摘要：In the real world, we often observe that the underlying distribution of some Gaussian
processes tends to become skewed, when some undesirable assignable cause takes
place in the process. Such phenomena are common in the field of manufacturing
and in chemical industries, among others, where a process deviates from a normal
model and becomes a skew-normal. The Azzalini’s skew-normal (hereafter ASN)
distribution is a well-known model for such processes. In other words, we assume
that the in-control (hereafter IC) distribution of the process under consideration is
normal, that is a special case of the ASN model with asymmetry parameter zero,
whereas the out-of-control (hereafter OOC) process distribution is ASN with any nonzero
asymmetry parameter. In the ASN model, a change in asymmetry parameter
also induces shifts in both the mean and variance, even if, both the location and
scale parameters remain invariant. Traditionally, researchers consider a shift either
in the mean or in variance or in both the parameters of the normal distribution.
Some inference and monitoring issues related to deviation from symmetry are essential
problems that are largely overlooked in literature. To this end, we propose various test
statistics and design for sequential monitoring schemes for the asymmetry parameter
of the ASN model. We examine and compare the performance of various procedures
based on an extensive Monte-Carlo experiment. We provide an illustration based on
an interesting manufacturing case study. We also offer some concluding remarks and
future research problems.
关键词：disruption of symmetry; distance skewness; maximum likelihood estimator; MonteCarlo;
simulations; skew-normal distribution; statistical process monitoring.
