changepoint | R Documentation |
changepoint
(univariate data) and mchangepoint
(multivariate data) test for the presence of a
sustained location and/or dispersion shift. Both functions can be applied
to individual and subgrouped observations.
changepoint.normal.limits
and
mchangepoint.normal.limits
precompute
the corresponding control limits when the in-control distribution is
normal.
changepoint(x, subset, score = c("Identity", "Ranks"), only.mean = FALSE,
plot = TRUE, FAP = 0.05, seed = 11642257, L = 10000, limits = NA)
mchangepoint(x, subset, score = c("Identity", "Signed Ranks", "Spatial Signs",
"Spatial Ranks", "Marginal Ranks"), only.mean = FALSE,
plot = TRUE, FAP = 0.05, seed = 11642257, L = 10000, limits = NA)
changepoint.normal.limits(n, m, score = c("Identity", "Ranks"),
only.mean = FALSE, FAP = 0.05, seed = 11642257, L = 100000)
mchangepoint.normal.limits(p, n, m, score = c("Identity", "Signed Ranks", "Spatial Signs",
"Spatial Ranks", "Marginal Ranks"), only.mean = FALSE,
FAP = 0.05, seed = 11642257, L = 100000)
x |
See below, for the meaning of p, n and m. |
p |
integer: number of monitored variables. |
n |
integer: size of each subgroup (number of observations gathered at each time point). |
m |
integer: number of subgroups (time points). |
subset |
an optional vector specifying a subset of subgroups/time points to be used |
score |
character: the transformation to use; see |
only.mean |
logical; if |
plot |
logical; if |
FAP |
numeric (between 0 and 1): the desired false alarm probability. |
seed |
positive integer; if not |
L |
positive integer: the number of Monte Carlo replications used to
compute the control limits. Unused by |
limits |
numeric: a precomputed vector of length m containing the control limits. |
After an optional rank transformation (argument score
),
changepoint
and mchangepoint
compute,
for \tau=2,\ldots,m
, the normal likelihood ratio test statistics
for verifying whether the mean and dispersion (or only the mean when
only.mean=TRUE
) are the same before and after \tau
.
See Sullivan and Woodall (1999, 2000) and Qiu (2013), Chapter 6 and
Section 7.5.
Note that
the control statistic is equivalent to that proposed by
Lung-Yut-Fong et al. (2011)
when score="Marginal Ranks"
and only.mean=TRUE
.
As suggested by Sullivan and Woodall (1999, 2000),
control limits proportional to the
in-control mean of the likelihood ratio test statistics
are used. Further, when plot=TRUE
, the control
statistics divided by the time-varying control limits
are plotted with a “pseudo-limit” equal to one.
When only.mean=FALSE
, the decomposition of the
likelihood ratio test statistic suggested
by Sullivan and Woodall (1999, 2000)
for diagnostic purposes is also
computed, and optionally plotted.
changepoint
and mchangepoint
return an
invisible list with elements
glr |
control statistics. |
mean , dispersion |
decomposition
of the control statistics in the two parts due to changes in the mean and
dispersion, respectively. These elements are present only when
|
limits |
control limits. |
score , only.mean , FAP ,
L , seed |
input arguments. |
changepoint.normal.limits
and mchangepoint.normal.limits
return a numeric vector
containing the control limits.
When limits
is NA
, changepoint
and mchangepoint
compute the control limits by permutation.
The resulting control charts are distribution-free.
Pre-computed limits, like those computed using
changepoint.normal.limits
and
mchangepoint.normal.limits
,
are recommended only for univariate data when score=Ranks
.
Indeed, in all the other cases, the resulting control
chart will not be distribution-free.
However, note that, when score
is Signed Ranks
, Spatial
Signs
, Spatial Ranks
the normal-based control limits are distribution-free in the class
of all multivariate elliptical distributions.
Giovanna Capizzi and Guido Masarotto.
A. Lung-Yut-Fong, C. Lévy-Leduc, O. Cappé O (2011) “Homogeneity and change-point detection tests for multivariate data using rank statistics”. arXiv:11071971, https://arxiv.org/abs/1107.1971.
P. Qiu (2013) Introduction to Statistical Process Control. Chapman & Hall/CRC Press.
J. H. Sullivan, W. H. Woodall (1996) “A control chart for preliminary analysis of individual observations”. Journal of Quality Technology, 28, pp. 265–278, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00224065.1996.11979677")}.
J. H. Sullivan, W. H. Woodall (2000) “Change-point detection of mean vector or covariance matrix shifts using multivariate individual observations”. IIE Transactions, 32, pp. 537–549 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/07408170008963929")}.
data(gravel)
changepoint(gravel[1,,])
mchangepoint(gravel)
mchangepoint(gravel,score="Signed Ranks")
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