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Ordinal data are the most frequently encountered type of data in the social sciences. Many statistical methods can be used to process such data. One common method is to assign scores to the data, convert them into interval data, and further perform statistical analysis. There are several authors who have recently developed assigning score methods to assign scores to ordered categorical data. This paper proposes an approach that defines an assigning score system for an ordinal categorical variable based on underlying continuous latent distribution with interpretation by using three case study examples. The results show that the proposed score system is well for skewed ordinal categorical data.

In multiple-decision procedures, a crucial objective is to determine the association between the probability of a correct decision (CD) and the sample size. A review of some methods is provided, including a subset selection formulation proposed by Huang and Panchapakesan, a multidecision procedure for testing the homogeneity of means by Huang and Lin, and a similar procedure for testing the homogeneity of variances by Lin and Huang. In this paper, we focus on the use of the Lin and Huang method for testing the null hypothesis H0 of homogeneity of means for k exponential distributions. We discuss the decision rule R, evaluation of the critical value C, and the infimum of P(CD∣R) for k independent random samples from k exponential distributions. In addition, we also observed that a lower bound for the probability of CD relative to the number of the common sample size is determined based on the desired probability of CD when the largest mean is sufficiently larger than the other means. We explain the results by using two examples.

The importance of the ready times can be found in wafer fabrication with the presence of unequal ready times. It is sometimes advantageous to form a non-full batch, while in other situations, it is a better strategy to wait for future job arrivals in order to increase the fullness of the batch. On the other hand, scheduling with learning effect has received growing attention nowadays. However, research with learning and ready times is relatively unexplored. Motivated by this observation, we consider a single-machine problem with learning effect and ready times where the objective is to minimize the total weighted completion time. We develop a branch-and-bound algorithm and a simulated annealing algorithm for the problem. The results show that the branch-and-bound algorithm can solve instances up to 15 jobs, and the average error percentage of the simulated annealing algorithm is less than 0.25%.

Under weak conditions, this paper provides a best lower and a best upper bounding fractional linear generating function for any probability generating function when they have the same mean. These bounds can be used to obtain bounds for the expectation and the percentiles of the extinction-time distribution of a Galton-Watson branching process and other parameters of interest. For the special case of the four points probability generating function, the best bounds obtained are better than the bounds derived by Agresti (1974).

Under weak conditions, this paper provides a best lower and a best upper bounding fractional linear generating function for any probability generating function when they have the same mean. These bounds can be used to obtain bounds for the expectation and the percentiles of the extinction-time distribution of a Galton-Watson branching process and other parameters of interest. For the special case of the four points probability generating function, the best bounds obtained are better than the bounds derived by Agresti (1974).