plot_ccc function

Constructs a control chart for the cycle lengths of a categorical series

plot_ccc constructs a control chart for the cycle lengths of a categorical series UTF-8

plot_ccc(
  series,
  mu_t,
  lcl_t,
  ucl_t,
  plot = TRUE,
  title = "Control chart (cycles)",
  ...
)

Arguments

• series: An object of type tsibble (see R package tsibble), whose column named Value contains the values of the corresponding CTS. This column must be of class factor and its levels must be determined by the range of the CTS.
• mu_t: The mean of the process measuring the cycle lengths.
• lcl_t: The lower control limit.
• ucl_t: The upper control limit.
• plot: Logical. If plot = TRUE (default), returns the control chart. Otherwise, returns the standardized statistic.
• title: The title of the graph.
• ...: Additional parameters for the function.

Returns

If plot = TRUE (default), represents the control chart for the cycle lengths. Otherwise, the function returns a matrix with the values of the standardized statistic for each time t

Details

Constructs a control chart of a CTS based on cycle lengths. The chart is based on the standardized statistic $T_t=T_t^{(L)}+T_t^{(U)}$, with $T_t^{(L)}=\min \left(0, \frac{C_t-\mu_t}{\left|L C L_t-\mu_t\right|}\right)$

and $T_t^{(U)}=\max \left(0, \frac{C_t-\mu_t}{\left|U C L_t-\mu_t\right|}\right)$, where $Z_t$ expresses the length of a cycle ending with a specific category, $\mu_t$ denotes the mean of $Z_t$ and $LCL_t$ and $UCL_t$ are lower and upper individual control limits, respectively. Note that an out-of-control alarm is signalled if $T_t<-1$ or $T_t>1$.

Examples

sequence_1 <- SyntheticData1[which(SyntheticData1$Series==1),]
cycle_cc <- plot_ccc(series = sequence_1, mu_t = c(1, 1.5, 1),
lcl_t = rep(10, 600), ucl_t = rep(10, 600)) # Representing
# a control chart for the cycle lengths
cycle_cc <- plot_ccc(series = sequence_1, mu_t = c(1, 1.5, 1),
lcl_t = rep(10, 600), ucl_t = rep(10, 600), plot = FALSE) # Computing the
# corresponding standardized statistic

References

Rdpack::insert_ref(key="weiss2008visual",package="ctsfeatures")

Author(s)

Ángel López-Oriona, José A. Vilar