A Note on Minimax Mixture of Distributions Free Procedure for Inventory Model with Variable Lead Time

In recent papers, Moon and Choi (1998) and Hariga and Ben-Daya (1999)considered a continuous review inventory model with a mixture of backordersand lost sales in which the lead time, the order quantity, and the reorder pointare decision variables was studied. Moreover, they also develop a minimaxdistribution free procedure for the problem. While the demands of differentcustomers are not identical in the lead time, then we can't only use a singledistribution (such as Moon & Choi (1998) and Hariga & Ben-Daya (1999))to describe the demand of the lead time. Hence, we correct and extend the modelof Moon and Choi (1998) and Hariga and Ben-Daya (1999) by considering thelead time demand with the mixture of distributions. In addition, we also applythe minimax mixture of distributions free approach to the model by simultaneouslyoptimizing the order quantity, the reorder point, and the lead time to devise a practical procedure which can be used without specific information on demand distribution.     

A Note on the Prediction Intervals for a Future Ordered Observation from a Pareto Distribution

In the researching of products' reliability, the result of life testing is used as the basis for the evaluation and improvement of reliability. During life testing, however, the future observation in an ordered sample is often expected to be predicted so as to show how long a sample of units might run until all fail in life testing. Therefore, we propose five new pivotal quantities to obtain prediction intervals of future order statistics based on right type II censored samples from the Pareto distribution with known shape parameter, then compares the lengths of the prediction intervals when using the pivotal quantity of Ouyang and Wu (1994) based on best linear unbiased estimator (BLUE) of scale parameter, and these five pivotal quantities. An advantage of these five pivotal quantities is that these are easier to calculate than the pivotal quantity of Ouyang and Wu (1994) based on BLUE of scale parameter, since they need to compute the tables of coefficients of BLUE of scale parameter.     

A Note on EOQ Model for Items with Mixtures of Exponential Distribution Deterioration,Shortages and Time-varying Demand

An inventory model is considered in which inventory is depleted not only by demand, but also by deterioration. In this paper, we derive the EOQ model for inventory of items that deteriorates at a mixtures of exponential distributed rate, assuming the demand rate with a continuous function of time. Moreover, the proposed model cannot be solved directly in a closed form, thus we used the computer software IMSL MATH/LIBRARY (1989) to find the optimal reorder time Further, we also find that the optimal procedure is independent of the form of the demand rate. Finally, we also assume that the holding cost is a continuous, nonnegative and non-decreasing function of time in order to generalize EOQ model. Moreover, four numerical examples and sensitivity analyses are provided to assess the solution procedure.     

Implementing lifetime performance index for the pareto lifetime businesses of the service industries

Process capability analysis is an effective means of measuring process performance and potential capability. In the service industries, process capability indices (PCIs) are utilized to assess whether business quality meets the required level. Hence, the performance index C _L is used as a means of measuring business performance, where L is the lower specification limit. In the technology of data transformation, this study constructs a uniformly minimum variance unbiased estimator (UMVUE) of C _L based on the right type II censored sample from the pareto distribution. The UMVUE of C _L is then utilized to develop a novel hypothesis testing procedure in the condition of known L. Finally, we give one practical example and the Monte Carlo simulation to assess the behavior of this test statistic for testing null hypothesis under given significance level. Moreover, the managers can then employ the new testing procedure to determine whether the business performance adheres to the required level.     

On characterizing distributions by conditional expectations of functions of order statistics

In the present paper, we give some general theorems on characterizations based on conditional expectations of the functions of order statistics. In addition, we indicate special forms of the theorems for the familiar probability distributions.     

Multiple and Partial Correlation Coefficients of Fuzzy Sets

In many applications, multiple correlation and partial correlation for three or more fuzzy sets are very important, but Chiang and Lin (1999, Fuzzy Sets and Systems 102: 221–226) do not solve this problem. Here, we propose a method to calculate the multiple correlation and partial correlation for fuzzy data, by adopting the concepts from the multivariate correlation model. In order to fit into normal framework, we use empirical logit transform (see, Agresti, [1990, Categorical Data Analysis. New York: Wiley]; Johnson and Wichern, [1992, Applied Multivariate Statistical Analysis 3rd edn. Engelwood Cliffs; Prentice-Hall.]) for membership function grades to achieve this.     

Optimal Estimation of the Parameters of the Gompertz Distribution Based on the Doubly Type II Censored Sample

In this paper, we develop exact confidence intervals and exactjoint confidence regions for the parameters of the Gompertzdistribution under the doubly type II censored sample. We alsoprovide optimal criteria for finding a best exact confidenceinterval and a best exact joint confidence region among theseinterval estimations. Finally, we give a numerical example toillustrate our proposed method. Furthermore,when compared to estimation of Chen (1997), our proposedmethod can get a better parameter estimation.     

One-Sample Bayesian Predictive Interval of Future Ordered Observations for the Pareto Distribution

Nigm et al. (2003, statistics 37: 527–536) proposed Bayesian method to obtain predictive interval of future ordered observation Y _(j) (r < j≤ n ) based on the right type II censored samples Y ₍₁₎ < Y ₍₂₎ < ... < Y _(r) from the Pareto distribution. If some of Y ₍₁₎ < ... < Y _(r-1) are missing or false due to artificial negligence of typist or recorder, then Nigm et al.’s method may not be an appropriate choice. Moreover, the conditional probability density function (p.d.f.) of the ordered observation Y _(j) (r < j ≤ n ) given Y ₍₁₎ <Y ₍₂₎ < ... < Y _(r) is equivalent to the conditional p.d.f. of Y _(j) (r < j ≤ n ) given Y _(r). Therefore, we propose another Bayesian method to obtain predictive interval of future ordered observations based on the only ordered observation Y _(r), then compares the length of the predictive intervals when using the method of Nigm et al. (2003, statistics 37: 527–536) and our proposed method. Numerical examples are provided to illustrate these results.