BS 5703-3:1981

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 Basic decision rules
0.5 Practical points about cusum masks
0.6 Scaling the chart
1 Scope
2 References
3 Symbols and terminology
3.1 General
3.2 Symbols and terms
4 Cusum decision procedures
4.1 Purpose of decision rules
4.2 Principles of decision rules
4.3 Run length properties of the decision rule
5 Scope of methods for process and quality control
5.1 Definition of 'process'
5.2 Process parameters
5.3 Nature of possible changes
5.4 Formulation of target value
5.5 One-way and two-way control
5.6 Control to specification limits
6 Cusum schemes for means
6.1 Limitations of basic schemes
6.2 Semi-parabolic mask
6.3 Alternative standard schemes
6.4 Design of schemes with specific characteristics
7 Control of short-term variation
7.1 Introduction
7.2 Cusum schemes for sample ranges
7.3 Cusum schemes for standard deviation
7.4 Control of between-sample variation
7.5 Two-way control of standard deviation
8 Tabulation methods
8.1 General
8.2 One-sided tabulation for sample means
8.3 Two-sided tabulation for sample means
8.4 Two-way tabulation for sample means, with one-way
      tabulation for ranges
8.5 Two-way control of standard deviation, using
      tabulation for transformation method
9 Computer application of cusum methods
9.1 General
9.2 Logic and flow charts
9.3 Computer algorithms
10 Preparatory analysis of process capability (or
      feasibility) data
10.1 Elements of variation
10.2 Within-sample variation
10.3 Measuring other sources of variation
10.4 Use of retrospective cusum analysis
10.5 Serial dependence
10.6 Use of components of variation
Tables
1 Data for cusum plotting
2 Cusum calculations for tabulation procedure
3 Effect of operating two-way control on ARL curve
      of cusum scheme
4 Data for construction of a semi-parabolic cusum
      mask
5 Comparison of semi-parabolic mask with basic cusum
      rule, and with Shewhart charts
6 Cusum parameters for alternative decision rules
7 Average run length data for alternative decision
      rules
8 Alternative sampling procedures yielding 1 h mean
      time to detection of three-unit shift
9 Evaluation of scheme with K = 1.5, h = 2.8, with
      mu a = 0, mu r = 3, sigma e = 2.3
10 Cusum schemes for range in samples from a normal
      population
11 ARL data for cusum range schemes
12 Cusum schemes for standard deviation in samples
      from a normal population
13 ARL data for standard deviation schemes
14 Critical values for ratio of local estimate of
      sigma e to target value, for sample sequences of
      length m (0.01 significance level, two-tail test)
15 Critical values for ratio of two local estimates
      of sigma e in sequences of length m1, m2 (0.01
      significance level, two-tail test)
16 Lower control chart limits for sample ranges and
      sample estimates of standard deviation
17 Parameters for cusum schemes for two-way control
      of standard deviation, based on transformation
      method
18 ARL data for cusum schemes for two-way control of
      standard deviation (transformation method)
19 Cusum tabulation for ash content data
20 Two-way cusum tabulation for staple fibre length
21 Cusum mean and range tabulations for simulated
      package weight data
22 Example of cusum tabulation for transformation
      method
23 Critical values of (sigma u/sigma o) x square root
      of (nm)
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 General-purpose truncated V-mask
6 Truncated V-mask applied to cusum chart: no
      indication of shift
7 Truncated V-mask applied to cusum chart:
      indication of shift
8 Average run length data for cusum and control
      charts
9 Semi-parabolic cusum mask
10 ARL curves for C1 (and S1) schemes
11 ARL curves for C2 (and S2) schemes
12 General construction of truncated mask
13 Masks for C1 and C2 schemes
14 Intercept chart for h, f,
      (modulus (mu a - mu r))/sigma e, La and Lr
15 Nonogram for ARL of cusum schemes for normally
      distributed variable (mean level on AQL side of
      reference value)
16 Nonogram for ARL of cusum schemes for normally
      distributed variable (mean level on RQL side of
      reference value)
17 Nonogram for ARL of cusum schemes for normally
      distributed variable (mean level within
      0.5 sigma e of reference value ARL or RQL side)
18 Flow chart for upper-sided cusum tabulation
19 Flow chart for lower-sided cusum tabulation
20 Flow chart for two-sided cusum tabulation