Quantile Based Statistical Failure Analysis for Wafer Level Test Comparison

In semiconductor manufacturing or testing, when changing the items such as parts, materials or equipment, many engineers use the equivalence test to hedge the risk of new process. Equivalence Test Procedure (ETP) uses a modified algorithm of Cohen's d and F-ratio for comparing two test samples when it evaluates the statistical allowance in the second stage. These logics are estimated under the assumption of normality for the underlying population. However, there are many wafer level test items such as Fail Bit Count (FBC) where their populations are non-normal distribution. Because the standard deviation in the two algorithms is over-estimated in wafer level test distribution, the two algorithms fail to represent the size of difference for the two samples exactly. Therefore, we introduce quantile comparison equivalence criteria (QCEC) which is robust to overall data distribution and outlier-free. To instruct engineers about the change cause of the data distribution, we create new statistics called ‘Center or Dispersion’ (CoD) that distinguish between center difference and dispersion difference. For practical application, we conduct the case study on Dynamic Random Access Memory (DRAM) FBC data. For wafer level test 199 items, it is found that the QCEC's accuracy improves by 20% compared to the accuracy of Cohen's d. It also shows a 75% improvement over the accuracy of the F-ratio.

Inferring inter- and intrachromosomal Dobzhansky-Muller incompatibilities from imbalanced segregation of recombinant haplotypes in hybrid populations

Dobzhansky-Muller incompatibilities (DMIs) are a major component of reproductive isolation between species. DMIs imply negative epistasis, exposed when two diverged populations hybridize. Mapping the locations of DMIs has largely relied on classical genetic mapping, but these approaches are stymied by low power and the challenge of identifying DMI loci on the same chromosome, because strong initial linkage of parental haplotypes weakens statistical tests. Here, we propose new statistics to infer negative epistasis from haplotype frequencies in hybrid populations. When two divergent populations hybridize, the variance of two-locus heterozygosity decreases faster with time at DMI loci than at random pairs of loci. If two populations hybridize at near-even admixture proportions, the deviation of the observed variance from its expectation is negative, which enables us to detect signals of intermediate to strong negative epistasis both within and between chromosomes. When the initial proportion of the two parental populations is uneven, only strong DMIs can be detected with our method, unless migration reintroduces haplotypes from the minor parental population. We use the two new statistics to infer candidate DMIs from three hybrid populations of swordtail fish. We identify numerous new DMI candidates some of which are inferred to interact with several loci within and between chromosomes. Moreover, we discuss our results in the context of an expected enrichment in intrachromosomal over interchromosomal DMIs.

New Statistics, Old Schools: An Overview of Current Introductory Undergraduate and Graduate Statistics Pedagogy Practices

Background A philosophical shift in statistics regarding emphasis on “New Statistics” (NS; Cumming, G. (2014). The new statistics: Why and how. Psychological Science, 25(1), 7-29.) over conventional null hypothesis significance testing (NHST) raises the question of appropriate material coverage in undergraduate statistics courses. Objective We examined current practices in statistics pedagogy at the graduate and undergraduate levels for both NS and NHST. Method Using an online survey of a nationwide sample of current graduate students ( n = 452) and graduate faculty ( n = 162), we examined statistics pedagogy and perceptions of best approaches for teaching undergraduate statistics. Results In undergraduate statistics courses, coverage of NS material involves modest instruction in effect sizes and confidence intervals, while NHST remains dominant. Graduate courses have more balanced coverage. Effect size estimation was regarded as the most important NS knowledge for success in graduate school and the topic most in need of increased undergraduate coverage. Conclusion Undergraduate statistics courses could increase NS coverage, particularly effect size estimation, to better align with and prepare students for graduate work. Teaching Implications This research summarizes graduate program expectations and graduate student experiences regarding undergraduate statistics that current instructors can use to shape the content of their classes.

Objective Method for Determining the Importance of Unprecedented Restlessness as a Rice Crisis Indicator at the National Level

In this study, we use restlessness as an input for a rice crisis indicator, since restlessness rather than rice price provides a comparable year-to year context. We outline the significant increase in the use of unprecedented restlessness (UR) as an indicator for rice crises. The UR approach involves a precedence analysis, in contrast with the existing approach, the price shock analysis. We test UR as a new indicator for rice crises at the national level, which can be applied in Asia and other countries around the world where rice is the staple food. Strong indicators point out the effectiveness of strategic government programs and are able to assess solutions and detect rice crises, while weak indicators are only reliable in detecting whether or not there has been a crisis. UR is tested across 43 countries using two new statistics: success probability (SP) and constraint probability (CP). As a consequence of SP and CP calculations, a large number of IMR control charts for UR analysis are constructed to provide evidence that UR is a strong indicator. The optimum validity measurement result is achieved with SP = 8/26 = 0.31 and CP = 8/14 = 0.57. This means that the UR detects and is followed by only 31% of riot events. Since the value of SP is less than 0.6, we can conclude that the UR indicator is not considered valid as an indicator of rice crises at the national level. The values of CP and SP are determined subjectively as equal to 0.6. This is the main cause of the emergence of new problems in the calibration of UR as an indicator of rice crises. The subjective success criteria trigger a question regarding why the value is 0.6, for which there is no scientific justification. Based on this background, we continue to objectively establish success criteria for UR validity. After conducting a risk analysis involving a crisis recovery cost (CRC) to crisis anticipation cost (CAC) ratio, it is found that the probability of the CRC-to-CAC ratio having values greater than 7 is 0.76, which means the CRC-to-CAC ratio tends to be higher than 7. Objectively, it is concluded that UR, which has been defined as rice crisis indicator at the national level, is an important indicator.

Statistical Tests of Symbolic Dynamics

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

Improving relevance: Istat experience on experimental statistics

In line with Eurostat and other National Statistical Institutes, Istat has been publishing experimental statistics since April 2018. Experimental statistics inform users on topics not fully exploited by official statistics, and differ from them because they are not yet entirely developed. This enlargement of Istat statistical supply was fostered by the satisfaction of users’ needs and the increased availability of new data sources. An internal procedure was set up to select, evaluate and disseminate experimental statistics before their publication on a dedicated area of the Istat website. At Istat, the primary purpose of experimental statistics is to improve relevance. Indeed, they are new statistics or improved existing outputs, which have a value added for the users in terms of “new” or “additional” information available. Important features of experimental statistics are the use of non-traditional data sources, the use of innovative methodologies, the geo-spatial reference or other types of data visualisation, the integration of multiple sources. Up to now, improving timeliness seems to be a less important motivational factor for developing experimental statistics. Recently, the transition from experimental to official statistics was tackled, leading to the definition of a set of criteria to be satisfied.

DEVELOPING MODELS FOR FORECASTING AGRICULTURAL ENTERPRISES SALES VOLUME

The financial and economic activities of economic entities in modern terms require constant plans comparison with real developments. Taking into account the peculiarities of the economic situation in the country, comparing the supply and demand, analysis of financial results, etc. The development of market relations increases the responsibility and independence of enterprises in making decisions about strategy and tactics for the future. That is why, while taking substantiating management decisions the application of techniques and methods of economic and mathematical modeling is relevant. One of the types of communication between the producer and the consumer is sales volume. It directly affects the amount of costs, profits and profitability of the enterprise. Therefore, the analysis and forecasting of such an indicator is important to increase the competitiveness of economic entities. Statistical data of one of the agricultural enterprises of Poltava region are analyzed, several influential factors are highlighted. It is proposed to perform a regression analysis, develop a linear multifactor model and build an adaptive model for forecasting the volume of sales of agricultural enterprises to select the optimal model for forecasting the studied indicator for the future. The author performed calculations on the obtained models. The analysis of the obtained results confirmed model’s adequacy, so they can be used for forecasting. As a result of comparison forecasts of sales volumes at the enterprise the adaptive model is recommended for practical application as it has the best quality of the forecast and the minimum sum of deviations squares. This model giving more weight to the latest statistics provides an optimistic forecast for the future. Thus, developing economic and mathematical forecasting models will provide an opportunity to improve the operational planning of production the certain types of products, as well as allow (after receiving new statistics) to quickly change the production monthly plans. Thus, conditions will be created to improve the quality of management, increase competitiveness and ensure the stabilization of the financial state at agricultural enterprises.