getContl: Compute Control Limits for Attribute FSI CUSUM Chart

In attrCUSUM: Tools for Attribute VSI CUSUM Control Chart

Description

Computation of suitable control limits for attribute FSI-CUSUM control chart for mean increase based on specified reference value and in-control ANSS/ARL.

Usage

getContl(anss.target = 370.4, refv, c.zero = 0, process, maxndec = 7L,
  maxnumsubI = 6000L)

Arguments

anss.target	A predetermined in-control ANSS/ARL (≤50000L), default is 370.4.
refv	A reference value of CUSUM statistic.
c.zero	An initial state of CUSUM statistic (default is 0).
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.

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:

refv.act	A reference value of CUSUM statistic used actually for computation.
c.zero.act	An initial state of CUSUM statistic used actually for computation.
sol1,sol2	Vector of control limits and corresponding ANSS/ARLs

References

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

See Also

getAve.

Examples

# Example 1: Poisson distribution
getContl(anss.target = 200, refv = 5, c.zero = 0,
         process = function(x) dpois(x, lambda = 4))

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