getAve: Compute ATSs and Other Informations on Attribute VSI CUSUM...

Description Usage Arguments Details Value References See Also Examples

View source: R/attrCUSUM_getxxx_and_utils.R

Description

Computation of ANSSs, ATSs and other related informations on attribute VSI CUSUM control chart for mean increase based on the Markov chain approach.

Usage

1
2
getAve(refv, contl, c.zero = 0, warnl = 0, ds = 1, dl = NULL,
  di = NULL, process, maxndec = 7L, maxnumsubI = 6000L)

Arguments

refv

A reference value of CUSUM statistic.

contl

A control limit in CUSUM control scheme.

c.zero

An initial state of CUSUM statistic (default is 0).

warnl

A warning limit in VSI control scheme (default is 0).

ds

The shorter sampling interval in VSI CUSUM control scheme (default is 1).

dl

The longer sampling interval in VSI CUSUM control scheme.

di

The sampling interval at initial state in VSI CUSUM control scheme.

process

An object of function standing for pmf of count process of interest. See 'Details'.

maxndec

The maximum number of decimal places of refv ( 7L).

maxnumsubI

The maximum number of sub-intervals in [100,6000] to be used in applying the Markov chain approach.

Details

For CUSUM control chart for detecting mean increase, the CUSUM statistic (C_{t}) are defined as following:

C_{t}=max(C_{t-1}, 0) + X_{t} - k, t=1,2,...,

wherein X_{t} is a count process of interest, k is the reference value and C_{0} is the initial state.

The argument process is an object of function such that for given integer-valued vector x, process(x) returns P(X=x) where X is a random variable of interest.

If the number of sub-intervals for transient states of Markov chain is greater than maxnsubI, it will be set to be a suitable value being less than or equal maxnsubI.

For ANSS, it is the same as that psi.s + psi.l + 1.

For ATS, it is the same as that (psi.s * ds) + (psi.l * dl) + di.

Invalid arguments rise an error with a helpful message.

This function currently provides only the case for monitoring of mean increase. We leave other issues as our future work.

Value

A list including followings:

endpoints

Endpoints used for implementation of a matrix of transition probabilities.

numsubI

Number of sub-intervals used for implementation of a matrix of transition probabilities.

lensubI

Length of sub-intervals used for implementation of a matrix of transition probabilities.

Q

A matrix of transition probabilities for Markov chain approach.

I_minus_Q

Matrix (I - Q) where I is an identity matrix of the same size as the Q.

I_minus_Q_inv

Inverse matrix of (I - Q).

I_minus_Q_inv_1

Row sums of I_minus_Q_inv.

initpr

A matrix of initial probabilities for Markov chain approach.

ds

The shorter sampling interval in VSI CUSUM control scheme.

dl

The longer sampling interval in VSI CUSUM control scheme.

di

The sampling interval at initial state in VSI CUSUM control scheme.

psi.s

Long-run proportion of shorter sampling intervals except initial state. See details

psi.l

Long-run proportion of longer sampling intervals except initial state. See details

refv.act

A reference value of CUSUM statistic used actually for computation.

contl.act

A control limit in CUSUM control scheme used actually for computation.

warnl.act

A warning limit in VSI control scheme used actually for computation.

c.zero.act

An initial state of CUSUM statistic used actually for computation.

ANSS

The computed average number of samples to signal for FSI CUSUM chart.

ATS

The computed average time to signal for FSI CUSUM chart.

References

Reynolds et al. (1990). CUSUM Charts with Variable Sampling Intervals, Technometrics, 32(4), 371-384.

See Also

getContl, getAve_Poisson, getAve_binomial.

Examples

1
2
3
4
# Example 1: Poisson distribution
getAve(refv = 5, contl = 8, c.zero = 0, warnl = 1, ds = 0.1,
       dl = NULL, di = NULL, process = function(x) dpois(x, lambda = 4),
       maxndec = 7L, maxnumsubI = 500L)

attrCUSUM documentation built on May 2, 2019, 9:25 a.m.