Foreword
Cooperating organizations
Guide
0 Introduction
0.1 Basis of cusum chart
0.2 Simple example of cusum chart
0.3 Monitoring or retrospective analysis
1 Scope
2 References
3 Symbols and terminology
4 Simple decision rules (a) Monitoring and control
4.1 Introduction
4.2 Cusum V-masks
4.3 Practical considerations concerning cusum masks
4.4 The full V-mask
4.5 Local decision lines
4.6 Average run length characteristics of basic
decision rule
4.7 A semi-parabolic mask
5 Simple decision rules (b) Retrospective analysis
5.1 Introduction
5.2 'Span' tests
5.3 Construction of decision lines
5.4 Ad hoc tests of significance
5.5 Distribution-free cusum tests
5.6 A comparison of the four procedures
5.7 An example of application of the tests over a
longer series
5.8 Automatic procedures
6 Examples of applications
6.1 Introduction
6.2 Setting up a monitoring procedure from a
specification
6.3 Control of volatile matter in a synthetic resin
6.4 Ash-content in coal
6.5 Evaluation of the performance of a blending machine
6.6 Systematic patterns in fabric coating
6.7 Faults in kitted fabric
7 Extended cusum techniques
7.1 General
7.2 Cusums without charts
7.3 Application of automatic cusum procedure to package
weight control
7.4 Binary data, or counts of events containing
frequent zeros
7.5 An application of cusums to binary data
7.6 Data elements of varying size or importance
7.7 Estimation of standard error for weighted data
7.8 Application of weighted cusum to machine stoppages
7.9 Monitoring vehicle fuel consumption
Appendices
A The full V-mask
B Local decision lines
C Monitoring non-normal variables
D Construction of decision lines for retrospective
analysis
E Ad hoc tests of significance for retrospective
analysis
F Distribution-free cusum tests
G A comparison of the four procedures
H An example of application of the tests over a
longer series
J Rigorous procedure for obtaining standard errors
for weighted data
Tables
1 Data for cusum plotting
2 Average run length data for cusum and control
charts
3 Effect of incorrect value of sigma 3 on ARL
4 Data for construction of a semi-parabolic cusum
mask
5 Batch % volatile matter
6 Average run length data for cusum scheme for %
volatile matter
7 Data for ash-content in coal
8 Percentage of soluble ingredient present in
discharge from a blending machine
9 Span tests on cusum segments
10 Ad hoc significance tests on cusum segments
11 Cusum calculations for modified procedure
12 Data with varying sample sizes for weighted cusum
13 Machine stoppages data
14 Fuel consumption data, 1500 cc saloon car
15 Further fuel consumption details
16 Percentage points for cusum score (+1, -1) about
median (distribution-free tests)
17 Scores and cumulatives of sequence 8 to 24
18 Scores and cumulatives of sequence 8 to 31
19 Difference modulus (x1 - x2) indicated as
significant by various cusum tests (normally
distributed variable)
20 Data and cusum calculations
21 Cusum span tests on data of table 20
22 Tests of significance between mean levels of
segments
23 Use of distribution-free cusum tests
Figures
1 Conventional chart of data from table 1
2 Cusum chart of data from table 1
3 Cusum chart of data from table 1, with target value
12
4 Cusum chart of data from table 1, with target value
15 but compressed cusum scale
5 Some typical run length distributions
6 General-purpose truncated V-mask
7 Truncated V-mask applied to cusum chart: no
indication of shift
8 Truncated V-mask applied to cusum chart: indication
of shift
9 Average run length data for cusum and control
charts
10 Semi-parabolic cusum mask
11 Application of span test to cusum chart
12 Nomogram for evaluating maximum vertical height
(Vmax) of cusum over span of m sample intervals
13 Cusum chart for % volatile matter
14 Cusum chart of ash-content data from table 7
15 Cusum chart of data from blending experiment
16 Conventional chart of data from blending experiment
17 Cusum charts of resin deposition data
18 Cusum chart for fabric faults (T = 7, sigma = 6)
19 Alternative presentation of decision lines
20 Modified cusums, S1 and S2
21 Generalized cusum mask construction
22 Cusum chart of ammunition firing trials (binary
data)
23 Weighted cusum chart for data of table 12
24 Weighted cusum chart of machine stoppages data
25 Cusum charts for fuel use, 1500 cc saloon car
26 Full cusum V-mask
27 Alternative method of constructing full V-mask
28 Full V-mask applied to cusum chart (T = 15, sigma e
= 2)
29 Construction of local decision line
30 Decision line constructed on cusum chart (T = 15,
sigma e = 2)
31 Test for significance of change in cusum slope,
based on decision line
32 Cusum chart for retrospective analysis of data in
table 20
33 Typical span and decision line tests