We use a volume-limited sample of quasars in the Sloan Digital Sky Survey (SDSS) DR7 quasar catalog to identify quasar groups and address their statistical significance. This quasar sample has a uniform selection function on the sky and nearly a maximum possible contiguous volume that can be drawn from the DR7 catalog. Quasar groups are identified by using the Friend-of-Friend algorithm with a set of fixed comoving linking lengths. We find that the richness distribution of the richest 100 quasar groups or the size distribution of the largest 100 groups are statistically equivalent with those of randomly-distributed points with the same number density and sky coverage when groups are identified with the linking length of 70 h−1Mpc. It is shown that the large-scale structures like the huge Large Quasar Group (U1.27) reported by Clowes et al. (2013) can be found with high probability even if quasars have no physical clustering, and does not challenge the initially homogeneous cosmological models. Our results are statistically more reliable than those of Nadathur (2013), where the test was made only for the largest quasar group. It is shown that the linking length should be smaller than 50 h−1Mpc in order for the quasar groups identified in the DR7 catalog not to be dominated by associations of quasars grouped by chance. We present 20 richest quasar groups identified with the linking length of 70 h−1Mpc for further analyses.

This paper aims to propose a new steps of hypothesis testing using analysis process and improvement process in the six sigma DMAIC. The six sigma implementation models proposed in this paper consist of six steps. The first step is to establish a research hypothesis by specification directionality and FBP(Falsibility By Popper). The second step is to translate the research hypothesis such as RHAT(Research Hypothesis Absent Type) and RHPT(Research Hypothesis Present Type) into statistical hypothesis such as H0(Null Hypothesis) and H1(Alternative Hypothesis). The third step is to implement statistical hypothesis testing by PBC(Proof By Contradiction) and proper sample size. The fourth step is to interpret the result of statistical hypothesis test. The fifth step is to establish the best conditions of product and process conditions by experimental optimization and interval estimation. The sixth step is to draw a conclusion by considering practical significance and statistical significance. Important for both quality practitioners and academicians, case analysis on six sigma projects with implementation guidelines are provided.

The research presents a guideline for quality practitioners to provide a full comprehension of differences in theoretical and practical interpretations of assumed sampling errors of and significance probability of calculated p-value. Besides, the study recommends the use of statistical inferences methods with known parameters to identify the improvement effects. In practice, the quality practitioners obtain the known parameters through systematic quality Database (DB) activities.

수공구조물 설계시 실측 유량의 자료 부족으로 홍수량의 빈도해석 결과보다는 강우자료를 수집하여 강우-유출 관계에 따라 산정된 설계강우량을 이용하여 특정 빈도에 해당하는 설계 홍수량을 사용하는 것이 일반적이다. 과거에는 첨두유량 산정을 위하여 합리식과 같은 경험식을 이용하였으나 지속기간이 장기화됨에 따라 실제 사상과는 다른 유출양상이 나타나게 되므로 확률강우량 시간분포의 정확성이 중요하게 되었다. 현재 실무에서는 설계강우량의 시간분포 방법으로 Huff의 4분위 방법 중 3분위를 사용하고 있으며 분위별 곡선에 대한 회귀식은 지속기간 전반에 걸쳐 정확도가 높은 이유로 6차식을 적용하고 있다. 그러나 통계 모델링에서는 간결함의 원리에 따라 회귀식이 간결할 필요가 있으며, 통계적 유의수준에 기초하여 회귀계수를 결정할 필요가 있다. 따라서 본 연구에서는 기상청 관할 69개 강우관측지점을 대상으로 설계강우량의 시간분포 방법으로 사용되고 있는 Huff 4분위 방법의 시간분포 회귀식에 대한 유의성 검정을 실시하였다. 기상청 관할 69개 강우관측지점의 Huff 4분위 방법의 시간분포 회귀식의 유의성 검정결과 대부분의 지점에서 4차식까지 회귀계수가 유의한 것으로 나타나 통계학적으로 Huff의 4분위 방법의 시간분포 회귀식은 4차까지만 고려하여도 무방한 것으로 분석되었다.