Economic and Economic-Statistical Design of Multivariate Bayesian Control Chart with Variable Sampling Intervals

Due to the proper performance of Bayesian control chart in detecting process shifts, it recently has become the subject of interest. It has been proved that on Bayesian and traditional control charts, the economic and statistical performances of the variable sampling interval (VSI) scheme are superior to those of the fixed ratio sampling (FRS) strategy in detecting small to moderate shifts. This paper studies the VSI multivariate Bayesian control chart based on economic and economic-statistical designs. Since finding the distribution of Bayesian statistic is t complicated, we apply Monte Carlo method and we employ artificial bee colony (ABC) algorithm to obtain the optimal design parameters (sample size, sampling intervals, warning limit and control limit). In the end, this case study is compared with VSI Hotelling’s T2 control chart and it is shown that this approach is more desirable statistically and economically.

Gain control of saccadic eye movements is probabilistic

Saccades are rapid eye movements that orient the visual axis toward objects of interest to allow their processing by the central, high-acuity retina. Our ability to collect visual information efficiently relies on saccadic accuracy, which is limited by a combination of uncertainty in the location of the target and motor noise. It has been observed that saccades have a systematic tendency to fall short of their intended targets, and it has been suggested that this bias originates from a cost function that overly penalizes hypermetric errors. Here, we tested this hypothesis by systematically manipulating the positional uncertainty of saccadic targets. We found that increasing uncertainty produced not only a larger spread of the saccadic endpoints but also more hypometric errors and a systematic bias toward the average of target locations in a given block, revealing that prior knowledge was integrated into saccadic planning. Moreover, by examining how variability and bias covaried across conditions, we estimated the asymmetry of the cost function and found that it was related to individual differences in the additional time needed to program secondary saccades for correcting hypermetric errors, relative to hypometric ones. Taken together, these findings reveal that the saccadic system uses a probabilistic-Bayesian control strategy to compensate for uncertainty in a statistically principled way and to minimize the expected cost of saccadic errors.