ISO 7870-2:2023 管理図 — Part 2: シューハート管理図 | ページ 2

3.1 一般的なプレゼンス

このドキュメントの目的のために、ISO 3534-2 で指定されている用語と定義が適用されます。

ISO および IEC は、次のアドレスで標準化に使用する用語データベースを維持しています。

3.2.1 このドキュメントの目的のために、次の記号が適用されます

n	サブグループのサイズ;サブグループごとの標本観測数
k	サブグループ数
L	下側規格限界
L _	下限管理限界
L CLi	i 番目のth グループの管理限界の下限
CL	センターライン
U _	管理上限
U CLi	i 番目のth グループの上限管理限界
X	測定された品質特性 (個々の値は ( X 1 、 X 2 、 X 3 、...) として表されます) X の代わりに記号Y が使用されることがあります。
	( X バー) サブグループ平均
	( X 二重棒) サブグループ平均の平均
µ	真の工程平均
μ0	μの所定の値または事前に指定された値
σ	真の工程標準偏差
σ0	与えられた、または事前に指定されたσの値
	サブグループの中央値
	サブグループ中央値の平均
R	サブグループ範囲
	サブグループ範囲の平均
R m	サブグループの移動範囲
	平均移動範囲
s	サブグループ標本標準偏差
	サブグループ標本標準偏差の平均
p	サブグループ内の不適合アイテムの割合
	すべてのサブグループの不適合項目の平均比率
n.p	サブグループ内の不適合アイテムの数
p _	p の与えられた値
n p0	npの特定の値 (特定のp 0に対して)
c	サブグループ内の不適合の数
c 0	与えられたc の値
	すべてのサブグループの不適合の平均数
u	サブグループ内の単位あたりの不適合数
	ユニットあたりの平均不適合数

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives ).

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any patent rights identified during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents ).

Any trade name used in this document is information given for the convenience of users and does not constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISO's adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html .

This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods, Subcommittee SC 4, Applications of statistical methods in process management.

This second edition cancels and replaces the first edition (ISO 7870-2:2013), which has been technically revised.

The main changes are as follows:

• various clauses have been modified for better understanding;
• some examples for control charts have been modified;
• new examples for control charts have been included.

A list of all parts in the ISO 7870 series can be found on the ISO website.

Introduction

A traditional approach to manufacturing has been to depend on production to make the product and on quality control to inspect the final product and screen out items not meeting specifications. This strategy of detection is often wasteful and uneconomical because it involves after-the-event inspection when the wasteful production has already occurred. Instead, it is much more effective to institute a strategy of prevention to avoid waste by not producing unusable output in the first place. This can be accomplished by gathering process information and analysing it so that timely action can be taken on the process itself.

Dr. Walter Shewhart in 1924 developed the control chart method for controlling the quality during production. Control chart theory recognizes two kinds of variability. The first kind is random variability (also known as natural/inherent/uncontrollable variation) arising due to causes known as chance/common/random causes. This is due to the wide variety of causes that are consistently present and not readily identifiable, each of which constitutes a very small component of the total variability but none of them contributes any significant amount. Nevertheless, the sum of the contributions of all of these unidentifiable random causes is measurable and is assumed to be inherent to the process. The elimination or correction of common causes may well require a decision to allocate resources to fundamentally change the process and system.

The second kind of variability represents a real change in the process. Such a change can be attributed to some identifiable causes that are not an inherent part of the process and which can, at least theoretically, be eliminated. These identifiable causes are referred to as “assignable causes” (also known as special/unnatural/systematic/controllable causes) of variation. They may be attributable to such matters as the lack of uniformity in material, a broken tool, workmanship or procedures, the irregular performance of equipment, or environmental changes.

A process is said to be in a state of statistical control, or simply “in control”, if the process variability results only from random causes. Once this level of variation is determined, any deviation from this level is assumed to be the result of assignable causes that should be identified and eliminated.

The major statistical tool used to do this is the control chart, which is a method of presenting and comparing information based on a sequence of observations representing the current state of a process against limits established after consideration of inherent process variability. The control chart method helps first to evaluate whether a process has attained, or continues in, a state of statistical control. When the process is deemed to be stable and predictable, then further analysis regarding the ability of the process to satisfy the requirements of the customer may be conducted. The control chart also can be used to provide a continuous record of a quality characteristic of the process output while process activity is ongoing. Control charts aid in the detection of unnatural patterns of variation in data resulting from repetitive processes and provide criteria for detecting a lack of statistical control. The use of a control chart and its careful analysis leads to a better understanding of the process and will often result in the identification of ways to make valuable improvements.

1 Scope

This document establishes a guide to the use and understanding of Shewhart control chart approach to the methods for statistical control of a process.

This document is limited to the treatment of statistical process control methods using only Shewhart system of charts. Some supplementary material that is consistent with Shewhart approach, such as the use of warning limits, analysis of trend patterns and process capability is briefly introduced. However, there are several other types of control charts which can be used in different situations.

2 Normative references

The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.

3 Terms and definitions

3.2 Symbols

3.2.1 For the purposes of this document, the following symbols apply

n	Subgroup size; the number of sample observations per subgroup
k	Number of subgroups
L	Lower specification limit
LCL	Lower control limit
LCLi	Lower control limit for ith subgroup
CL	Centre line
UCL	Upper control limit
UCLi	Upper control limit for ith subgroup
X	Measured quality characteristic (individual values are expressed as (X1, X2, X3,...). Sometimes the symbol Y is used instead of X
	(X bar) Subgroup average
	(X double bar) Average of the subgroup averages
μ	True process mean
μ0	A given or prespecified value of μ
σ	True process standard deviation
σ0	A given or prespecified value of σ
	Median of a subgroup
	Average of the subgroup medians
R	Subgroup range
	Average of subgroup ranges
Rm	Subgroup moving range
	Average moving range
s	Subgroup sample standard deviation
	Average of subgroup sample standard deviations
p	Proportion of nonconforming items in a subgroup
	Average proportion of nonconforming items for all subgroups
np	Number of nonconforming items in a subgroup
p0	A given value of p
np0	A given value of np (for a given p0)
c	Number of nonconformities in a subgroup
c0	A given value of c
	Average number of nonconformities for all subgroups
u	Number of nonconformities per unit in a subgroup
	Average number of nonconformities per unit

Bibliography

1	ISO 7870-4, Control charts — Part 4: Cumulative sum charts
2	ISO 7870-6, Control charts — Part 6: EWMA control charts
3	ISO 22514 (all parts), Statistical methods in process management — Capability and performance
4	Shewhart W.A., Economic Control of Manufactured Product. D. Van Nostrand, Co, New York, 1931, pp. 501
5	Nelson L.S., The Shewhart Control Chart — Test for Special Causes. J. Qual. Technol.1984 October, 16 (4) pp. 237–239
6	Nelson L.S., Interpreting Shewhart Control Charts. J. Qual. Technol.1985 April, 17 (2) pp. 114–116
7	Klein M., Two Alternatives to the Shewhart Control Chart. J. Qual. Technol.2000, 32 pp. 427–431
8	Montgomery D.C., Introduction to statistical quality control. John Wiley & Sons, Eighth Edition,2019
9	Prabhu S.S., Montgomery D.C., Runger G.C., A Combined Adaptive Sample Size and Sampling Interval Control Scheme. J. Qual. Technol.1994, 26 pp. 164–176