shewhart {dfphase1}R Documentation

Univariate Shewhart-type control charts

Description

shewhart computes, and, optionally, plots, Shewhart-type Phase I control charts for detecting changes in location and scale of univariate subgrouped data.

shewhart.normal.limits pre-computes the corresponding control limits when the in-control distribution is normal.

Usage

shewhart(x, subset, stat = c("XbarS", "Xbar", "S", "Rank", "lRank", "sRank"),
  aggregation = c("median", "mean"), plot = TRUE, FAP = 0.05,
  seed = 11642257, L = if (stat %in% c("XbarS", "Xbar", "S")) 1000 else 100000,
  limits = NA)

shewhart.normal.limits(n, m, stat = c("XbarS", "Xbar", "S", "Rank", "lRank", "sRank"),
  aggregation = c("median", "mean"), FAP = 0.05,
  seed = 11642257, L = 100000)

Arguments

x

a nxm data numeric matrix (n observations gathered at m time points).

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

stat

character: the control statistic[s] to use; see Details.

aggregation

character: it specify how to aggregate the subgroup means and standard deviations. Used only when stat is XbarS, Xbar or S.

plot

logical; if TRUE, control statistic[s] is[are] displayed.

FAP

numeric (between 0 and 1): desired false alarm probability.

seed

positive integer; if not NA, the RNG's state is resetted using seed. The current .Random.seed will be preserved. Unused by shewhart when limits is not NA.

L

positive integer: number of Monte Carlo replications used to compute the control limits. Unused by shewhart when limits is not NA.

limits

numeric: a precomputed vector of control limits. The vector should contain (A,B1,B2) when stat=XbarS, (A) when stat=Xbar, (B1,B2) when stat=S, (C,D) when stat=Rank, (C) when stat=lRank and (D) when stat=sRank. See Details for the definition of the critical values A, B1, B2, C and D.

Details

The implemented control charts are:

Value

shewhart returns an invisible list with elements

Xbar

subgroup means; this element is present only if stat is XbarS or Xbar.

S

subgroup standard deviation; this element is present only if stat is XbarS or S.

lRank

rank-based control statistics for detecting changes in location; this element is present only if stat is Rank or lRank.

sRank

rank-based control-statistics for detecting changes in scale; this element is present only if stat is Rank or sRank.

limits

control limits.

center, scale

estimates mu.hat and sigma.hat of the in-control mean and standard deviation; these elements are present only if stat is XbarS, Xbar and S.

stat, L, aggregation, FAP, seed

input arguments.

shewhart.normal.limits returns a numeric vector containing the limits.

Note

  1. If argument limits is NA, shewhart computes the control limits using (i) the permutation approach if stat is Xbars, Xbar, S and (ii) the distribution-free unconditional distribution when stat is Rank, lRank and sRank. In both cases, the resulting control chart is distribution-free.

  2. Pre-computed limits, such as those computed using shewhart.normal.limits, are not recommended when stat is XbarS, Xbar or S. Indeed, the resulting control chart will not be distribution-free.

  3. When stat is Rank, lRank or sRank, the control limits computed by shewhart.normal.limits are distribution-free in the class of all univariate continuous distributions. So, if user plan to apply rank-based control charts on a repeated number of samples of the same size, pre-computing the control limits using mshewhart.normal.limits can reduce the overall computing time.

Author(s)

Giovanna Capizzi and Guido Masarotto.

References

L. A. Jones-Farmer, V. Jordan, C. W. Champs (2009) “Distribution-free Phase I control charts for subgroup location”, Journal of Quality Technology, 41, pp. 304–316.

L. A. Jones-Farmer, C. W. Champ (2010) “A distribution-free Phase I control chart for subgroup scale”. Journal of Quality Technology, 42, pp. 373–387.

Examples

# A simulated example
set.seed(12345)
y <- matrix(rt(100,3),5)
y[,20] <- y[,20]+3
shewhart(y)
# Reproduction of the control charts shown
# by Jones-Farmer et. al. (2009,2010)
data(colonscopy)
u <- shewhart.normal.limits(NROW(colonscopy),NCOL(colonscopy),stat="lRank",FAP=0.1)
u
# control limits based on a limited number of replications
# to avoid a (relatively) long execution time
shewhart(colonscopy,stat="lRank",limits=u,L=10000)
shewhart(colonscopy,stat="sRank",FAP=0.1,L=10000)

[Package dfphase1 version 1.1.1 Index]