the methods described in the various embodiments of the present application.

[0092] The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application, and any equivalent structure or equivalent process transformation, or direct or indirect application in other related technical fields, is also included in the patent protection scope of the present application.

[0093] It can be understood that the system provided by the embodiments of the present application corresponds to the method provided by the embodiments of the present application, and the explanation, examples and beneficial effects of the related content can refer to the corresponding part in the above-mentioned method.

Claims

1. A method for outlier screening and control limit determination of limited univariate reliability data based on normal quantiles, characterized by, The method for determining the abnormal value screening and control limit of the limited single variable reliability data based on normal quantile comprises the following steps: acquiring a limited single variable reliability data set to be analyzed; sorting the limited single variable reliability data set, and calculating an empirical cumulative distribution function value of each data point based on the sorted limited single variable reliability data set; calculating a standard normal distribution quantile corresponding to each empirical cumulative distribution function value; establishing a functional relationship model between the standard normal distribution quantile and the observation value of the sorted limited single variable reliability data set, wherein the functional relationship model is established in any one of the following ways: performing regression analysis on all data points; or selecting at least two representative data points and establishing a linear proportional relationship based on the coordinate values of the representative data points; or performing regression analysis on part of the data points at the high end and / or low end of the data, respectively; substituting a target cumulative distribution function value into the functional relationship model to extrapolate and calculate an extreme quantile, which is used as the abnormal value screening and control limit.

2. The method for outlier screening and control limit determination of finite univariate reliability data based on normal quantile of claim 1, wherein, The empirical cumulative distribution function value F(t) is calculated by the formula F(t) = i / (N + 1), wherein i is the ranking of each data point in the sorted limited single variable reliability data set, and N is the total sample size of the sorted limited single variable reliability data set.

3. The method for outlier screening and control limit determination of finite univariate reliability data based on normal quantile of claim 1, wherein, The regression analysis is linear regression or nonlinear regression, and the nonlinear regression is quadratic polynomial regression.

4. The method for outlier screening and control limit determination of finite univariate reliability data based on normal quantile of claim 1, wherein, The linear proportional relationship is: quantile (F3) = quantile (F1) + k × [quantile (F2) - quantile (F1)]; wherein k is a proportional coefficient, F1 and F2 are the empirical cumulative distribution function values of the selected two representative points, and F3 is the target cumulative distribution function value to be solved.

5. The method for outlier screening and control limit determination of finite univariate reliability data based on normal quantile of claim 1, wherein, The regression analysis on part of the data points at the high end and / or low end of the data is used for prediction of the extreme quantile at the high end, and the last M data points after sorting are used for fitting, and prediction of the extreme quantile at the low end, and the first K data points after sorting are used for fitting, wherein M and K are positive integers set according to the sample size and accuracy requirements.

6. The method for outlier screening and control limit determination of finite univariate reliability data based on normal quantile of claim 1, wherein, The regression analysis on all data points in the functional relationship model is used for data in normal distribution, the linear proportional relationship based on the coordinate values of the representative data points in the functional relationship model is a distribution-free method, and the regression analysis on part of the data points at the high end and / or low end of the data in the functional relationship model is used for data in non-normal distribution.

7. The method for outlier screening and control limit determination of finite univariate reliability data based on normal quantile of claim 1, wherein, The target cumulative distribution function value includes a target high-end cumulative distribution function value and a target low-end cumulative distribution function value.

8. A device for outlier screening and control limit determination of finite univariate reliability data based on normal quantiles, characterized by, The device for determining the abnormal value screening and control limit of the limited single variable reliability data based on normal quantile is applied to the method for determining the abnormal value screening and control limit of the limited single variable reliability data based on normal quantile, and comprises: an acquisition module for acquiring a limited single variable reliability data set to be analyzed; a calculating module configured to sort the limited single-variable reliability data set and calculate an empirical cumulative distribution function value of each data point based on the sorted limited single-variable reliability data set; the calculating module is configured to calculate a standard normal distribution quantile corresponding to each empirical cumulative distribution function value; a constructing module configured to establish a functional relationship model between the standard normal distribution quantile and the observed value of the sorted limited single-variable reliability data set, wherein the functional relationship model is established in any of the following ways: performing regression analysis on all data points; or selecting at least two representative data points and establishing a linear proportional relationship based on the coordinate values of the representative data points; or performing regression analysis on part of the data points at the high end and / or low end of the data points, respectively; the calculating module is configured to substitute a target cumulative distribution function value into the functional relationship model to extrapolate and calculate an extreme quantile, and the extreme quantile is used as an abnormal value screening and control limit.

9. A normal quantile based outlier screening and control limit determination device for limited univariate reliability data, characterized by, The abnormal value screening and control limit determination device based on the normal quantile of the limited single-variable reliability data comprises a memory, a processor, and an abnormal value screening and control limit determination program based on the normal quantile of the limited single-variable reliability data stored on the memory and executable on the processor, wherein the abnormal value screening and control limit determination program based on the normal quantile of the limited single-variable reliability data is configured to implement the steps of the abnormal value screening and control limit determination method based on the normal quantile of the limited single-variable reliability data according to any one of claims 1 to 7.

10. A storage medium, characterized by The storage medium stores an abnormal value screening and control limit determination program based on the normal quantile of the limited single-variable reliability data, and the abnormal value screening and control limit determination program based on the normal quantile of the limited single-variable reliability data is implemented when executed by the processor to implement the steps of the abnormal value screening and control limit determination method based on the normal quantile of the limited single-variable reliability data according to any one of claims 1 to 7.

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