A certain continuous random variable can be often observed as a discrete random variable based on specification limits. In this paper, a compound normally distributed random variable X will be observed as a binary random variable Z based on one-sided specification limit. Beta-binomial approximation of the distribution of X is derived as follows : Firstly, it is analytically examined that the parameter P of the conditional binomial distribution which Z follows distributes approximately with the beta density. Secondly, using the moment method, the distribution of P is approximated to the beta distribution and the degree of approximation is numerically examined. Lastly, it is concluded that the compound normal distribution observed as attributes can be approximated to the beta-binomial distribution.

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This paper surveys two procedures to obtain the modified maximum likelihood estimates for a three-parameter Weibull distribution. We refer to some shortcomings of these procedures and propose a modification. Moreover we evaluate these estimates using a Monte-Calro experiment. While Shibata's method is simple and fairly good, simulation results of the proposed modified method show that bias, variance and mean square error of the Weibull shape estimator have been slightly reduced.

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To estimate the variance of estimator of the difference of two means in split-plot design, "generalized effective number of replications[2]" may be applied to each blocks splitted. To facilitate the estimation in case that factorial effect may be obtained from two or more column effects in orthogonal arrays, the error structure of estimators of interaction is considered.

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