getARL: Average Run Length (ARL)

In SNSchart: Sequential Normal Scores in Statistical Process Management

Description

Get the ARL getRL

Usage

getARL(
  n,
  m,
  theta = NULL,
  Ftheta = NULL,
  dist,
  mu,
  sigma,
  dist.par = c(0, 1, 1),
  chart,
  chart.par,
  scoring = "Z",
  Chi2corrector = "None",
  replicates = 10000,
  isParallel = TRUE,
  print.RL = FALSE,
  progress = FALSE,
  calibrate = FALSE,
  arl0 = 370,
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE,
  isFixed = FALSE,
  rounding.factor = NULL
)

Arguments

n	scalar. Subroup size
m	scalar. Reference sample size
theta	scalar. Value corresponig with the Ftheta quantile.
Ftheta	scalar. Quantile of the data distribution. The values that take are between (0,1).
dist	character string. Select from: "Uniform: Continuous Uniform distribution . "Normal": Normal distribution (default). "Normal2": Squared Normal distribution (also known as Chi-squared). "DoubleExp": Double exponential distribution (also known as Laplace distribution). "DoubleExp2": Double exponential squared distribution from a DoubleExp(0,1). "LogNormal": Lognormal distribution. "Gamma": Gamma distribution. "Weibull": Weibull distribution. "t": Student-t distribution.
mu	vector. Two elements, the first one is the mean of the reference sample and the second one is the mean of the monitoring sample.
sigma	vector. Two elements, the first one is the sd of the reference sample and the second one is the sd of the monitoring sample.
dist.par	vector. Distribution parameters. c(par.a, par.b). Default c(0,1).
chart	character string. Selected type of chart. Three options are available: Shewhart, CUSUM, EWMA
chart.par	vector. The size depends on the selected chart: Shewhart scheme: is c(k), where k comes from UCL = mu + kσ, LCL = mu - kσ. CUSUM scheme: is c(k, h, t) where k is the reference value and h is the control limit, and t is the type of the chart (1:positive, 2:negative, 3:two sides) EWMA scheme: is c(lambda, L), where lambda is the smoothing constant and L multiplies standard deviation to get the control limit
scoring	character string. If "Z" (normal scores) (default). If "Z-SQ" (normal scores squared).
Chi2corrector	character string. Only when scoring is Z-SQ. Select from "approx: Z^2*(m + 1 + 1.3)/(m+1). "exact": Z^2/mean(Z). "none": Z^2. If "approx" () (default). If "exact" (normal scores squared).
replicates	scalar. Number of replicates to get the ARL
isParallel	logical. If TRUE the code runs in parallel according to the number of cores in the computer,otherwise the code runs sequentially. Default TRUE.
print.RL	logical. If TRUE return the vectors of RL for each iteration.
progress	logical. If TRUE it shows the progress in the console.
calibrate	logical. If TRUE the RL is limit to 10 times the target ARL.
arl0	scalar. Expected value of the RL. Default 370.
alignment	character string. Aligment of the data X and Y. Select from "unadjusted": nothing is sustracte from X and Y (default). "overallmean": overall mean is sustracted from X and Y. "overallmedian": overall median is sustracted from X and Y. "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector. "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector. "referencemean": mean from Y is subtracted from X and Y. "referencemedian": median from Y is subtracted from X and Y. "constantvalue": a constant value is subtracted from X and Y.
constant	scalar. Only used when the alignment is selected "constantvalue". Default NULL.
absolute	logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)
isFixed	logical. If TRUE the reference sample does not update, otherwise the reference sample is updated whenever the batch is in control.
rounding.factor	scalar. positive value that determine the range between two consecutive rounded values.

Value

Multiple output. Select by output$

• ARL: scalar. Average Run Length for the RLs of all the replicates.

• SDRL: scalar. Standard Deviation Run Length for the RL in all the replicates.

• MRL: bolean. Median Run Length for the RLs of all the replicates.

• QRL: vector. It retrieve the quantiles (0.05, 0.1, 0.2, 0.25, 0.5, 0.75, 0.8, 0.9, 0.95) for all the RLs.

Examples

n <- 5 # subgroup size
m <- 100 # reference-sample size
dist <- "Normal"
mu <- c(0, 0) # c(reference sample mean, monitoring sample mean)
sigma <- c(1, 1) # c(reference sample sd, monitoring sample sd)

#### Normal distribution parameters
dist.par <- c(0, 1) # c(location, scale)

#### Other Parameters
replicates <- 2
print.RL <- TRUE
isParallel <- FALSE
calibrate <- FALSE
progress <- TRUE
arl0 <- 370

#### Control chart parameters
chart <- "Shewhart"
chart.par <- c(3)
shewhart <- getARL(n, m,
  theta = NULL, Ftheta = NULL, dist, mu, sigma, dist.par = dist.par,
  chart = chart, chart.par = chart.par, print.RL = print.RL,
  replicates = replicates, isParallel = isParallel,
  calibrate = calibrate, arl0 = arl0
)

chart <- "CUSUM"
chart.par <- c(0.25, 4.4181, 3)
cusum <- getARL(n, m,
  theta = NULL, Ftheta = NULL, dist, mu, sigma, dist.par = dist.par,
  chart = chart, chart.par = chart.par, print.RL = print.RL,
  replicates = replicates, isParallel = isParallel,
  calibrate = calibrate, arl0 = arl0
)

chart <- "EWMA"
chart.par <- c(0.2, 2.962)
shewhart <- getARL(n, m,
  theta = NULL, Ftheta = NULL, dist, mu, sigma, dist.par = dist.par,
  chart = chart, chart.par = chart.par, print.RL = print.RL,
  replicates = replicates, isParallel = isParallel,
  calibrate = calibrate, arl0 = arl0
)

SNSchart documentation built on April 7, 2021, 9:07 a.m.