Description Usage Arguments Details Value References See Also Examples
View source: R/attrCUSUM_getxxx_and_utils.R
Computation of ANSSs, ATSs and other related informations on attribute VSI CUSUM control chart for mean increase based on the Markov chain approach.
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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 |
maxnumsubI |
The maximum number of sub-intervals in [100,6000] to be used in applying the Markov chain approach. |
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.
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_minus_Q_inv |
Inverse matrix of |
I_minus_Q_inv_1 |
Row sums of |
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. |
Reynolds et al. (1990). CUSUM Charts with Variable Sampling Intervals, Technometrics, 32(4), 371-384.
getContl
, getAve_Poisson,
getAve_binomial.
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