The cumulative sum (CUSUM) control chart is widely used in industry for the detection of small and moderate shifts in process location and dispersion. For efficient monitoring of process variability, we present several CUSUM control charts for monitoring changes in standard deviation of a normal process. The newly developed control charts based on well-structured sampling techniques - extreme ranked set sampling, extreme double ranked set sampling and double extreme ranked set sampling, have significantly enhanced CUSUM chart ability to detect a wide range of shifts in process variability. The relative performances of the proposed CUSUM scale charts are evaluated in terms of the average run length (ARL) and standard deviation of run length, for point shift in variability. Moreover, for overall performance, we implore the use of the average ratio ARL and average extra quadratic loss. A comparison of the proposed CUSUM control charts with the classical CUSUM R chart, the classical CUSUM S chart, the fast initial response (FIR) CUSUM R chart, the FIR CUSUM S chart, the ranked set sampling (RSS) based CUSUM R chart and the RSS based CUSUM S chart, among others, are presented. An illustrative example using real dataset is given to demonstrate the practicability of the application of the proposed schemes.
Statistical methods are reported in a scientific paper to summarise the data that has been collected for a study and to enable its analysis. These methods should be described with enough detail to allow a knowledgeable reader who has access to the original data to verify the reported results. This article provides basic guidelines to aid authors in reporting the statistical aspects of the results of their studies clearly and accurately.
The method of backcalculation estimates past HIV infection rates from available AIDS incidence data and an estimate of the incubation period. The method is used on the Malaysian data to model the AIDS epidemic because it makes use of the Malaysian AIDS incidence data which is fairly reliable and is more reflective of the trend of the epidemic as compared to the HIV infection rate recorded. An application is made on the monthly AIDS incidence data in Malaysia from January 1995 until August 1996 released by the Ministry of Health, Malaysia using the backcalculation program from Bacchetti et al and the incubation period distribution from Brookmeyer to generate the current HIV infection rate for Malaysia (until August 1996).
Based on a synthesis of literature, earlier studies, analyses and observations on high school students, this study developed an initial framework for assessing students' statistical reasoning about descriptive statistics. Framework descriptors were established across five levels of statistical reasoning and four key constructs. The former consisted of idiosyncratic reasoning, verbal reasoning, transitional reasoning, procedural reasoning, and integrated process reasoning. The latter include describing data, organizing and reducing data, representing data, and analyzing and interpreting data. In contrast to earlier studies, this initial framework formulated a complete and coherent statistical reasoning framework. A statistical reasoning assessment tool was then constructed from this initial framework. The tool was administered to 10 tenth-grade students in a task-based interview. The initial framework was refined, and the statistical reasoning assessment tool was revised. The ten students then participated in the second task-based interview, and the data obtained were used to validate the framework. The findings showed that the students' statistical reasoning levels were consistent across the four constructs, and this result confirmed the framework's cohesion. Developed to contribute to statistics education, this newly developed statistical reasoning framework provides a guide for planning learning goals and designing instruction and assessments.