JP2003114713A - Method for analyzing cause for quality degradation - Google Patents
Method for analyzing cause for quality degradationInfo
- Publication number
- JP2003114713A JP2003114713A JP2001311140A JP2001311140A JP2003114713A JP 2003114713 A JP2003114713 A JP 2003114713A JP 2001311140 A JP2001311140 A JP 2001311140A JP 2001311140 A JP2001311140 A JP 2001311140A JP 2003114713 A JP2003114713 A JP 2003114713A
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- variable
- score
- cause
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- variables
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Links
- 238000000034 method Methods 0.000 title claims abstract description 173
- 230000015556 catabolic process Effects 0.000 title abstract 6
- 238000006731 degradation reaction Methods 0.000 title abstract 6
- 230000007547 defect Effects 0.000 claims description 38
- 238000000513 principal component analysis Methods 0.000 claims description 23
- 230000002950 deficient Effects 0.000 claims description 6
- 238000004519 manufacturing process Methods 0.000 claims description 6
- 230000002596 correlated effect Effects 0.000 abstract description 7
- 238000004364 calculation method Methods 0.000 abstract description 3
- 239000011159 matrix material Substances 0.000 description 19
- 239000013598 vector Substances 0.000 description 8
- 238000004458 analytical method Methods 0.000 description 7
- 238000010586 diagram Methods 0.000 description 7
- 238000007726 management method Methods 0.000 description 7
- 230000005856 abnormality Effects 0.000 description 4
- 229910000831 Steel Inorganic materials 0.000 description 3
- 230000000875 corresponding effect Effects 0.000 description 3
- 238000000605 extraction Methods 0.000 description 3
- 238000012544 monitoring process Methods 0.000 description 3
- 239000010959 steel Substances 0.000 description 3
- 230000007423 decrease Effects 0.000 description 2
- 239000006185 dispersion Substances 0.000 description 2
- 238000007781 pre-processing Methods 0.000 description 2
- 238000003908 quality control method Methods 0.000 description 2
- 241000519695 Ilex integra Species 0.000 description 1
- 230000003993 interaction Effects 0.000 description 1
- 238000010606 normalization Methods 0.000 description 1
- 238000012847 principal component analysis method Methods 0.000 description 1
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/30—Computing systems specially adapted for manufacturing
Landscapes
- General Factory Administration (AREA)
- Testing And Monitoring For Control Systems (AREA)
- Complex Calculations (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
Description
【０００１】[0001]
【発明の属する技術分野】本発明は、品質管理における
品質不良の原因解析の方法に関し、特に多変量統計管理
手法を用いた品質不良の原因解析の方法に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of analyzing the cause of quality defects in quality control, and more particularly to a method of analyzing the cause of quality defects using a multivariate statistical management technique.
【０００２】[0002]
【従来の技術】製造プロセスにおいては、品質変数が所
定の範囲内にあるかを判断することで品質の良否を決定
できる場合もあるが、適切な品質センサが存在しない場
合や、設備上あるいはプロセスの都合上直接計測が困難
な場合もあり、この場合、プロセスの状態を示すプロセ
ス変数が所定の正常な範囲内にあるかどうかで品質の良
否を決定することも少なくない。品質管理を行う上で最
もよく知られている統計的管理手法として単変量管理手
法がある。単変量管理手法では単変量管理図を使用し
て、プロセス変数が所定の範囲、例えば信頼限界を超え
た場合にプロセス異常が発生したと考え、製品を不良と
して判定する。単変量管理手法は各プロセス変数が互い
に相関をもたず、独立に単変量正規分布にしたがうと仮
定しているため、鉄鋼プロセスのようにプロセス変数の
数が多くなると、各プロセス変数が相関をもち相互作用
する場合も増えるので、独立なプロセス変数を選ぶこと
が難しくなり、実用的ではない。プロセス変数が多く互
いに相関をもち、相互作用するプロセスを監視する方法
としては多変量管理手法がある。多変量管理手法では、
プロセス変数を直接監視する代わりに、主成分分析によ
ってプロセス変数の線形結合である、互いに相関のない
スコア変数を監視する方法がよく知られている。互いに
相関のあるプロセス変数を多変量管理手法で扱う場合、
主成分分析で得られたスコア変数を用いることで、プロ
セス変数の数であるプロセス空間の次元をスコア変数の
数にまで減少させることが可能である。すなわち、スコ
ア変数を用いることで、プロセス変数で記述されたプロ
セス空間の情報をより低次元の情報に要約できる。各製
品のスコア変数をプロットした散布図を使って、プロセ
ス異常あるいは品質不良を判定することは従来よく行わ
れている。2. Description of the Related Art In a manufacturing process, there are cases where the quality of a product can be determined by determining whether a quality variable is within a predetermined range. In some cases, it is difficult to directly measure the quality, and in this case, quality is often determined based on whether or not the process variable indicating the process state is within a predetermined normal range. The univariate control method is the most well-known statistical control method for quality control. In the univariate control method, a univariate control chart is used, and when a process variable exceeds a predetermined range, for example, a confidence limit, it is considered that a process abnormality has occurred, and a product is determined to be defective. The univariate control method assumes that the process variables do not correlate with each other, but independently follows a univariate normal distribution, so when the number of process variables increases, such as in steel processes, each process variable becomes correlated. Since there are more cases of mochi interaction, it becomes difficult to select independent process variables, which is not practical. There is a multivariate management method as a method of monitoring the interacting processes that have many process variables and are correlated with each other. In the multivariate management method,
Instead of directly monitoring the process variables, it is well known to monitor the score variables, which are linear combinations of the process variables, which are uncorrelated with each other, by principal component analysis. When dealing with process variables that are correlated with each other by the multivariate management method,
By using the score variables obtained by the principal component analysis, it is possible to reduce the dimension of the process space, which is the number of process variables, to the number of score variables. That is, by using the score variable, the information of the process space described by the process variable can be summarized into lower dimensional information. It has been a common practice to judge a process abnormality or defective quality by using a scatter diagram in which score variables of each product are plotted.
【０００３】[0003]
【発明が解決しようとする課題】従来の主成分分析を用
いた多変量管理手法においては、各スコア変数を監視す
ることでプロセスが正常な範囲内にあるかどうかを適切
に判定することが可能であるが、プロセス変数の数が増
えるとプロセス空間を要約するに足るスコア変数の個数
も増えていき、プロセス異常あるいは品質不良の原因を
解析することが困難になる場合も多い。また、監視する
のはプロセス変数の線形結合で表されるスコア変数であ
るので、どのスコア変数が正常な範囲内から外れたかを
判定することはできても、どのプロセス変数がその原因
であったか判断するのは難しい。一方、従来の単変量管
理手法では、どのプロセス変数が正常な範囲内を外れた
かを直ちに示すことはできるが、プロセス変数が互いに
相関をもつ場合を適切に扱うことはできない。In the conventional multivariate management method using principal component analysis, it is possible to appropriately judge whether or not the process is within a normal range by monitoring each score variable. However, as the number of process variables increases, the number of score variables sufficient to summarize the process space also increases, and it is often difficult to analyze the cause of a process abnormality or quality defect. Also, since it is the score variable that is represented by the linear combination of process variables that is monitored, it is possible to determine which score variable is out of the normal range, but which process variable is the cause. It's hard to do. On the other hand, the conventional univariate management method can immediately show which process variable is out of the normal range, but cannot properly handle the case where the process variables are correlated with each other.
【０００４】したがって本発明は、多数のプロセス変数
が存在し互いに相関をもつプロセス変数が含まれる場合
でも、どのプロセス変数がプロセス異常や品質不良の原
因であるかを直ちに示すことを課題とする。Therefore, it is an object of the present invention to immediately indicate which process variable is the cause of a process abnormality or quality defect even when a large number of process variables are present and include process variables correlated with each other.
【０００５】[0005]
【課題を解決するための手段】請求項１の発明に係る品
質不良の原因解析方法は、製品の品質に基づき製造プロ
セスを解析する方法であって、品質不良と指定した製品
と同品種の製品に関する、プロセスデータを検索・収集
する工程と、収集した同品種の製品のプロセスデータか
ら主成分分析を利用して、プロセス変数の線形結合であ
るスコア変数を得る工程と、残差変数を計算し、前記残
差変数が前記プロセスの正常な許容範囲内にあるかを判
断する工程と、前記指定した製品が残差変数の許容範囲
を外れていたとき、残差変数の値への各プロセス変数の
寄与度を計算する工程と、各プロセス変数の寄与度を比
較して、残差変数の値に主に寄与しているプロセス変数
を品質不良の原因の候補として抽出する工程と、前記指
定した製品が残差変数の許容範囲を外れていないとき、
距離変数を計算し、前記距離変数が、前記プロセスの正
常な許容範囲内にあるかを判断する工程と、前記指定し
た製品が距離変数の許容範囲を外れていたとき、距離変
数の値への各スコア変数の寄与度を計算する工程と、各
スコア変数の寄与度を比較して、距離変数の値に主に寄
与しているスコア変数を品質不良の原因の候補として抽
出する工程と、候補として抽出されたスコア変数への各
プロセス変数の寄与度を計算する工程と、上記の抽出さ
れたスコア変数に主に寄与しているプロセス変数を品質
不良の原因の候補として抽出する工程と、からなること
を特徴とする。According to a first aspect of the present invention, there is provided a method of analyzing a cause of quality defects, which is a method of analyzing a manufacturing process based on the quality of a product, wherein the product is of the same kind as the product designated as the quality defect. Regarding the process of searching and collecting process data, the process of obtaining a score variable that is a linear combination of process variables using the principal component analysis from the collected process data of the same type of product, and calculating the residual variable. , A step of determining whether the residual variable is within a normal allowable range of the process, and when the specified product is outside the allowable range of the residual variable, each process variable to the value of the residual variable The step of calculating the contribution degree of each of the process variables and the step of comparing the contribution degrees of the respective process variables and extracting the process variables mainly contributing to the value of the residual variable as a candidate of the cause of the quality defect. Product is residual When you're not out of the acceptable range of a few,
Calculating a distance variable and determining whether the distance variable is within a normal tolerance of the process; and when the specified product is outside the tolerance of the distance variable, A step of calculating the contribution of each score variable, a step of comparing the contribution of each score variable, extracting a score variable mainly contributing to the value of the distance variable as a candidate for the cause of poor quality, and a candidate From the step of calculating the contribution of each process variable to the score variable extracted as, and the step of extracting the process variables mainly contributing to the above extracted score variable as a candidate for the cause of poor quality, It is characterized by
【０００６】請求項１の発明では、主成分分析法によっ
て得られたスコア変数を使って、プロセス空間を低次元
のモデル空間へ要約する。残差変数はプロセス空間の情
報をモデル空間の情報で表したときにスコア変数だけで
は表せなかった量を示す。距離変数はモデル空間におけ
る中心から各製品の空間座標までの距離を表す量であ
る。残差変数が許容範囲内にない場合、残差変数の値に
主に寄与しているプロセス変数を品質不良原因として抽
出する。残差変数は許容範囲内にあるが、距離変数が許
容範囲外であるとき、まず距離変数の値に主に寄与して
いるスコア変数を品質不良の原因の候補として抽出し、
さらに抽出されたスコア変数に主に寄与しているプロセ
ス変数を最終的に品質不良原因として抽出する。かかる
構成により、多数のプロセス変数が存在し互いに相関を
もつプロセスを、より少ない数のスコア変数で扱い、品
質不良原因の候補であるプロセス変数を体系的に抽出す
ることが可能である。According to the first aspect of the invention, the process space is summarized into a low-dimensional model space by using the score variables obtained by the principal component analysis method. The residual variable indicates an amount that cannot be represented by the score variable alone when the information of the process space is represented by the information of the model space. The distance variable is a quantity representing the distance from the center in the model space to the spatial coordinates of each product. If the residual variable is not within the allowable range, the process variable that mainly contributes to the value of the residual variable is extracted as the cause of quality defect. The residual variable is within the allowable range, but when the distance variable is outside the allowable range, the score variables that mainly contribute to the value of the distance variable are first extracted as candidates for the cause of poor quality,
Furthermore, the process variables mainly contributing to the extracted score variables are finally extracted as the cause of the quality defect. With such a configuration, it is possible to treat a process having a large number of process variables and having a correlation with each other with a smaller number of score variables, and systematically extract process variables that are candidates for the cause of quality defects.
【０００７】請求項２の発明に係る品質不良の原因解析
方法は、請求項１に記載の品質不良の原因解析方法であ
って、上記残差変数は量Ｑi であって、前記の式（１）
のように定義され、製品ｉが残差変数Ｑi の許容範囲を
外れていたとき、Ｑi の各項ｑijのうち最大の項に相当
するプロセス変数を、品質不良の原因の候補とすること
を特徴とする。請求項２の発明では、品質が不良であっ
たｉ番目の製品の、ｊ番目のプロセス変数であるｘ
ijを、スコアｔikと負荷量ｐjkとで表したときの残差自
乗和で残差変数を表し、残差変数への各プロセス変数の
寄与度をＱi の各項ｑijとして定量的に比較することに
より、寄与度最大のプロセス変数を品質不良の原因とし
て抽出できる。A method of analyzing the cause of quality defects according to the invention of claim 2 is the method of analyzing the cause of quality defects according to claim 1, wherein the residual variable is a quantity Q i , and 1)
When the product i is out of the allowable range of the residual variable Q i , the process variable corresponding to the maximum term of each term q ij of Q i is set as the candidate of the cause of the quality defect. It is characterized by In the invention of claim 2, x is the j-th process variable of the i-th product of which the quality is poor.
ij is represented by the score t ik and the load p jk, and the residual variable is represented by the residual sum of squares, and the contribution of each process variable to the residual variable is quantitatively set as each term q ij of Q i. The process variable with the largest contribution can be extracted as the cause of the quality defect by comparing with.
【０００８】請求項３に係る品質不良の原因解析方法
は、請求項２に記載の品質不良の原因解析方法であっ
て、上記距離変数は量Ｄi であって、式（２）のように
定義され、製品ｉが請求項２に記載の残差変数Ｑi の許
容範囲を外れてはいないが、距離変数Ｄi の許容範囲を
外れていたとき、Ｄi の各項ｔik 2 ／ｓk 2 のうち最大
の項に相当するスコア変数を品質不良の原因の候補とす
ることを特徴とする。請求項３の発明では、主成分分析
で得られたモデル空間内での分散を考慮して、距離変数
Ｄi を、標本標準偏差で規格化したスコア変数の自乗和
として定義している。距離変数Ｄi への各スコア変数の
寄与度はＤi の各項ｔik 2 ／ｓk 2 で定量的に比較する
ことができ、寄与度最大のスコア変数を品質不良の原因
として抽出できる。A method of analyzing the cause of quality defects according to claim 3 is the method of analyzing the cause of quality defects according to claim 2, wherein the distance variable is the quantity D i , and is expressed by the equation (2). is defined, but the product i is not the out of the allowable range of the residual variable Q i according to claim 2, the distance variable D when i was outside the allowable range, each term of D i t ik 2 / s It is characterized in that the score variable corresponding to the maximum term of k 2 is used as a candidate for the cause of poor quality. According to the third aspect of the invention, the distance variable D i is defined as the sum of squares of the score variables normalized by the sample standard deviation in consideration of the variance in the model space obtained by the principal component analysis. The contribution of each score variable to the distance variable D i can be quantitatively compared by each term t ik 2 / s k 2 of D i , and the score variable with the maximum contribution can be extracted as the cause of poor quality.
【０００９】請求項４に係る品質不良の原因解析方法
は、請求項３に記載の品質不良の原因解析方法であっ
て、品質不良の原因の候補とされたスコア変数が（３）
式のように定義され、上式のスコア変数に寄与している
品質不良原因の候補として、ｘijｐjkがスコア変数ｔik
と同符号で大きさが最大の項に相当するプロセス変数を
抽出することを特徴とする。請求項４の発明では、品質
不良原因のスコア変数が抽出されたとき、そのスコア変
数への寄与度をｘijｐjkの符号大きさを定量的に比較す
ることで、最終的に品質不良の原因であるプロセス変数
を抽出できる。According to a fourth aspect of the present invention, there is provided a quality failure cause analysis method according to the third aspect, wherein the score variable which is a candidate for the quality failure cause is (3).
X ij p jk is a score variable t ik as a candidate of a quality defect cause defined in the above equation and contributing to the score variable in the above equation.
It is characterized by extracting a process variable having the same sign as and having a maximum magnitude. According to the invention of claim 4, when the score variable causing the poor quality is extracted, the contribution to the score variable is quantitatively compared with the code size of x ij p jk , so that the quality of the poor quality is finally determined. The process variable that is the cause can be extracted.
【００１０】[0010]
【発明の実施の形態】以下、添付図を参照し、実施例を
あげて本発明の実施の形態を具体的に説明する。BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
【００１１】[0011]
【実施例】本実施例は、鉄鋼などの製造プロセスにおけ
る品質不良の原因を見出す解析システムに本発明の手法
を適用した例である。図１に本実施例における品質不良
の原因解析の手順を示す。EXAMPLE This example is an example in which the method of the present invention is applied to an analysis system for finding the cause of quality defects in the manufacturing process of steel and the like. FIG. 1 shows the procedure for analyzing the cause of quality defects in this embodiment.
【００１２】各製品の品質が格納された品質データベー
ス２に対して、品質不良であった製品の問合せを行い
（工程１）、品質不良の多かった品種を解析対象として
指定する（工程３）。解析対象として指定した品種の製
品が通過したプロセスに関して、プロセスデータベース
５に問合せを行い、プロセスデータの検索・収集を行う
（工程４）。次に収集されたプロセスデータに対して主
成分分析を行う（工程６）。この主成分分析の手順につ
いてしばらく詳細に説明する。The quality database 2 in which the quality of each product is stored is inquired about a product having a poor quality (step 1), and a product having a lot of poor quality is designated as an analysis target (step 3). The process database 5 is inquired about the process through which the product of the type specified as the analysis target has passed, and the process data is searched and collected (step 4). Next, a principal component analysis is performed on the collected process data (step 6). The procedure of this principal component analysis will be described in detail for a while.
【００１３】各プロセス変数の単位とそのとる値の範囲
はそれぞれ異なるので、プロセスデータの前処理とし
て、各プロセス変数の平均が０、分散が１になるように
正規化を行う。前処理を行った後のプロセスデータをｎ
×ｍのデータ行列Ｘで表す。ここで、ｎは解析対象であ
る製品の個数で、ｍはプロセス変数の個数を表す。Ｘの
成分ｘijは製品ｉにおけるプロセス変数ｊの値を表す。Since the unit of each process variable and the range of its value are different, normalization is performed as preprocessing of the process data so that the average of each process variable is 0 and the variance is 1. The process data after preprocessing is n
It is represented by a data matrix X of × m. Here, n is the number of products to be analyzed, and m is the number of process variables. The component x ij of X represents the value of the process variable j in product i.
【００１４】主成分分析においてはＸを次のように分解
する。
Ｘ＝ＴＰ′＋Ｅ ・・・（４）
ここで、Ｔはスコア行列と呼ばれるｎ×ｒの直交行列で
あり、Ｐは負荷量行列と呼ばれるｍ×ｒの正規直交行列
であり、「′」は転置行列を表す。ｒは抽出する主成分
の数であり、スコア行列Ｔの成分であるスコア変数の個
数に等しくｒ≦ｍである。Ｅは残差行列と呼ばれ、ｎ×
ｍの行列である。また、スコア行列Ｔは、Ｔ′Ｔ＝diag
（λ1 ，λ2 ，...,λr ）となるように規格化されてい
る。ここでdiag（λ1 ，λ2 ，...,λr ）は相関行列
Ｘ′Ｘの固有値λ1 ，λ2 ，...,λr（λ1 ≧λ
2 ≧....≧λr ≧０）を対角項とする対角行列である。In the principal component analysis, X is decomposed as follows. X = TP ′ + E (4) Here, T is an n × r orthogonal matrix called a score matrix, P is an m × r orthonormal matrix called a loading matrix, and “′” is Represents a transposed matrix. r is the number of principal components to be extracted, and r ≦ m, which is equal to the number of score variables that are components of the score matrix T. E is called the residual matrix, and n ×
is a matrix of m. The score matrix T is T'T = diag
It is standardized to be (λ 1 , λ 2 , ..., λ r ). Where diag (λ 1 , λ 2 , ..., λ r ) is the eigenvalues λ 1 , λ 2 , ..., λ r (λ 1 ≧ λ of the correlation matrix X′X
2 ≧ .... ≧ λ r ≧ 0) is the diagonal matrix.
【００１５】主成分分析の直感的な意味について説明す
る。ここで負荷量行列を、第ｋ主成分の負荷量ベクトル
ｐk を使ってＰ＝（ｐ1 ，ｐ2 ，...,ｐr ）と表す。第
１主成分の負荷量ベクトルｐ1 の方向は、プロセス変数
を座標軸とするプロセス空間において、分散が最大の方
向である。第２主成分の負荷量ベクトルｐ2 は、第１主
成分の負荷量ベクトルに直交する方向で分散が最大の方
向である。一般に、第ｋ主成分の負荷量ベクトルｐk の
方向は、第１主成分から第ｋ−１主成分に直交する方向
で分散が最大の方向である。スコアｔikはｒ個の負荷量
ベクトルを座標軸とするモデル空間における、製品ｉの
第ｋ主成分軸の座標値である。このように主成分分析
は、プロセス空間の座標軸を、分散の大きい方向に沿う
ように回転させて、互いに相関のないスコア変数を得る
ことができ、低次元のモデル空間でプロセス空間を表現
することが可能である。図２は２次元のプロセス空間か
ら分散が最大の方向を第１主成分にとる例の概念図であ
る。The intuitive meaning of principal component analysis will be described. Here, the load amount matrix is expressed as P = (p 1 , p 2 , ..., P r ) using the load amount vector p k of the k-th principal component. The direction of the load vector p 1 of the first principal component is the direction in which the variance is maximum in the process space having the process variable as the coordinate axis. The load vector p 2 of the second principal component is the direction having the maximum variance in the direction orthogonal to the load vector of the first principal component. In general, the direction of the load vector p k of the k-th principal component is the direction from the first principal component to the (k−1) -th principal component in which the variance is maximum. The score t ik is the coordinate value of the k-th principal component axis of the product i in the model space having r load vectors as coordinate axes. In this way, in principal component analysis, the coordinate axes of the process space can be rotated along the direction of large variance to obtain score variables that are uncorrelated with each other, and the process space can be expressed in a low-dimensional model space. Is possible. FIG. 2 is a conceptual diagram of an example in which the direction of maximum dispersion is taken as the first principal component from the two-dimensional process space.
【００１６】主成分分析における主成分抽出の計算方法
について説明する。負荷量ベクトルはＸ′Ｘの固有ベク
トルであるので、基本的にはＸ′Ｘの固有値問題を解
き、固有値の大きい順にｒ個の固有ベクトルを並べれ
ば、第１主成分から第ｒ主成分までの負荷量ベクトルを
得たことになる。ただし本発明では、数値計算上メモリ
や計算時間の負荷がかからないように、すべての固有ベ
クトルを求めるのではなく、固有値の大きい順に固有ベ
クトルを求める方法として、NIPALS（Nonlinear Iterat
ive PArtial Least Squares ）というアルゴリズムを利
用している。NIPALSは比較的高速で収束も安定している
といわれている。A method of calculating the principal component extraction in the principal component analysis will be described. Since the load vector is an X'X eigenvector, basically, if the X'X eigenvalue problem is solved and r eigenvectors are arranged in descending order of eigenvalue, the load from the first principal component to the r-th principal component We have a quantity vector. However, in the present invention, the NIPALS (Nonlinear Iteratat) is used as a method of obtaining eigenvectors in descending order of eigenvalues, instead of obtaining all eigenvectors so that memory and calculation time are not imposed on the numerical calculation.
ive PArtial Least Squares) is used. NIPALS is said to be relatively fast and stable in convergence.
【００１７】主成分分析において主成分の数ｒの決定方
法について説明する。主成分分析では（４）式のように
データ行列Ｘをスコア行列Ｔと負荷量行列Ｐの転置行列
Ｐ′の積で近似し、近似されなかった分を残差行列Ｅで
表す。主成分分析で近似できなかった量は残差行列Ｅの
成分ｅijを用いて、以下の（５）式のような残差自乗和
で表すことができる。A method of determining the number r of principal components in the principal component analysis will be described. In the principal component analysis, the data matrix X is approximated by the product of the score matrix T and the transposed matrix P ′ of the load matrix P as shown in equation (4), and the unapplied portion is represented by the residual matrix E. The amount that cannot be approximated by the principal component analysis can be represented by the residual sum of squares as in the following equation (5) using the component e ij of the residual matrix E.
【数４】 [Equation 4]
【００１８】図３は主成分の数と（５）式の残差自乗和
の関係を表すグラフである。主成分数を増やすと残差自
乗和は減少するが、プロセス変数の数より少ない数のス
コア変数を得るためには残差自乗和が小さくなる主成分
数を選択する必要がある。主成分数を増やしても残差自
乗和の減少分が大きくないところで主成分の抽出を打ち
切る方法もあるが、残差自乗和が主成分数０のときの残
差自乗和の２０〜３０％程度になるところで主成分の抽
出を打ち切る方法もある。後者の方法で残差自乗和が２
５％になる主成分数を採ると４０個程度のプロセス変数
を５個程度のスコア変数に減らすことが可能であること
がわかった。FIG. 3 is a graph showing the relationship between the number of principal components and the residual sum of squares of equation (5). Although the residual sum of squares decreases as the number of principal components increases, it is necessary to select the number of principal components whose residual sum of squares becomes smaller in order to obtain a smaller number of score variables than the number of process variables. There is also a method of canceling the extraction of the principal component when the decrease in the residual sum of squares is not large even if the number of principal components is increased, but 20 to 30% of the residual sum of squares when the residual sum of squares is 0 There is also a method of stopping the extraction of the main component at a certain point. With the latter method, the residual sum of squares is 2
It was found that it is possible to reduce about 40 process variables to about 5 score variables by taking the number of principal components to be 5%.
【００１９】以上が主成分分析についての説明である。
主成分分析で得られたスコア変数のつくるモデル空間で
は各サンプルは原点を平均として分布する。したがっ
て、原点から離れたサンプルは平均からずれていること
を示す。この平均からのずれを残差変数や距離変数で評
価し、品質不良原因をプロセス変数に帰すのが本発明の
方法の目的である。以下再び図１にもどり、本発明の、
品質不良原因の解析方法の手順について説明する。The above is the description of the principal component analysis.
In the model space created by the score variable obtained by the principal component analysis, each sample is distributed with the origin as the average. Therefore, samples far from the origin are shown to be off-average. The purpose of the method of the present invention is to evaluate the deviation from the average with the residual variable and the distance variable and to attribute the cause of the quality defect to the process variable. Hereinafter, returning to FIG. 1 again, according to the present invention,
The procedure of the method of analyzing the cause of quality defects will be described.
【００２０】品質不良とされた製品ｉについてその原因
をプロセス変数に求めるため、まず製品ｉについて残差
計算を行い、製品ｉの残差が許容範囲内にあるか判断を
行う（工程７）。製品ｉの残差変数Ｑi は（１）式のよ
うに計算できる。図２と同じく２次元（平面）のプロセ
ス空間から１次元のモデル空間（直線）を得る場合を考
えると、残差変数Ｑi の直感的な意味は、図４に示すよ
うに製品ｉを表す点からモデル空間である直線までの距
離の自乗を意味する。プロセス変数ｘijが正規分布にし
たがうという仮定をおくと、残差変数Ｑi はχ自乗分布
にしたがうので、許容範囲の上限としてはχ自乗分布の
信頼限界を採ることができる。本発明では許容範囲の上
限として９５％信頼限界を採っている。図５に各製品ｉ
についての残差変数Ｑi の値を、９５％信頼限界を添え
て示す。横軸は各製品のサンプルＮｏ．である。In order to find the cause of the product i which is determined to be poor quality as a process variable, the residual difference is first calculated for the product i and it is judged whether the residual difference of the product i is within the allowable range (step 7). Residual variable Q i of the product i can be calculated as (1). Considering the case of obtaining a one-dimensional model space (straight line) from a two-dimensional (planar) process space as in FIG. 2, the intuitive meaning of the residual variables Q i is that the product i is represented as shown in FIG. It means the square of the distance from a point to a straight line in the model space. Assuming that the process variables x ij follow a normal distribution, the residual variables Q i follow a χ square distribution, and thus the confidence limit of the χ square distribution can be taken as the upper limit of the allowable range. In the present invention, the upper limit of the allowable range is the 95% confidence limit. Figure 5 shows each product i
The value of the residual variable Q i for is shown with 95% confidence limits. The horizontal axis is the sample No. of each product. Is.
【００２１】例えば、サンプルＮｏ．３３０の製品の残
差は９５％信頼限界外にあるので、各プロセス変数の残
差への寄与度を計算し（工程８）、品質不良の原因であ
るプロセス変数を抽出する（工程９）。残差変数Ｑi の
各項ｑijはサンプルＮｏ．ｉの製品の残差に対するプロ
セス変数ｊ寄与度を表す。図６にサンプルＮｏ．３３０
の製品における各プロセス変数の残差の寄与度を示す。
図６から変数Ｎｏ．１９のプロセス変数がサンプルＮ
ｏ．３３０の残差に最も大きく寄与していることがわか
る。したがって、サンプルＮｏ．３３０の品質不良の原
因としては変数Ｎｏ．１９のプロセス変数を抽出でき
る。For example, sample No. Since the residual of the product of 330 is outside the 95% confidence limit, the contribution of each process variable to the residual is calculated (step 8), and the process variable that is the cause of the quality defect is extracted (step 9). Each term q ij of the residual variable Q i is the sample number. Represents the process variable j contribution to the product residual for i. The sample No. is shown in FIG. 330
Shows the contribution of residuals of each process variable in the product.
From FIG. 6, the variable No. 19 process variables are sample N
o. It can be seen that it contributes most to the residual of 330. Therefore, the sample No. As the cause of the poor quality of No. 330, the variable No. 19 process variables can be extracted.
【００２２】品質不良とされた製品ｉにおいて、残差変
数の値が９５％信頼限界内にあった場合、距離変数Ｄi
の計算を行う（工程１０）。製品ｉの距離変数Ｄi は
（２）式のように計算できる。図７は主成分数が２個の
場合の第１主成分と第２主成分のスコア変数（Ｔ１，Ｔ
２）に関する散布図である。プロセス変数は平均が０に
なるように規格化されており、各スコア変数はプロセス
変数の線形結合であるので、各スコア変数の平均も０に
なる。したがって、モデル空間に各製品のスコア変数を
プロットするとこれらの点は原点の周りに集積する。ま
た、各主成分の分散ｓk 2 と主成分分析で求めた固有値
λk に関してはｓk 2 ＝λk ／（ｎ−１）の関係がある
ので、一般にｓ1 2 ≧ｓ2 2 ≧....≧ｓr 2 の関係が成
り立つ。したがって、第１主成分のスコア変数の分散は
第２主成分の分散より大きく、距離変数Ｄi は各スコア
変数ｔikの標本標準偏差ｓk で規格化されたスコア変数
の自乗和からなるので、９５％信頼限界に相当する等確
率線は楕円になる。すなわち、距離変数Ｄi の各項は各
主成分の分布の広がりを考慮した確率的距離であり、ス
コア変数の大きさに関して第１主成分のほうが第２主成
分のほうよりも大きかった（ｔi1 2 ＞ｔi2 2 ）として
も、確率的距離としては第１主成分のほうが第２主成分
のほうより小さい（ｔi1 2 ／ｓ1 2 ＜ｔi2 2 ／ｓ2 2 場
合もありうる。図８に各製品ｉについての距離変数Ｄi
の値を、９５％信頼限界を添えて示す。横軸は各製品の
サンプルＮｏ．である。If the value of the residual variable is within the 95% confidence limit in the product i of which the quality is poor, the distance variable D i
Is calculated (step 10). The distance variable D i of the product i can be calculated as in equation (2). FIG. 7 shows score variables (T1, T1) of the first principal component and the second principal component when the number of principal components is two.
It is a scatter diagram regarding 2). The process variables are standardized so that the mean is 0, and since each score variable is a linear combination of the process variables, the mean of each score variable is also 0. Therefore, when plotting the score variables for each product in the model space, these points are clustered around the origin. Further, since the variance s k 2 of each principal component and the eigenvalue λ k obtained by the principal component analysis have a relation of s k 2 = λ k / (n-1), generally s 1 2 ≧ s 2 2 ≧. ... ≧ s r 2 holds. Accordingly, the dispersion of the first principal component score variable is greater than the variance of the second principal component, the distance variable D i consists of square sum of the normalized scores variable sample standard deviation s k of each score variable t ik , The 95% confidence limits are elliptic. That is, each term of the distance variable D i is a stochastic distance considering the spread of distribution of each principal component, and the first principal component is larger than the second principal component with respect to the size of the score variable (t Even if i1 2 > t i2 2 ), the first principal component may be smaller than the second principal component as the stochastic distance (t i1 2 / s 1 2 <t i2 2 / s 2 2) . FIG. 8 shows the distance variable D i for each product i.
Values are shown with 95% confidence limits. The horizontal axis is the sample No. of each product. Is.
【００２３】次に、残差変数の値が９５％信頼限界内に
あったが、距離変数Ｄi の値が９５％信頼限界外であっ
たサンプルＮｏ．７９０について、距離変数の値への各
スコア変数の寄与度を計算し（工程１１）、品質不良の
原因であるスコア変数を抽出する（工程１２）。距離変
数Ｄi の各項ｔik 2 ／ｓk 2 は、サンプルＮｏ．ｉの製
品の、距離変数の値に対するｋ番目のスコア変数ｔikの
寄与度を表す。図９にサンプルＮｏ．７９０の製品にお
ける各スコア変数の距離変数の値への寄与度を示す。図
９から第２主成分のスコア変数がサンプルＮｏ．７９０
の残差に最も大きく寄与していることがわかる。したが
って、サンプルＮｏ．７９０の品質不良の原因としては
第２主成分のスコア変数を抽出できる。Next, in the case of sample No. 1 in which the value of the residual variable was within the 95% confidence limit, but the value of the distance variable D i was outside the 95% confidence limit. For 790, the degree of contribution of each score variable to the value of the distance variable is calculated (step 11), and the score variable that causes the poor quality is extracted (step 12). Each term t ik 2 / s k 2 of the distance variable D i is the sample number. It represents the contribution of the kth score variable t ik to the value of the distance variable of the product of i. The sample No. is shown in FIG. The degree of contribution of each score variable to the value of the distance variable in the 790 products is shown. From FIG. 9, the score variable of the second principal component is the sample No. 790
It can be seen that it contributes most to the residual of. Therefore, the sample No. The score variable of the second principal component can be extracted as the cause of the poor quality of 790.
【００２４】残差変数の値が９５％信頼限界内にあった
が、距離変数Ｄi の値が９５％信頼限界外であった製品
について、距離変数の値への寄与度が大きかったスコア
変数を抽出したら、次にこの抽出されたスコア変数に対
する各プロセス変数の寄与度を計算し（工程１３）、最
終的に品質不良の原因であるプロセス変数を抽出する
（工程１４）。製品ｉの第ｋ主成分のスコア変数は
（３）式のように表され、各項ｘijｐjkがプロセス変数
ｊのスコア変数ｔikに対する寄与度となる。ただし、ス
コア変数ｔikは＋側にも−側にも外れうるので、ｘijｐ
jkがｔikと同符号でその絶対値が大きい項に相当するプ
ロセス変数が候補として抽出される（工程１３）。図１
０はサンプルＮｏ．７９０の第２主成分のスコア変数へ
の寄与度を示す。図９で第２主成分のスコア変数は＋だ
ったので、図１０の第２主成分のスコア変数への寄与度
が＋で最大のもの探すと、それは変数Ｎｏ．２７のプロ
セス変数であることがわかる。すなわちサンプルＮｏ．
７９０の品質不良の原因としては変数Ｎｏ．２７のプロ
セス変数を抽出できる。For a product in which the value of the residual variable was within the 95% confidence limit, but the value of the distance variable D i was outside the 95% confidence limit, the score variable having a large contribution to the value of the distance variable. After extracting, the contribution of each process variable to the extracted score variable is calculated (step 13), and finally the process variable that is the cause of the poor quality is extracted (step 14). The score variable of the k-th principal component of the product i is expressed as in equation (3), and each term x ij p jk is the contribution of the process variable j to the score variable t ik . However, since the score variable t ik can be deviated to the + side or − side, x ij p
A process variable corresponding to a term whose jk has the same sign as t ik and whose absolute value is large is extracted as a candidate (step 13). Figure 1
0 is sample No. The degree of contribution of the second principal component of 790 to the score variable is shown. Since the score variable of the second principal component is + in FIG. 9, when the contribution of the second principal component to the score variable of FIG. It can be seen that there are 27 process variables. That is, sample No.
No. 790 is the cause of poor quality. Twenty-seven process variables can be extracted.
【００２５】以上、本発明を、鉄鋼製造プロセスを例に
とって説明したが、本発明は、主成分分析を使った多変
量統計管理手法が適用できるその他の製造プロセスにも
適用可能である。Although the present invention has been described above taking the steel manufacturing process as an example, the present invention is also applicable to other manufacturing processes to which the multivariate statistical management method using principal component analysis can be applied.
【００２６】[0026]
【発明の効果】本発明によれば、品質不良のあった製品
と同品種の製品に関して、プロセスデータを検索・収集
し、主成分分析を利用して、上記プロセスが正常な許容
範囲内にあるかを示す残差変数と距離変数を計算する。
残差変数が許容範囲を外れていたときは、残差変数の値
への各プロセス変数の寄与度を計算・比較して、寄与度
の大きいプロセス変数を品質不良の原因の候補として抽
出する。残差変数の許容範囲を外れていないが、距離変
数の許容範囲を外れていたときは、距離変数の値への各
スコア変数の寄与度を計算・比較して、距離変数の値に
主に寄与しているスコア変数を品質不良の原因の候補と
して抽出する。さらにこのとき、候補として抽出された
スコア変数への各プロセス変数の寄与度を計算・比較
し、上記の抽出されたスコア変数に主に寄与しているプ
ロセス変数を最終的な品質不良の原因の候補として抽出
する。したがって、多数のプロセス変数が存在し互いに
相関をもつプロセス変数が含まれる場合でも、従来困難
であった品質不良の原因特定を体系的に、かつ定量的に
直ちに行うことが可能である。また解析結果を操業にフ
ィードバックすることで迅速な操業の改善が可能であ
る。According to the present invention, with respect to the product of the same kind as the product having the defective quality, the process data is searched and collected, and the principal component analysis is used to make the above process within the normal allowable range. Calculate the residual and distance variables that indicate
When the residual variable is out of the allowable range, the contribution of each process variable to the value of the residual variable is calculated and compared, and the process variable having a large contribution is extracted as a candidate for the cause of poor quality. If it is not outside the allowable range of the residual variable but outside the allowable range of the distance variable, the contribution of each score variable to the value of the distance variable is calculated and compared, and the value of the distance variable is mainly The contributing score variables are extracted as candidates for the cause of poor quality. Furthermore, at this time, the contribution of each process variable to the score variables extracted as candidates is calculated and compared, and the process variables mainly contributing to the above extracted score variables are identified as the cause of the final quality defect. Extract as a candidate. Therefore, even when a large number of process variables are present and process variables that are correlated with each other are included, it is possible to immediately and systematically and quantitatively immediately identify the cause of quality defects, which was difficult in the past. Also, by feeding back the analysis results to the operation, it is possible to improve the operation quickly.
【図１】本発明による品質不良の原因解析の方法におけ
る解析手順を示したものである。FIG. 1 shows an analysis procedure in a method of cause analysis of quality defects according to the present invention.
【図２】プロセス変数間に相関がある場合、主成分分析
によってより低次元のモデル空間で元のプロセス空間を
要約できることを概念的に示した図である。FIG. 2 is a diagram conceptually showing that an original process space can be summarized in a lower dimensional model space by a principal component analysis when there is a correlation between process variables.
【図３】本発明による（５）式で表される残差自乗和
と、スコア変数の数である主成分の数の関係を例示した
グラフである。FIG. 3 is a graph exemplifying the relationship between the residual sum of squares represented by formula (5) according to the present invention and the number of principal components, which is the number of score variables.
【図４】本発明による残差変数Ｑi の意味を概念的に示
した図である。FIG. 4 is a diagram conceptually showing the meaning of a residual variable Q i according to the present invention.
【図５】本発明による、各製品のサンプルＮｏ．に対す
る残差変数Ｑi の値を、その９５％信頼限界とともに例
示した棒グラフである。FIG. 5 is a sample No. of each product according to the present invention. 6 is a bar graph illustrating the value of the residual variable Q i for, along with its 95% confidence limits.
【図６】本発明による残差変数Ｑi の値が許容範囲から
外れていたサンプルＮｏ．３３０の製品について、各プ
ロセス変数の寄与度を示した棒グラフである。FIG. 6 shows a sample No. in which the value of the residual variable Q i according to the present invention is out of the allowable range. 3 is a bar graph showing the contribution of each process variable for 330 products.
【図７】主成分分析で得られた第１主成分と第２主成分
のスコア変数に関する散布図を９５％信頼限界である楕
円とともに示した図である。FIG. 7 is a diagram showing a scatter diagram regarding score variables of the first principal component and the second principal component obtained by the principal component analysis together with an ellipse which is a 95% confidence limit.
【図８】本発明による、各製品のサンプルＮｏ．に対す
る距離変数Ｄi の値を、その９５％信頼限界とともに例
示した棒グラフである。FIG. 8 shows a sample No. of each product according to the present invention. 6 is a bar graph illustrating the value of the distance variable D i for, along with its 95% confidence limits.
【図９】本発明による残差変数Ｑi の値が許容範囲内で
はあったが、距離変数Ｄi の値が許容範囲外であったサ
ンプルＮｏ．７９０の製品について、各スコア変数の寄
与度を示した棒グラフである。9 is a sample No. in which the value of the residual variable Q i according to the present invention is within the allowable range, but the value of the distance variable D i is outside the allowable range. 9 is a bar graph showing the contribution of each score variable for 790 products.
【図１０】サンプルＮｏ．７９０の製品の不良原因と特
定された、第２主成分のスコア変数への各プロセス変数
の寄与度を示した棒グラフである。10 is a sample No. 7 is a bar graph showing the contribution of each process variable to the score variable of the second principal component, which is identified as the cause of the defective product of 790 products.
１ 品質不良製品を問合せる工程
２ 品質データベース
３ 解析対象製品を指定する工程
４ プロセスデータを検索・収集する工程
５ プロセスデータベース
６ 主成分分析を行う工程
７ 残差変数を計算し、許容範囲内か判断する工程
８ 残差寄与度を計算する工程
９ 残差寄与度を比較しプロセス変数を抽出する工程
１０ 距離変数を計算し、許容範囲内か判断する工程
１１ 距離寄与度を計算する工程
１２ 距離寄与度を比較しスコア変数を抽出する工程
１３ スコア寄与度を計算する工程
１４ スコア寄与度を比較しプロセス変数を抽出する工
程1 Process for inquiring about defective products 2 Quality database 3 Process for specifying products to be analyzed 4 Process for searching / collecting process data 5 Process database 6 Process for performing principal component analysis 7 Residual variables are calculated to determine whether they are within the allowable range Step 8 Calculating residual error contribution 9 Detecting process variables by comparing residual error contributions 10 Calculating a distance variable and determining whether it is within an allowable range 11 Calculating distance contribution 12 Distance contribution Of comparing score degrees and extracting score variables 13 Step of calculating score contribution rates 14 Step of comparing score contribution rates and extracting process variables
───────────────────────────────────────────────────── フロントページの続き (51)Int.Cl.7 識別記号 ＦＩ テーマコート゛(参考） Ｇ０６Ｆ 17/60 １５０ Ｇ０６Ｆ 17/60 １５０ ─────────────────────────────────────────────────── ─── Continued Front Page (51) Int.Cl. 7 Identification Code FI Theme Coat (Reference) G06F 17/60 150 G06F 17/60 150
Claims (4)
する方法であって、品質不良と指定した製品と同品種の
製品に関する、プロセスデータを検索・収集する工程
と、 収集した同品種の製品のプロセスデータから主成分分析
を利用して、プロセス変数の線形結合であるスコア変数
を得る工程と、 残差変数を計算し、前記残差変数が前記プロセスの正常
な許容範囲内にあるかを判断する工程と、 前記指定した製品が残差変数の許容範囲を外れていたと
き、残差変数の値への各プロセス変数の寄与度を計算す
る工程と、 各プロセス変数の寄与度を比較して、残差変数の値に主
に寄与しているプロセス変数を品質不良の原因の候補と
して抽出する工程と、 前記指定した製品が残差変数の許容範囲を外れていない
とき、距離変数を計算し、前記距離変数が、前記プロセ
スの正常な許容範囲内にあるかを判断する工程と、 前記指定した製品が距離変数の許容範囲を外れていたと
き、距離変数の値への各スコア変数の寄与度を計算する
工程と、 各スコア変数の寄与度を比較して、距離変数の値に主に
寄与しているスコア変数を品質不良の原因の候補として
抽出する工程と、 候補として抽出されたスコア変数への各プロセス変数の
寄与度を計算する工程と、 前記の抽出されたスコア変数に主に寄与しているプロセ
ス変数を品質不良の原因の候補として抽出する工程と、
からなることを特徴とする品質不良の原因解析方法。1. A method for analyzing a manufacturing process based on product quality, which comprises: searching and collecting process data regarding a product of the same type as a product designated as defective quality; Using a principal component analysis from the process data, obtaining a score variable that is a linear combination of process variables, and calculating a residual variable to determine whether the residual variable is within the normal tolerance range of the process. And the step of calculating the contribution of each process variable to the value of the residual variable when the specified product is outside the allowable range of the residual variable, and the contribution of each process variable is compared. , A step of extracting a process variable mainly contributing to the value of the residual variable as a candidate for the cause of the quality defect, and calculating a distance variable when the specified product is not outside the allowable range of the residual variable. , The distance Determining whether the variable is within the normal tolerance of the process, and calculating the contribution of each score variable to the value of the distance variable when the specified product is outside the tolerance of the distance variable. And the step of comparing the contribution of each score variable, extracting the score variables that mainly contribute to the value of the distance variable as candidates for the cause of poor quality, and the steps of extracting the score variables to the score variables extracted as candidates. Calculating the contribution of each process variable, and extracting the process variables mainly contributing to the extracted score variable as a candidate for the cause of quality defects,
A method of analyzing the cause of quality defects, which comprises:
法であって、前記残差変数は量Ｑi であって、次のよう
に定義され、 【数１】 ここで、ｍはプロセス変数の数、ｒはスコア変数の個数
であって、ｘijはｉ番目の製品のｊ番目のプロセス変数
であって、ｔikはｉ番目の製品のｋ番目のスコア変数で
あって、ｐjkはｊ番目のプロセス変数とｋ番目のスコア
変数間の負荷量であって、製品ｉが残差変数Ｑi の許容
範囲を外れていたとき、Ｑi の各項ｑijのうち最大の項
に相当するプロセス変数を、品質不良の原因の候補とす
ることを特徴とする品質不良の原因解析方法。2. The method of analyzing the cause of quality defects according to claim 1, wherein the residual variable is a quantity Q i and is defined as follows: Here, m is the number of process variables, r is the number of score variables, x ij is the j th process variable of the i th product, and t ik is the k th score variable of the i th product. a is, p jk is a load between j-th process variable and k-th score variable, when the product i was outside the allowable range of the residual variable Q i, each term of Q i q ij A method of analyzing the cause of quality defects, characterized in that the process variable corresponding to the largest term is set as a candidate for the cause of quality defects.
法であって、前記距離変数は量Ｄi であって、次のよう
に定義され、 【数２】 ここで、ｓk はすべての製品におけるｋ番目のスコア変
数の標本標準偏差であって、製品ｉが請求項２に記載の
残差変数Ｑi の許容範囲を外れてはいないが、距離変数
Ｄi の許容範囲を外れていたとき、Ｄi の各項ｔik 2 ／
ｓk 2 のうち最大の項に相当するスコア変数を品質不良
の原因の候補とすることを特徴とする品質不良の原因解
析方法。3. The method of analyzing the cause of quality defects according to claim 2, wherein the distance variable is a quantity D i and is defined as follows: Here, s k denotes a sample standard deviation of k-th score variables in all products, but the product i is not out of the allowable range of the residual variable Q i according to claim 2, the distance variable D When i is out of the allowable range, each term of D i t ik 2 /
A method for analyzing the cause of quality defects, wherein a score variable corresponding to the maximum term of s k 2 is used as a candidate for the cause of quality defects.
法であって、品質不良の原因の候補とされたスコア変数
が次式のように定義され、 【数３】 上式のスコア変数に寄与している品質不良原因の候補と
して、ｘijｐjkがスコア変数ｔikと同符号で大きさが最
大の項に相当するプロセス変数を抽出することを特徴と
する品質不良の原因解析方法。4. The method of analyzing the cause of quality defects according to claim 3, wherein a score variable that is a candidate for the cause of quality defects is defined by the following equation: As a candidate of the cause of quality defects contributing to the score variable in the above equation, a quality characterized by extracting a process variable in which x ij p jk has the same sign as the score variable t ik and corresponds to a term having the maximum magnitude. How to analyze the cause of defects.
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