Improved quality control charts for monitoring the process mean,using double-ranked set sampling methods

Statistical control charts are widely used in the manufacturing industry. The Shewhart-type control charts are developed to improve the monitoring process mean by using the double quartile-ranked set sampling, quartile double-ranked set sampling, and double extreme-ranked set sampling methods. In terms of the average run length, the performance of the proposed control charts are compared with the existing control charts based on simple random sampling, ranked set sampling and extreme-ranked set sampling methods. An application of real data is also considered to investigate the performance of the suggested process mean control charts. The findings of the study revealed that the newly suggested control charts are superior to the existing counterparts.     

Family Transitions,Conduct Problems,and Self-Esteem in Elementary School in Kuwait: A Quasi-Experimental Design

ABSTRACT

This study investigated whether family transitions (disruptions due to parents’ divorce, separation, marriage, or death) were related to problems in the conduct and self-esteem of 331 boys aged 8 to 10 years old in elementary school in Kuwait. The boys were divided into two groups: one whose families had undergone a transition within the past 3 years and one whose families had not undergone such a transition. The two groups were compared on conduct and self-esteem as measured by the Child Behavior Checklist 6–18 and on the Self-Esteem Index. A two-tailed t test was used. The study revealed statistically significant relationships between the two groups. Transitions in the families of young Kuwaiti boys seem to be precursors to problems with conduct but not with self-esteem. Kuwaiti tribal culture may help explain why self-esteem does not suffer after a family transition. The findings suggest a greater need for social services to work with schools to gather information from families to track students and offer services to these families. Future research could study the broader factors surrounding conflict in families undergoing transitions to determine the later impact on children.     

A new sampling method for estimating the population mean

A double L ranked set sampling (DLRSS) method is suggested for estimating the population mean. The DLRSS is compared with the simple random sampling (SRS), ranked set sampling (RSS) and L ranked set sampling (LRSS) methods based on the same number of measured units. The conditions for which the suggested estimator performs better than the other estimators are derived. It is found that, the suggested DLRSS estimator is an unbiased of the population mean, and is more efficient than its counterparts using SRS, RSS, and LRSS methods. Real data sets are used for illustration.     

FACTOR INCOME DISTRIBUTION AND ENDOGENOUS ECONOMIC GROWTH: PIKETTY MEETS ROMER

What is the relationship between the economy's long-run growth rate, its capital-income ratio, and its factor income distribution? A satisfactory answer requires an endogenous growth and savings rate. We scrutinize Piketty's (2014) theory in a richly parameterized variant of Romer's (1990) seminal model with and without population growth. The economy's growth and savings rate are exogenous in Piketty's theory and endogenous in Romer's. In contrast to Piketty's Second Fundamental Law of Capitalism a smaller growth rate may be associated with a smaller capital-income ratio. Moreover, it may go together with a greater or a smaller capital share. (JEL E10,E21,E25,O33,O41)     

Reconfiguration of dominating sets

We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph G is a set S of vertices such that each vertex is either in S or has a neighbour in S. In a reconfiguration problem, the goal is to determine whether there exists a sequence of feasible solutions connecting given feasible solutions s and t such that each pair of consecutive solutions is adjacent according to a specified adjacency relation. Two dominating sets are adjacent if one can be formed from the other by the addition or deletion of a single vertex. For various values of k, we consider properties of \(D_k(G)\), the graph consisting of a node for each dominating set of size at most k and edges specified by the adjacency relation. Addressing an open question posed by Haas and Seyffarth, we demonstrate that \(D_{\varGamma (G)+1}(G)\) is not necessarily connected, for \(\varGamma (G)\) the maximum cardinality of a minimal dominating set in G. The result holds even when graphs are constrained to be planar, of bounded tree-width, or b-partite for \(b \ge 3\). Moreover, we construct an infinite family of graphs such that \(D_{\gamma (G)+1}(G)\) has exponential diameter, for \(\gamma (G)\) the minimum size of a dominating set. On the positive side, we show that \(D_{n-\mu }(G)\) is connected and of linear diameter for any graph G on n vertices with a matching of size at least \(\mu +1\).     

Two new goals for selection based on proportions

Procedures are derived for selecting, with controlled probability of error, (1) a subset of populations which contains all populations better than a dual probability/proportion standard and (2) a subset of populations which both contains all populations better than an upper probability/proportion standard and also contains no populations worse than a lower probability/proportion standard. The procedures are motivated by current investigations in the area of computer performance evaluation.     

Estimating the population mean in the case of missing data using simple random sampling

In this paper, we suggest three new ratio estimators of the population mean using quartiles of the auxiliary variable when there are missing data from the sample units. The suggested estimators are investigated under the simple random sampling method. We obtain the mean square errors equations for these estimators. The suggested estimators are compared with the sample mean and ratio estimators in the case of missing data. Also, they are compared with estimators in Singh and Horn [Compromised imputation in survey sampling, Metrika 51 (2000), pp. 267–276], Singh and Deo [Imputation by power transformation, Statist. Papers 45 (2003), pp. 555–579], and Kadilar and Cingi [Estimators for the population mean in the case of missing data, Commun. Stat.-Theory Methods, 37 (2008), pp. 2226–2236] and present under which conditions the proposed estimators are more efficient than other estimators. In terms of accuracy and of the coverage of the bootstrap confidence intervals, the suggested estimators performed better than other estimators.     

Paired double-ranked set sampling

Abstract

In environmental monitoring and assessment, the main focus is to achieve observational economy and to collect data with unbiased, efficient and cost-effective sampling methods. Ranked set sampling (RSS) is one traditional method that is mostly used for accomplishing observational economy. In this article, we propose an unbiased sampling scheme, named paired double RSS (PDRSS) for estimating the population mean. We study the performance of the mean estimators under PDRSS based on perfect and imperfect rankings. It is shown that, for perfect ranking, the variance of the mean estimator under PDRSS is always less than the variance of mean estimator based on simple random sampling, paired RSS and RSS. The mean estimators under RSS, median RSS, PDRSS, and double RSS are also compared with the regression estimator of population mean based on SRS. The procedure is also illustrated with a case study using a real data set.     

Self-transcendence and depression among AIDS Memorial Quilt panel makers

Self-transcendence is a process that can help individuals reestablish well-being after experiencing a significant, life-altering event. In this study, we sought to identify the relationship between self-transcendence and depression in individuals who lost loved ones to HIV/AIDS and to describe and compare self-transcendence, self-transcendence variables of acceptance and spirituality, and depression among bereaved individuals who created AIDS Memorial Quilt panels with those who did not. The findings support Reed's self-transcendence theory, with inverse correlations between self-transcendence and depression obtained from both the total group and the panel makers. Significant differences were also found between certain self-transcendence variables and depression among the study participants related to gender and ethnicity. In addition, thematic analysis of panel maker interviews revealed five themes: Quilt panel making provides validation, Quilt panel making creates a living memory, liberating acceptance of loss, community of survivors, and connection to a higher power. These findings assist in understanding the complexities of the grief process and support the usefulness of Quilt panel making as an intervention for coping with grief related to HIV/AIDS.