Jong-u Wu

Correlation of intuitionistic fuzzy sets by centroid method

Abstract In this paper, we propose a method to calculate the correlation coefficient of intuitionistic fuzzy sets by means of “centroid”. This value obtained from our formula tell us not only the strength of relationship between the intuitionistic fuzzy sets, but also whether the intuitionistic fuzzy sets are positively or negatively related. This approach looks better than previous methods which only evaluate the strength of the relation. Furthermore, we extend the “centroid” method to interval-valued intuitionistic fuzzy sets. The value of the correlation coefficient between interval-valued intuitionistic fuzzy sets lies in the interval [−1,1], as computed from our formula.

Statistical inference about the shape parameter of the Burr type XII distribution under the failure-censored sampling plan

In this paper, we propose m pivotal quantities to test the shape parameter and establish confidence interval of the shape parameter of the two-parameter Burr type XII distribution under the failure-censored plan (see [J. Statist. Comput. Simul. 52 (1995) 337]). Next, we find the best test statistic based on their most power of test among all test statistics. Moreover, we also obtain the best pivotal quantities with the shortest tolerance length. Finally, we give two examples and the Monte Carlo simulation to assess the behavior (including higher power and more shorter length of confidence interval) of these pivotal quantities for testing null hypotheses under given significance level and establishing confidence interval of the shape parameter under the given confidence coefficient.

Estimation of parameters of the Gompertz distribution using the least squares method

The Gompertz distribution has been used to describe human mortality and establish actuarial tables. Recently, this distribution has been again studied by some authors. The maximum likelihood estimates for the parameters of the Gompertz distribution has been discussed by Garg et al. [J. R. Statist. Soc. C 19 (1970) 152]. The purpose of this paper is to propose unweighted and weighted least squares estimates for parameters of the Gompertz distribution under the complete data and the first failure-censored data (series systems; see [J. Statist. Comput. Simulat. 52 (1995) 337]). A simulation study is carried out to compare the proposed estimators and the maximum likelihood estimators. Results of the simulation studies show that the performance of the weighted least squares estimators is acceptable.

Computational algorithm for inventory model with a service level constraint, lead time demand with the mixture of distributions and controllable negative exponential backorder rate

Abstract In this paper, let the backorder rate be a control variable to widen applications of Wu and Tsai’s model [J.W. Wu, H.Y. Tsai, Mixture inventory model with back orders and lost sales for variable lead time demand with the mixtures of normal distribution, International Journal of Systems Science 32 (2001) 259–268.]. And, we also assume that the backorder rate is dependent on the length of lead time through the amount of shortages. In addition, we assume that the lead time demand follows a mixture of normal distributions, and then we relax the assumption about the form of the mixture of distributions for the lead time demand and apply the minimax distribution free procedure to solve the problem. Further, instead of having a stock-out term in the objective function, a service level constraint is added to the models. Finally, we develop two computational algorithms to find the optimal order quantity and the optimal lead time. Furthermore, two numerical examples are also given to illustrate the results.

CRITERIA FOR THE UNIQUE DETERMINATION OF PROBABILITY DISTRIBUTIONS BY MOMENTS

Summary A positive probability law has a density function of the general form Q(x) exp(−x 1/λ L(x)), where Q is subject to growth restrictions, and L is slowly varying at infinity. This law is determined by its moment sequence when λ 2. It is still determined when λ = 2 and L(x) does not tend to zero too quickly. This paper explores the consequences for the induced power and doubled laws, and for mixtures. The proofs couple the Carleman and Krein criteria with elementary comparison arguments.

Computational algorithmic procedure for optimal inventory policy involving ordering cost reduction and back-order discounts when lead time demand is controllable

Abstract In many practical situations, the ordering cost can be reduced by capital investment and the back-order rate is dependent on the amount of shortages and back-order price discounts. Hence, in this paper, we consider an inventory model with random yield in which the ordering cost can be reduced through capital investment, lead time can be shortened at an extra crashing cost and allow the back-order rate as a control variable to widen applications of Wu and Tsai’s [J.W. Wu, H.Y. Tsai, Mixture inventory model with back-orders and lost sales for variable lead time demand with the mixtures of normal distribution, International Journal of Systems Science 32 (2001) 259–268] model. Moreover, we also consider the back-order rate that proposed by combining Ouyang and Chuang [L.Y. Ouyang, B.R. Chuang, Mixture inventory model involving variable lead time and controllable backorder rate, Computers & Industrial Engineering 40 (2001) 339–348] (or Lee [W.C. Lee, Inventory model involving controllable backorder rate and variable lead time demand with the mixtures of distribution, Applied Mathematics and Computation 160 (2005) 701–717]) with Pan and Hsiao [J.C.-H. Pan, Y.C. Hsiao, Inventory models with back-order discounts and variable lead time, International Journal of Systems Science 32 (2001) 925–929; J.C.-H. Pan, Y.C. Hsiao, Integrated inventory models with controllable lead time and backorder discount considerations, International Journal of Production Economics 93–94 (2005) 387–397] (also see Pan et al. [J.C.-H. Pan, M.C. Lo, Y.C. Hsiao, Optimal reorder point inventory models with variable lead time and backorder discount considerations, European Journal of Operational Research 158 (2004) 488–505]) to present a new general form. The objective is to simultaneously optimize the order quantity, ordering cost, back-order discount and lead time. In addition, we also develop an algorithmic procedure and use the computer software Compaq Visual Fortran V6.0 (inclusive of IMSL) to find the optimal inventory policy. Finally, a numerical example is also given to illustrate the results.

Estimation of the parameters of the Gompertz distribution under the first failure-censored sampling plan

In this paper, we provide a method for constructing an exact confidence interval and an exact joint confidence region for the parameters of the Gompertz distribution under the first failure-censored sampling plan [1]. Moreover, when compared to ordinary sampling plans, the sampling plan of Balasooriya [1] has an advantage in terms of shorten test-time and a saving of resources. Finally, we give an example to illustrate our proposed method. Results from simulation studies assessing the performance of our proposed method are included.

Computational procedure of performance assessment of lifetime index of businesses for the pareto lifetime model with the right type II censored sample

Abstract Process capability analysis has been developed for assessing quality performance. In the paper, process capability analysis is utilized to measure business performance. In practice, lifetime performance index CL 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 maximum likelihood estimator (MLE) of CL under the pareto distribution with the right type II censored sample. The MLE of CL is then utilized to develop the new hypothesis testing procedure in the condition of known L. Finally, we give two examples 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.

Computational testing algorithmic procedure of assessment for lifetime performance index of products with two-parameter exponential distribution

Process capability indices (PCIs) are used to measure process potential and performance. Since the lifetime of products generally may possess an exponential, gamma or Weibull distribution, etc., so under a two-parameter exponential distribution, this study constructs a maximum likelihood estimator (MLE) of the lifetime performance index based on the right type II censored sample. Then the MLE of the lifetime performance index is utilized to develop the new hypothesis testing algorithmic procedure in the condition of known L. Finally, a practical example is illustrated to employ the testing algorithmic procedure to determine whether the process is capable.

Computational algorithmic procedure of optimal inventory policy involving a negative exponential crashing cost and variable lead time demand

Abstract When the demand of the different customers are not identical in the lead time, we cannot use only a single distribution (such as Ouyang et al. (1996) [L.Y. Ouyang, N.C. Yeh, K.S. Wu, Mixture inventory model with backorders and lost sales for variable lead time, Journal of the Operational Research Society 47 (1996) 829–832] using normal distribution) to describe the demand of the lead time. Hence, in this paper, we extend the models of Ouyang et al. (1996) and Ouyang and Wu (1998) [L.Y. Ouyang, K.S. Wu, A minimax distribution free procedure for mixed inventory model with variable lead time, International Journal of Production Economics 56–57 (1998) 511–516] by considering the mixture of normal distributions and the mixture of free distributions (see Everitt and Hand (1981) [B.S. Everitt, D.J. Hand, Finite Mixture Distribution, Chapman and Hall, London, NY, 1981]), respectively. Moreover, we quote the continuous model which the total crashing cost is related to the lead time by a negative exponential function (such as Ben-Daya and Raouf (1994) [M. Ben-Daya, A. Raouf, Inventory models involving lead time as decision variable, Journal of the Operational Research Society 45 (1994) 579–582]). Finally, we give two algorithmic procedures to find the optimal inventory policy and two numerical examples to illustrate the results.