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Multivariate CUSUM control chart (Crosier 1988)

Source: R/chart-mcusum.R
shewhart_mcusum.Rd

Constructs a multivariate CUSUM chart for jointly monitoring p correlated variables. Like the univariate CUSUM it accumulates deviations from a target with a reference value k that decides when the accumulator resets; unlike a Hotelling T^2 chart it carries memory across observations and so detects small persistent shifts faster.

Usage

shewhart_mcusum(
  data,
  vars,
  index = NULL,
  target = NULL,
  cov = NULL,
  k = 0.5,
  h = NULL,
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

data

A data frame.

vars

Tidy-select expression for the columns to monitor jointly. At least 2 columns.

index

Optional tidy-eval column for the x-axis.

target

Optional length-p numeric vector. The in-control mean. Defaults to colMeans(data[, vars]).

cov

Optional p x p covariance matrix. Defaults to cov(data[, vars]).

k

Reference value, in sigma units. Default 0.5, tuned for shifts of 1 sigma. Lower k makes the chart sensitive to smaller shifts but increases false alarms.

h

Decision interval. If NULL, looked up in the Crosier (1988) Table 1 for k = 0.5, ARL_0 ~ 200, p = 2..10.

locale

One of "en", "pt", "es", "fr".

verbose

Logical. Print progress messages?

Value

A shewhart_chart object of subclass shewhart_mcusum. The augmented tibble has columns .y (the chart statistic), .upper (the decision interval h), and .flag_signal.

References

Crosier, R. B. (1988). Multivariate Generalizations of Cumulative Sum Quality-Control Schemes. Technometrics, 30(3), 291-303. doi:10.1080/00401706.1988.10488402

Pignatiello, J. J., & Runger, G. C. (1990). Comparisons of Multivariate CUSUM Charts. Journal of Quality Technology, 22(3), 173-186. doi:10.1080/00224065.1990.11979237

Examples

set.seed(1)
Sigma <- matrix(c(1, 0.6, 0.6, 1), 2, 2)
base  <- MASS::mvrnorm(60, c(0, 0), Sigma)
shift <- MASS::mvrnorm(40, c(0.6, 0.6), Sigma)
df    <- data.frame(t = 1:100,
                    x1 = c(base[, 1], shift[, 1]),
                    x2 = c(base[, 2], shift[, 2]))
fit <- shewhart_mcusum(df, vars = c(x1, x2), index = t,
                       target = c(0, 0), cov = Sigma)
print(fit)
#> 
#> ── Shewhart chart mcusum ───────────────────────────────────────────────────────
#> • Observations / subgroups: 100
#> • Phase: "phase_1"
#> • Sigma estimate ("mcusum"): NA
#> 
#> ── Control limits ──
#> 
#> # A tibble: 1 × 3
#>   chart  line  value
#>   <chr>  <chr> <dbl>
#> 1 MCUSUM UCL     5.5
#> ── Rule violations ──
#> 
#> ✔ No violations across 1 rule: "mcusum_h".
# \donttest{
ggplot2::autoplot(fit)

# }