A Performance Analysis of the Minimax Multivariate Quality Control Chart
Abstract
A performance analysis of three different Minimax control
charts is performed with respect to their Chi-Square control
chart counterparts under several different conditions. A
unique control chart must be constructed for each process
described by a unique combination of quality characteristic
mean vector and associated covariance matrix. The three
different charts under consideration differ in the number of
quality characteristic variables of concern. In each case,
without loss of generality the in-control quality
characteristic mean vector is assumed to have zero entries
and the associated covariance matrix is assumed to have
non-negative entries. The performance of the Chi-Square and
Minimax charts are compared under different values of the
sample size, the probability of a Type I error, and selected
shifts in the quality characteristic mean vector. Minimax
and Chi-Square charts that are compared share identical
in-control average run lengths (ARL) making the
out-of-control ARL the appropriate performance measure. A
combined Tausworthe pseudorandom number generator is used to
generate the out-of-control mean vectors. Issues regarding
multivariate uniform pseudorandom number generation are
addressed.
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- Masters Theses [18654]