BS 5703-4:1982

Foreword
Cooperating organizations
Guide
0 Introduction
0.1 Basis of cusum chart
0.2 Simple example of cusum chart
0.3 Monitoring of retrospective analysis
0.4 Scaling the chart
1 Scope
2 Terminology and symbols
3 Decision rules: general
4 Decision rules for counted data
5 Cusum procedures for Poisson variables
6 Cusum procedures for binomial variables
7 Cusums for low rates of occurrence of events
8 Testing the validity of Poisson or binomial
     distribution assumptions
9 Example of the application of cusum methods to
     counted data
Appendix
A Basic decision rules and practical points about
     cusum masks
Tables
1 Data for cusum plotting
2 Cusum data for Poisson variable with ma = 4
3 Cusum data for binomial variable n = 20, p = 0.03
4 Comparison of ARL curve for three discrete
     distributions
5 C1 and C2 schemes for Poisson variables
6 ARL characteristics of cusum schemes for Poisson
     variables
7 Cusum tabulation for data of table 2 using H = 8
     and K = 6
8 Cusum tabulation for data of table 2 using H = 3
     and K = 1.5
9 C1 and C2 schemes for binomial variables
10 ARL data for schemes for binomial variables
11 ARL's for schemes with H = 1, binary events
12 Examples of schemes for weapons trial application
     (7.4)
13 ARL's for schemes with H = 1, Poisson variables
14 ARL data for schemes with K = 0.1, Poisson variable
15 ARL data for schemes with K = 0.25, Poisson
     variable
16 Critical values of D for testing binomial or
     Poisson distribution assumptions
17 Observed and expected frequencies for dustbin data
18 Observed and expected frequencies for fabric fault
     data
19 Cusum calculations for dustbin data
20 Cusum calculations for fabric fault data
21 Cusum calculations for rearranged data of 8.6 (and
     table 20)
22 Comparison of alternative schemes for P1 = 0.005
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 Form and simple construction for cusum mask for
     counted data
6 Cusum and conventional charts of Poisson data
7 Cusum and conventional charts of binomial data
8 Cusum chart for data of table 2, using H = 8 and
     K = 6
9 Cusum chart for data of table 3, using H = 3 and
     K = 1.5
10 Cusum charts for data of tables 20 and 21
11 Conventional charts for data of tables 20 and 21
12 Cusum chart for data of table 19
13 General-purpose truncated V-mask
14 Truncated V-mask applied to cusum chart: no
     indication of shift
15 Truncated V-mask applied to cusum chart: indication
     of shift

Cusum methods applicable to binary data (sequences of trials where the outcomes are scored as 0 or 1) or counts of attributes or events. Common applications are in quality control (by counts of defectives or by gauging) but these methods are also used frequently in research and development e.g. proving trials where results are simply classified as a success or failure.