On Sequential Probability Sampling Plan for a Truncated Life Tests Using Rayleigh Distribution

This paper proposed a sequential probability sampling plan for a truncated life test using a Rayleigh distribution from a designed double sampling plans where the interest was to obtain the minimum sample size necessary to assure that the average life time of a product is longer than the default life time at the specified consumer’s and producer’s confidence level. Estimations of minimum sample, acceptance and rejection numbers obtained are analyzed and presented to explain the usefulness of sequential plans in relation to single and double sampling plan. Probability of acceptance (Pa), Average sample number (ASN) and Average outgoing quality (AOQ) for the plans are computed. The three regions; acceptance, continue sampling and rejection were determined. The five points necessary to plot ASN curve were also computed and presented.

The SPRT Sign Chart for Process Dispersion

A nonparametric sequential probability ratio test control chart to monitor the process dispersion based on the sequential sign statistic is proposed. The statistical performance of this chart is evaluated by comparing it with that of the charts for dispersion based on sign statistic in the existing literature. It is found that the proposed chart outperforms all these charts uniformly in detecting a shift of any size over a wide range. An implementation of the chart is illustrated through an example.

1035COVID-19: Boom or bust?

Background In the final weeks of 2019, a SARS-CoV-2 virus slipped furtively from animal to human in China. As of March 13, there have been 1,34,918 confirmed cases, out of which 4,990 is the death count. We are predicting extinction or explosion of the virus from the current realization of a Galton Watson process. Methods Based on the region wise reported number of cases, total was calculated. The observed offspring distribution was found by calculating the difference between the total number of cases in consecutive days. Hence the distribution modelled using Sequential Probability Ratio Tests (SPRT) to predict whether extinction or explosion will occur for the current realization of the process. Kolmogorov-Smirnov test was performed on the data to check the distribution of fit. Results We assume conservative approach of SPRT. The geometric distribution fits to the data taken from January 2020 to March 12, 2020. The SPRT on the offspring distribution predicts extinction of the disease if the number of cases reported on a new day are less than 58 then the disease will extinct, and will explode if more than 9,990 cases. Conclusions Our results show that if COVID-19 transmission is established, understanding the effectiveness of control measures in different settings will be crucial for understanding the likelihood that transmission can eventually be effectively mitigated. Key messages Our analysis highlights the value of recording individual cases and analyzing geographically heterogeneous data of COVID-19. Our results also have implications for estimation of transmission dynamics using the number of exported cases from a specific area.

Neurally-constrained modeling of human gaze strategies in a change blindness task

Despite possessing the capacity for selective attention, we often fail to notice the obvious. We investigated participants’ (n = 39) failures to detect salient changes in a change blindness experiment. Surprisingly, change detection success varied by over two-fold across participants. These variations could not be readily explained by differences in scan paths or fixated visual features. Yet, two simple gaze metrics–mean duration of fixations and the variance of saccade amplitudes–systematically predicted change detection success. We explored the mechanistic underpinnings of these results with a neurally-constrained model based on the Bayesian framework of sequential probability ratio testing, with a posterior odds-ratio rule for shifting gaze. The model’s gaze strategies and success rates closely mimicked human data. Moreover, the model outperformed a state-of-the-art deep neural network (DeepGaze II) with predicting human gaze patterns in this change blindness task. Our mechanistic model reveals putative rational observer search strategies for change detection during change blindness, with critical real-world implications.

Spatial Distribution and Development of Sequential Sampling Plans for Diaphorina citri Kuwayama (Hemiptera: Liviidae)

Vector control in huanglongbing management has been conducted on a calendar basis resulting in high production costs. We addressed this issue and proposed a sequential sampling plan to support decision making for intervention against Diaphorina citri Kuwayama, which is involved in the transmission of the bacteria Candidatus Liberibacter asiaticus, associated with such lethal disease. We analyzed 3,264,660 records from samples gathered from the Mexican trapping program for the monitoring of D. citri; it included weekly inspection of 86,004 yellow sticky traps distributed in the country. Spatial distribution of the insect, estimation of a common k (kc), and sequential sampling plans based on Sequential Probability Ratio Test (SPRT) were determined. Taylor’s power law coefficients were ≥1 indicating aggregation in the spatial distribution of the insect. Common k ranged from 0.0183 to 0.2253 and varied independently of geographic zone or citrus species. We obtained 18 sequential sampling plans, one for each state. In the Average Sample Number (ASN) function, the minimal number of samples to make a decision ranged from 17 to 65. In the Operational Characteristic (OC) function, probabilities for a correct intervention at the threshold of 0.2 D. citri adults/trap in most cases were above 80%. In a field evaluation, the application of sampling plans yielded savings obtained by reduction in the number of interventions for insect control.