Estimation of Several Intraclass Correlation Coefficients

An intraclass correlation coefficient observed in several populations is estimated. The basis is a variance-stabilizing transformation. It is shown that the intraclass correlation coefficient from any elliptical distribution should be transformed in the same way. Four estimators are compared. An estimator where the components in a vector consisting of the transformed intraclass correlation coefficients are estimated separately, an estimator based on a weighted average of these components, a pretest estimator where the equality of the components is tested and then the outcome of the test is used in the estimation procedure, and a James-Stein estimator which shrinks toward the mean.     

Designing an economically optimal repetitive group-sampling plan based on loss functions

Acceptance sampling is a quality assurance tool, which provides a rule for the producer and the consumer to make acceptance or rejection decision about a lot. This paper attempts to develop a more efficient sampling plan, variables repetitive group sampling plan, based on the total loss to the producer and consumer. To design this model, two constraints are considered to satisfy the opposing priorities and requirements of the producer and the consumer by using Acceptable quality level (AQL) and Limiting quality level (LQL) points on operating characteristic (OC) curve. The objective function of this model is constructed based on the total expected loss. In order to illustrate the application of the proposed model, an example is presented. In addition, the effects of process parameters on the optimal solution and the total expected loss are studied by performing a sensitivity analysis. Finally, the efficiency of the proposed model is compared with the variables single sampling plan, the variables double sampling plan and the repetitive group sampling plan of Balamurali and Jun (2006) in terms of average sample number, total expected loss and its difference with ideal OC curve.     

Designing optimal double-sampling plan based on process capability index

Process capability analysis is applied to monitor the process quality. Process capability can be quantified by process capability index. These indices have wide application in quality control methods and acceptance sampling plans. In this paper, we introduce a double-sampling plan based on process capability index. In this type of scheme, under a decision rule and with the specified rejection and acceptance numbers, the second sample is selected and the decision of rejection or acceptance is made based on the information obtained from two samples. The purpose of this scheme is to reduce the average sample number in order to reduce the time and cost of sampling. A comparison study has been conducted in order to evaluate the performance of proposed method in comparison with classical single sampling plans.     

A recursive approach for lot sentencing problem in the presence of inspection errors

In this paper, a new sequential acceptance sampling plans in the presence of inspection errors is developed. A suitable profit objective function is employed for optimizing the lot sentencing problem. A backward recursive approach is applied for obtaining the profit of different decisions in each stage of sampling. Required probabilities are obtained using Bayesian rule. A case study is solved for illustrating the application of proposed models and sensitivity analysis are carried out on the parameters of the proposed methodologies and the behaviour of models by changing the parameters are investigated.     

Comparison of spatial interpolation methods in the first order stationary multiplicative spatial autoregressive models

Three linear prediction methods of a single missing value for a stationary first order multiplicative spatial autoregressive model are proposed based on the quarter observations, observations in the first neighborhood, and observations in the nearest neighborhood. Three different types of innovations including Gaussian (symmetric and thin tailed), exponential (skew to right), and asymmetric Laplace (skew and heavy tailed) are considered. In each case, the proposed predictors are compared based on the two well-known criteria: mean square prediction and Pitman's measure of closeness. Parameter estimation is performed by maximum likelihood, least square errors, and Markov chain Monte Carlo (MCMC).     

A Finite Horizon Dynamic Programming Model for Production and Repair Decisions

In this research, a novel optimal single machine replacement policy in finite stages based on the rate of producing defective items is proposed. The primary objective of this paper is to determine the optimal decision using a Markov decision process to maximize the total profit associated with a machine maintenance policy. It is assumed that a customer order is due at the end of a finite horizon and the machine deteriorates over time when operating. Repair takes time but brings the machine to a better state. Production and repair costs are considered in the model and revenue is earned for each good item produced by the end of the horizon, there is also a cost for the machine condition at the end of the horizon. In each period, we must decide whether to produce, repair, or do nothing, with the objective of maximizing expected profit during the horizon.     

An optimization model for economic design of sampling plans based on conforming run length considering outgoing quality

In this article, a new economical acceptance sampling model is proposed based on Taguchi loss function. The objective function of the model consists of inspection cost, scrap cost, and Taguchi loss function including producer loss and consumer loss. The expected total cost includes the loss for an inspected item plus the loss for an accepted item which has not been inspected. Decision-making is based on conforming run length. It is assumed that the quality characteristics follow normal distribution. A numerical example is solved for illustrating application of this model. Sensitivity analysis is proposed for illustrating the effect of some important parameters on the objective function. Finally, we compared the results of the proposed method with classical Dodge–Romig sampling plans tables based on average outgoing quality limit. The results confirmed the superiority of proposed model.     

Efficient reassembling of graphs,part 1: the linear case

The reassembling of a simple connected graph \(G = (V,E)\) is an abstraction of a problem arising in earlier studies of network analysis. Its simplest formulation is in two steps:

1. (1)
   We cut every edge of G into two halves, thus obtaining a collection of \(n = |\,V\,|\) one-vertex components, such that for every \(v\in V\) the one-vertex component \(\{ v \}\) has \({{degree}}_{}(v)\) half edges attached to it.
    
2. (2)
   We splice the two halves of every edge together, not of all the edges at once, but in some ordering \(\Theta \) of the edges that minimizes two measures that depend on the edge-boundary degrees of assembled components.
    

A component A is a subset of V and its edge-boundary degree is the number of edges in G with one endpoint in A and one endpoint in \(V-A\) (which is the same as the number of half edges attached to A after all edges with both endpoints in A have been spliced together). The maximum edge-boundary degree encountered during the reassembling process is what we call the \(\varvec{\alpha }\) -measure of the reassembling, and the sum of all edge-boundary degrees is its \(\varvec{\beta }\) -measure. The \(\alpha \)-optimization (resp. \(\beta \)-optimization) of the reassembling of G is to determine an order \(\Theta \) for splicing the edges that minimizes its \(\alpha \)-measure (resp. \(\beta \)-measure). There are different forms of reassembling, depending on restrictions and variations on the ordering \(\Theta \) of the edges. We consider only cases satisfying the condition that if an edge between disjoint components A and B is spliced, then all the edges between A and B are spliced at the same time. In this report, we examine the particular case of linear reassembling, which requires that the next edge to be spliced must be adjacent to an already spliced edge. We delay other forms of reassembling to follow-up reports. We prove that \(\alpha \)-optimization of linear reassembling and minimum-cutwidth linear arrangment (\(\mathrm{CutWidth}\)) are polynomially reducible to each other, and that \(\beta \)-optimization of linear reassembling and minimum-cost linear arrangement (\(\mathrm{MinArr}\)) are polynomially reducible to each other. The known NP-hardness of \(\mathrm{CutWidth}\) and \(\mathrm{MinArr}\) imply the NP-hardness of \(\alpha \)-optimization and \(\beta \)-optimization.

     

Assigning students to academic majors

We address here the problem of assigning undergraduate students to academic major areas at a Middle-Eastern business school, which is quite different from what one usually faces in the West. Our formulation considers the student's preference in the light of his/her performance in certain bellwether courses and various practical constraints in arriving at an initial solution. We present a linear program that maximizes the overall value of the assignments to the students as well as the academic units concerned. We show through a real example how this approach has been implemented as one step in the major-assignment process.     

A Multi-Stage Two-Machines Replacement Strategy Using Mixture Models,Bayesian Inference,and Stochastic Dynamic Programming

If at least one out of two serial machines that produce a specific product in manufacturing environments malfunctions, there will be non conforming items produced. Determining the optimal time of the machines' maintenance is the one of major concerns. While a convenient common practice for this kind of problem is to fit a single probability distribution to the combined defect data, it does not adequately capture the fact that there are two different underlying causes of failures. A better approach is to view the defects as arising from a mixture population: one due to the first machine failures and the other due to the second one. In this article, a mixture model along with both Bayesian inference and stochastic dynamic programming approaches are used to find the multi-stage optimal replacement strategy. Using the posterior probability of the machines to be in state λ₁, λ₂ (the failure rates of defective items produced by machine 1 and 2, respectively), we first formulate the problem as a stochastic dynamic programming model. Then, we derive some properties for the optimal value of the objective function and propose a solution algorithm. At the end, the application of the proposed methodology is demonstrated by a numerical example and an error analysis is performed to evaluate the performances of the proposed procedure. The results of this analysis show that the proposed method performs satisfactorily when a different number of observations on the times between productions of defective products is available.