JP2010146197A - Control chart creation device and control chart creation program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To properly perform trend control when moderate long-term fluctuation is allowed, and short-term fluctuation is detected as an abnormal condition. <P>SOLUTION: The control chart creation device is provided with: an EWMA calculation part (11) for receiving data (X<SB>i</SB>) to be controlled which is sequentially supplied, and for generating EWMA data (Z<SB>i</SB>) showing the moving average with exponential weight of the data (X<SB>i</SB>); a difference calculation part (12) for calculating difference data (difference<SB>i</SB>) showing a difference between the data (X<SB>i</SB>) and the EWMA data (Z<SB>i</SB>); a cumulative sum calculation part (13) for generating cumulative sum data (Y<SB>1</SB>to Y<SB>i</SB>) for plot based on cumulative sum data (Y<SB>i</SB>) calculated based on the data (X<SB>i</SB>) and difference data (difference<SB>i</SB>); a control chart creation part (14) for creating a control chart based on the cumulative sum data (Y<SB>1</SB>to Y<SB>i</SB>) for plot; and an abnormal trend determination part (15) for determining whether an abnormal condition exists in a control process based on a parameter for determination held in advance by referring to the control chart. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a management chart creation device and a management chart creation program.

  In a mass production site where products are manufactured in large quantities, there may be variations among individual products. For example, even when the same product is manufactured by the same manufacturing method based on the same standard, slight variations may occur in a plurality of completed products. If the slight variation is within the range of the standard, the products within the range of the standard will be distributed to the market without any problem even at the inspection stage.

  In quality control (QC), it is very important to grasp such a slight variation tendency as a variation corresponding to the passage of time. A control chart is generally used as a method for grasping the fluctuation. There are many types of control charts. In recent years, management methods based on statistical process control (SPC) have been adopted in addition to X charts that are widely used in general. For example, management methods that incorporate the concept of statistical process management As an example, an exponential weighted moving average (EWMA) control chart and a cumulative sum (CUSUM) control chart are known (see, for example, Patent Documents 1 and 2).

  Patent Document 1 describes a technique that uses an exponential weighted moving average (EWMA) management value as an abnormality diagnosis parameter for diagnosing machine deterioration. Japanese Patent Application Laid-Open No. 2004-228561 describes a technique relating to storage management, and discloses a technique using a moving average method and cumulative sum management as the management method.

  Management items in quality management include management items that do not have target values, such as management of equipment parameters. For such management items, there may be a demand for allowing moderate long-term fluctuations and detecting short-term fluctuations as abnormal. For example, the growth rate of a polysilicon furnace, the power for lamp annealing, etc., vary gradually as a film is deposited on a quartz part. Therefore, it is necessary to manage such that long-term fluctuations are acceptable and short-term fluctuations due to equipment failures are abnormal.

  In conventional control charts (X control charts, Xbar-R control charts, EWMA control charts, etc.), management that allows long-term fluctuations is performed by drawing a management limit line that takes into account long-term fluctuations with a straight line. . In addition, management that allows long-term fluctuations is executed by frequently calculating and redrawing the management limit according to long-term fluctuations. In management using a cumulative sum management chart (CUSUM management chart), management that allows long-term fluctuations is executed by setting a V-mask management limit so as to allow long-term fluctuations.

  FIG. 1 is a diagram exemplifying a configuration of a control chart in which a control limit considering long-term fluctuations is set. In the control chart (X control chart, Xbar-R control chart, EWMA control chart, etc.), the control limit line is drawn with a straight line parallel to the horizontal axis. When calculating the control limit line, the standard deviation (σ) is usually estimated from the graph plot data for several tens to several months excluding past abnormal points, and the average value is equivalent to ± 3σ in the control items of the control chart The control limit line is calculated so that As shown in FIG. 1, when the management limit is calculated including long-term fluctuations and long-term fluctuations are taken into account, and the management limit is subtracted, the width between the management limit line and the center (total average) becomes wider.

  FIG. 2 is a diagram illustrating a configuration of a control chart in which the setting of the control limit is frequently changed in accordance with long-term fluctuation. When managing with an appropriate management width in accordance with long-term fluctuations in a management chart (X chart, Xbar-R chart, EWMA chart, etc.), use short-term data that is less affected by long-term fluctuations. Calculate control limits frequently. FIG. 2 illustrates a case where the control limit is obtained by calculating the average value and the standard deviation from the previous 7 plots every 7 plots. Based on the calculation result, an operation of redrawing the control limit line is performed, and the setting of the control limit is frequently changed according to long-term fluctuation.

  FIG. 3 illustrates a control chart in the case where the standard deviation of incidental fluctuations (long-term fluctuations and fluctuations not including abnormal fluctuations) that do not include long-term fluctuations is obtained. As shown in FIG. 3, the control limit line is obtained by calculating the average value from the previous 7 plots every 7 plots using the standard deviation.

  FIG. 4 is a diagram exemplifying a configuration of a control chart when a V mask management limit is set in consideration of long-term fluctuations in the cumulative sum management chart. The cumulative sum control chart is a graph in which values obtained by accumulating a difference between a fixed target value or an average value and an observed value are plotted on a graph. A control limit line by the V mask is drawn on the cumulative sum control chart, and when a past plot goes out of the V mask, it is detected that a deviation has occurred from the target value or the average value.

JP 2007-278105 A JP 2006-344186 A

  In the conventional management method, when a management limit is set in consideration of long-term fluctuations, short-term fluctuations that are desired to be abnormal may not be detected. For example, in the case where the control limit line is calculated by the method shown in FIG. 1, if the control limit line considering long-term fluctuation is calculated, the long-term fluctuation will depart from the total average. Therefore, the estimation of the standard deviation becomes large, and as a result, the width between the control limit line and the center (total average) becomes wide. Therefore, there may occur a problem that short-term fluctuations that are desired to be abnormal cannot be detected.

  Further, as shown in FIG. 2, when calculating the average value and the standard deviation from the management data, since the number of plots to be calculated is small, the accuracy of the estimated value of the average value and the standard deviation is poor, and the management limit width Is different each time, and even immediately after redrawing the management limit line, the management center and the transition center do not match. Therefore, an unnecessary alarm may occur (the 18th to 21st plots). Furthermore, there may be a problem that the transition fluctuation (31st plot) to be detected cannot be detected.

  Further, as shown in FIG. 3, the standard deviation of the accidental fluctuation is obtained, and even when only the average value is calculated from the management data, since the number of plots to be calculated is small, the accuracy of the estimated value of the average value is May be worse. At this time, even immediately after redrawing the control limit line, the management center and the transition center do not coincide with each other, so that an unnecessary alarm (21st plot) or a transition change to be detected (31st plot) cannot be detected. May occur.

  In addition, as shown in FIG. 4, when the management limit of the V mask is gently pulled so as to allow long-term fluctuation, the estimation of the standard deviation may be increased. In this case, the V mask angle of the control limit line becomes large, and a problem that short-term fluctuations are not detected may occur. Furthermore, there may be a problem that short-term fluctuations in the target value direction are difficult to detect.

  The means for solving the problem will be described below using the numbers used in [Best Mode for Carrying Out the Invention]. These numbers are added to clarify the correspondence between the description of [Claims] and [Best Mode for Carrying Out the Invention]. However, these numbers should not be used to interpret the technical scope of the invention described in [Claims].

In order to solve the above problems, receives the management object data to be supplied in sequence _{(X i),} EWMA data indicating the index weighted moving average of object data _{(X i)} (EWMA) a _{(Z i)} An EWMA calculation unit (11) to be generated, a difference calculation unit (12) for calculating difference data (difference _i ) indicating a difference between the management target data (X _i ) and the EWMA data (Z _i ), and the management Cumulative sum calculation for generating cumulative sum data (Y _{1 to} Y _i ) for plotting based on cumulative sum data (Y _i ) calculated based on target data (X _i ) and the difference data (difference _i ) Part (13), a control chart creation part (14) for generating a control chart based on the cumulative sum data for plotting (Y _{1 to} Y _i ), and a judgment table stored in advance with reference to the control chart Control process differences based on parameters Constituting a control chart creation device including an abnormality tendency determination unit for determining the presence or absence of (15).

  To briefly explain the effects obtained by typical inventions among those disclosed in the present application, moderate long-term fluctuations are allowed by a control chart that cumulatively sums the difference between the exponential weighted moving average and the observed value. Therefore, it is possible to appropriately manage the trend when it is desired to detect short-term fluctuations as abnormal.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. Note that components having the same function are denoted by the same reference symbols throughout the drawings for describing the embodiment, and the repetitive description thereof will be omitted.
[Configuration of the embodiment]
FIG. 5 is a block diagram illustrating the configuration of the management chart creation device 1 of this embodiment. The control chart creation device 1 includes an information processing device 2, a data input device 3, and a data output device 4.

  The information processing apparatus 2 creates a control chart and performs abnormality / trend determination based on the control chart. The data input device 3 is a man-machine interface provided outside the information processing device 2. The data input device 3 supplies data of items to be managed to the information processing device 2 in response to user operations. The data output device 4 is a man-machine interface provided outside the information processing device 2. The data input device 3 outputs the calculation result executed by the information processing device 2 in a format that can be recognized by the user.

  The information processing apparatus 2 includes an EWMA calculation unit 11, a difference calculation unit 12, a cumulative sum calculation unit 13, a control chart creation unit 14, an abnormal tendency determination unit 15, a setting parameter storage unit 16, and a calculation data storage unit 17 and so on.

The EWMA calculator 11 calculates data Z _i that is an exponential weighted moving average (EWMA). The EWMA calculator 11 is supplied with data X _{i of the} item to be managed via the data input device 3. Note that the subscript _i of the data X _i indicates the i-th data on the graph. The data Z _i is calculated by the following equation. λ is a weighted ratio and uses a value of 0 <λ ≦ 1 (for example, 0.2).
Z _i = λX _i + (1−λ) Z _i−1
The calculated result Z _i is stored in the calculation data storage unit 17.

The difference calculation unit 12 calculates the difference _i based on the following equation from the data X _i supplied via the data input device 3 and the EWMA result Z _i−1 calculated at the time of the previous input data.
Difference _i = X _i −Z _i−1

The cumulative sum calculator 13 adds the difference _i to the cumulative sum result Y _i-1 calculated at the time of the previous input data, and calculates Y _i to be plotted on the control chart based on the following equation.
Y _i = Y _i-1 + difference _i
The calculated Y _i is stored in the calculation data storage unit 17 and sent to the control chart creation unit 14.

The control chart creation unit 14 acquires past plot data (Y _{1 to} Y _i-1 ) from the calculation data storage unit 17 and creates a control chart graph. The abnormality tendency determination unit 15 determines the presence / absence of an abnormality using the abnormality control V mask of the created control chart and the conventional cumulative sum control chart (CUSUM control chart). The setting parameter storage unit 16 holds parameters used for the determination performed by the abnormal tendency determination unit 15.

  FIG. 6 is a diagram illustrating a cumulative sum management chart when the management limit of the V mask is set. FIG. 7 is a cumulative sum management chart illustrating the difference between the accumulated observed value and the target value. The cumulative sum management chart plots a value obtained by accumulating the difference between the fixed target value (or average value) and the observed value as shown in FIG.

  Returning to FIG. 6, (a) of FIG. 6 exemplifies parameters held in the above-described calculation data storage unit 17. FIG. 6B illustrates a configuration of a cumulative sum management chart including an abnormality determination V mask corresponding to the determination of abnormal points executed by the abnormal tendency determination unit 15. The abnormal tendency determination unit 15 puts a control limit line by the V mask on the cumulative sum control chart, and detects that a deviation from the target value (or average value) occurs when the past plot goes out of the V mask. To do.

[Operation of the embodiment]
Below, operation | movement of the control chart preparation apparatus 1 of this embodiment is demonstrated with reference to drawings. FIG. 8 is a graph illustrating data to be processed by the control chart creation device 1 of this embodiment. The data of items that we want to manage have been changing with short-term fluctuations and long-term fluctuations. The broken lines shown in FIG. 8 indicate long-term fluctuations. Referring to FIG. 8, it is shown that the transition suddenly changes upward at the 31st plot, causing short-term fluctuations.

FIG. 9 is a graph illustrating the transition of data Z _i generated corresponding to the operation of the EWMA calculation unit 11. The EWMA calculation unit 11 receives data X _i of an item to be managed supplied from the data input device 3, and outputs a calculation result as an exponential weighted moving average (EWMA). FIG. 9 shows an output when the EWMA calculator 11 receives data X _i as shown in FIG.

FIG. 10 is a graph illustrating the configuration of the difference _i calculated by the difference calculation unit 12. FIG. 10 shows the difference between the data X _{i of the} item to be managed and the exponential weighted moving average (EWMA result Z _i-1 ) shown in FIG. As described above, the difference calculation unit 12, from the EWMA result Z _i-1 computed during data X _i and the previous input data supplied via the data input device 3 calculates the difference _i. The output of the difference calculation unit 12 is supplied to the cumulative sum calculation unit 13, and the cumulative sum calculation unit 13 adds the difference _i to the cumulative sum result Y _i-1 calculated at the time of the previous input data, and adds it to the control chart. Calculate Y _i to plot. The calculated Y _i is stored in the calculation data storage unit 17 and sent to the control chart creation unit 14.

FIG. 11 is a diagram illustrating a configuration of a management chart graph generated by the management chart creation unit 14. The control chart creation unit 14 acquires past plot data (Y _{1 to} Y _i-1 ) from the calculation data storage unit 17 and creates a control chart graph. The abnormal tendency determination unit 15 refers to the control chart graph shown in FIG. 11 and detects an abnormality based on the occurrence of a management limit loss due to the V mask at the short-term change point of the 31st plot.

  As described above, in the conventional cumulative sum control chart, the difference between the fixed target value or the average value and the observed value is accumulated, but in the present invention, the exponent-weighted movement calculated up to the latest data is performed. Accumulate the difference between the mean and the observed value and plot it as a control chart. Thereby, the amount of fluctuation due to long-term fluctuations has little influence on the accumulated value, and short-term fluctuations can be detected with high sensitivity.

  The embodiment of the present invention has been specifically described above. The present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the scope of the invention.

FIG. 1 is a diagram exemplifying a configuration of a control chart in which a control limit considering long-term fluctuations is set. FIG. 2 is a diagram illustrating a configuration of a control chart in which the setting of the control limit is frequently changed in accordance with long-term fluctuation. FIG. 3 illustrates a control chart in the case where the standard deviation of the contingent variation that does not include long-term variation is obtained. FIG. 4 is a diagram exemplifying a configuration of a cumulative sum management chart when a V mask management limit is set in consideration of long-term fluctuations. FIG. 5 is a block diagram illustrating the configuration of the management chart creation device 1 of this embodiment. FIG. 6 is a diagram illustrating a cumulative sum management chart when the management limit of the V mask is set. FIG. 7 is a cumulative sum management chart illustrating the difference between the accumulated observed value and the target value. FIG. 8 is a graph illustrating data to be processed by the control chart creation device 1 of this embodiment. FIG. 9 is a graph illustrating the transition of data Z _i generated corresponding to the operation of the EWMA calculation unit 11. FIG. 10 is a graph illustrating the configuration of the difference _i calculated by the difference calculation unit 12. FIG. 11 is a diagram illustrating a configuration of a management chart graph generated by the management chart creation unit 14.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Control chart preparation apparatus 2 ... Information processing apparatus 3 ... Data input device 4 ... Data output apparatus 11 ... EWMA calculation part 12 ... Difference calculation part 13 ... Cumulative sum calculation part 14 ... Control chart preparation part 15 ... Abnormal tendency determination part 16 ... Setting parameter storage unit 17 ... Calculation data storage unit

Claims (10)

An EWMA calculation unit that receives the management target data supplied in order and generates EWMA data indicating an exponential weighted moving average (EWMA) of the management target data;
A difference calculation unit for calculating difference data indicating a difference between the management target data and the EWMA data;
A cumulative sum calculator for generating cumulative sum data for plotting based on the cumulative sum data calculated based on the management target data and the difference data;
A control chart creation unit for generating a control chart based on the cumulative sum data for plotting;
A control chart creation device comprising: an abnormal tendency determination unit that refers to the control chart and determines whether there is an abnormality in a management process based on a determination parameter that is stored in advance. The control chart creation device according to claim 1,
The managed data is
The processing target data that is the current processing target,
Including the processed data that was supplied before the processing target data and was the previous processing target;
When the EWMA calculation unit receives the processing target data,
The reference EWMA data indicating the exponential weighted moving average (EWMA) of the processed data is read, and the exponential weighted moving average (EWMA) of the processing target data is indicated based on the reference EWMA data and the processing target data. Generate processing target EWMA data,
When the difference calculation unit receives the processing target data,
Reading the reference EWMA data, supplying processing target difference data calculated based on the reference EWMA data and the processing target data to the cumulative sum calculation unit,
The cumulative sum calculator is
A control chart creation device that generates the processing target plot cumulative sum data by adding the processing target difference data to the processed plot cumulative sum data corresponding to the processed data. In the control chart creation device according to claim 2,
The processing target data is data X _i ,
The processed data is defined as data X _i-1 ,
When the reference EWMA data is EMWA data Z _i-1 ,
The EWMA calculator is
The processing target EWMA data Z _i is expressed by the following equation with λ as a weighting ratio: Z _i = λX _i + (1−λ) Z _i−1
Seeking more
The difference calculator is
When the processing target difference data is a difference _i , the processing target difference data is expressed by the following equation: Difference _i = X _i −Z _i−1
Seeking more
The cumulative sum calculator is
When the processed plot cumulative sum data is cumulative sum data Y _i−1 , the processing target plot cumulative sum data Y _i is expressed by the following formula: Y _i = Y _i−1 + difference _i
More control chart creation device. The control chart creation device according to claim 3, further comprising:
A calculation data storage unit,
The EWMA calculator is
The processing target EWMA data is stored in the calculation data storage unit so as to be read out as the reference EWMA data,
The cumulative sum calculator is
The control chart creation device that stores the processing target plot cumulative sum data in the calculation data storage unit so as to be read out as the processed plot cumulative sum data. In the control chart preparation apparatus of Claim 4,
The abnormal tendency determination unit,
A control chart creation device that generates a control limit line every time the cumulative sum data for plots to be processed is generated, and detects whether there is an abnormality in the management process based on whether or not it is within the range of the control limit line. A control chart creation program showing a procedure for causing a computer to function as a control chart creation device,
(A) receiving management object data supplied in sequence, and generating EWMA data indicating an exponent-weighted moving average (EWMA) of the management object data;
(B) calculating difference data indicating a difference between the management object data and the EWMA data;
(C) generating cumulative sum data for plotting based on the cumulative sum data calculated based on the management target data and the difference data;
(D) generating a control chart based on the cumulative sum data for plotting;
(E) A control chart creation program that causes a computer to function as a control chart creation device in accordance with a procedure indicated by the step of judging whether or not there is an abnormality in a management process based on a judgment parameter stored in advance with reference to the control chart. In the control chart creation program according to claim 6,
The managed data is
The processing target data that is the current processing target,
Including the processed data that was supplied before the processing target data and was the previous processing target;
In the step (a), when the processing target data is received,
The reference EWMA data indicating the exponential weighted moving average (EWMA) of the processed data is read, and the exponential weighted moving average (EWMA) of the processing target data is indicated based on the reference EWMA data and the processing target data. Generating a processing target EWMA data;
In the step (b), when the processing target data is received,
Reading the reference EWMA data, and supplying processing target difference data calculated based on the reference EWMA data and the processing target data to the cumulative sum calculation unit,
The step (c) includes a step of adding the processing target difference data to the processed plot cumulative sum data corresponding to the processed data to generate processing target plot cumulative sum data. In the control chart creation program according to claim 7,
The processing target data is data X _i ,
The processed data is defined as data X _i-1 ,
When the reference EWMA data is EMWA data Z _i-1 ,
The step (a) includes:
The processing target EWMA data Z _i is expressed by the following equation with λ as a weighting ratio: Z _i = λX _i + (1−λ) Z _i−1
Seeking more
The step (b)
When the processing target difference data is a difference _i , the processing target difference data is expressed by the following equation: Difference _i = X _i −Z _i−1
Seeking more
The step (c) includes:
When the processed plot cumulative sum data is cumulative sum data Y _i−1 , the processing target plot cumulative sum data Y _i is expressed by the following formula: Y _i = Y _i−1 + difference _i
More control chart creation program. In the control chart creation program according to claim 8,
The step (a) includes:
Storing the processing target EWMA data in a calculation data storage unit so as to be read out as the reference EWMA data;
The step (c) includes:
A control chart creating program comprising a step of storing the processing target plot cumulative sum data in the calculation data storage section so as to be read out as the processed plot cumulative sum data. In the control chart creation program according to claim 9,
The step (e) includes:
A control chart creation program including a step of generating a control limit line every time the cumulative sum data for processing target plots is generated, and detecting whether there is an abnormality in a management process based on whether or not it is within the range of the control limit line.

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