Ikuo Arizono

A Test for Normality Based on Kullback—Leibler Information

Abstract A goodness-of-fit test (based on sample entropy) for normality was given by Vasicek. The test, however, can be applied only to the composite hypotheses. In this article an extended test of fit for normality is introduced based on Kullback—Leibler information. The Kullback—Leibler information is an extended concept of entropy, so the test can be applied not only to the composite hypotheses, but also to the simple hypotheses. The power comparisons of the proposed test with some other tests are illustrated and discussed.

Scheduling for minimizing total actual flow time by neural networks

SUMMARY Scheduling problems are considered as combinatorial optimization problems. Hopfield and Tank (1985) showed that some combinatorial optimization problems can be solved using artificial neural network systems. However, their network model for solving the combinatorial optimization problems often attains a local optimum solution depending on the initial state of the network. Recently, some stochastic neural network models have been proposed for the purpose of avoiding convergence to a local optimum solution. In this paper a scheduling problem for minimizing the total actual flow time is solved by using the Gaussian machine model which is one of the stochastic neural network models.

Variable sampling plans for normal distribution indexed by Taguchi's loss function

Taguchi has presented an approach to quality improvement in which reduction of deviation from the target value is the guiding principle. In this approach any measured value x of a product characteristic X brings a loss to consumer in general, where the loss is expressed as a quadratic form with respect to the difference between the measured value x and the target value T of a product characteristic. Then, it is natural to reject the lot which may bring a large loss to consumer. This concept induces us to construct new variable sampling plans based on the Taguchis loss criterion. In this article, a design procedure of the sampling plans for assuring the loss in the Taguchis method is proposed. Some numerical results based on the proposed design procedures are illustrated.

Reliability tests for Weibull distribution with variational shape parameter based on sudden death lifetime data

In the traditional design of reliability tests for assuring the mean time to failure (MTTF) in Weibull distribution with shape and scale parameters, it has been assumed that the shape parameter in the acceptable and rejectable populations is the same fixed number. For the purpose of expanding applicability of the reliability testing, Hisada and Arizono have developed a reliability sampling scheme for assuring MTTF in the Weibull distribution under the conditions that shape parameters in the both populations do not necessarily coincide, and are specified as interval values, respectively. Then, their reliability test is designed using the complete lifetime data. In general, the reliability testing based on the complete lifetime data requires the long testing time. As a consequence, the testing cost becomes sometimes expensive. In this paper, for the purpose of an economical plan of the reliability test, we consider the sudden death procedure for assuring MTTF in Weibull distribution with variational shape parameter.

A new stochastic neural network model and its application to grouping parts and tools in flexible manufacturing systems

Recently, some stochastic neural network models have been presented for the purpose of overcoming the defect that the deterministic neural network models do not have the ability to escape from a local optimal solution. However, the specification of the values of various parameters and weights in these stochastic neural network models is more complicated than that in the deterministic neural network models. In this paper, a new stochastic neural network model is proposed in order to reduce the complication of specifying the values of parameters and weights. For a practical purpose, the proposed model is applied to the problem of grouping parts and tools in flexible manufacturing systems (FMSs).

Economical operation of (x, s) control chart indexed by Taguchi's loss function

Assume that lot quality characteristics obey a normal distribution. Kanagawa et al. have proposed the ( x, s ) control chart which enable the user to monitor both changes of the mean and variance simultaneously. Further, the results of Watakabe and Arizono enable the user to evaluate the performance for out-of-control state in the case of using the ( x, s ) control chart. On the other hand, Taguchi has presented an approach to quality improvement in which reduction of deviation from the target value is the guiding principle. In this approach, the loss is expressed as a quadratic form with respect to the difference between the measured value x of a product characteristic X and the target value T of a product quality characteristic. Then, we can evaluate the process quality based on the Taguchis loss criterion. We consider here the economical operation of the ( x, s ) control chart in conformity with the expected total operation cost function based on the sampling cost and the loss due to derivation in the process quality. First, we consider the economical operation of the ( x, s ) control chart in the situation that the loss to be considered is known. Further, the economical operation of the ( x, s ) control chart is also discussed under any loss instead of a known loss. Then, the relationship between the two economical operations proposed here corresponds to the relationship between the lot tolerance per cent defective plans under the fixed fraction defective and the average outgoing quality limit plans under any fraction defective in rectifying inspection plans.

A Study of Cumulative Sum Control Charts

The cumulative sum (CUSUM) control chart is known as a sensitive control chart to a slight change of the process quality characteristics. This control chart is designed based on a series of cumulative sum of the statistic derived from data. For normally distributed characteristics, it should be needed to monitor both changes of the mean and variance simultaneously. However, it is difficult to design the CUSUM or joint control chart using the statistics of and s or R jointly. By the way, Kanagawa et.al . have proposed the ( )control chart which enables the user to monitor both changes of the mean and variance simultaneously based on one statistic for normally distributed characteristics. When the CUSUM control chart is considered based on the ( ) control chart, it is possible to design and use the CUSUM control chart more easily than the joint CUSUM and either R or s control charts. Hence, we consider a CUSUM ( ) control chart in order to improve the performance for a slight change of the process quality characteristics in this article. In addition, the economical operation of the CUSUM ( ) control chart is also considered.

Proposal of variable sequential sampling plan having desired operating characteristics indexed by quality loss

The proportion of non-conforming items has been traditionally utilised as an evaluation criterion for quality of items. However, the proportion of non-conforming items is not necessarily useful as a proper evaluation criterion for controlling high-quality manufacturing in recent years. Accordingly, in order to achieve further quality improvement and innovation, more careful quality evaluation has been required newly. Then, a concept of quality loss in the Taguchi methods has been devised as a severe criterion of quality evaluation. Hereby, a variable single sampling plan having desired operating characteristics (OCs) indexed by quality loss has been proposed in the area of statistical quality control. By the way, the most economical sampling inspection in the average sample number (ASN) is the sequential sampling plan based on the Wald’s sequential probability ratio test. Then, from the viewpoint of cost reduction, we discuss a variable sequential sampling plan having desired OC indexed by quality loss with the aim of expansion of the utility of variable sampling plan for quality loss. As the result, the design procedure of the sequential sampling plan for satisfying some required design conditions indexed by quality loss is provided. In addition, the effectiveness of the proposed sequential sampling plan is verified through some numerical examples.

Design of accelerated reliability tests based on simple-step-stress model

The accelerated life tests can obtain information on lifetime characteristics of products quickly. Then, the products can be submitted to higher levels of stress in various ways such as constant, step, and progress stress. In a constant-stress model, products are run under a constant level of stress until all products fail or a time limit is reached. A step-stress model allows the stress setting to be changed at a prescribed time or upon the occurrence of a fixed number of failures. In a progress-stress model, the stress is continuously increased over time. Until now, under the assumption of the functional relationship between the parameters of lifetime distribution and applied stress, there are many studies about parameter estimation using data obtained from an accelerated life test. In this study, instead of the parameter estimate problem, the authors consider a new design procedure of accelerated life tests based on the simple-step-stress model for assuring the mean time to failure (MTTF) at usual stress with specified producer and consumer risks under the condition that the parameters of the lifetime distribution at two stress levels are provided. The practical usage of the proposed design procedure is illustrated through some numerical examples.

An improvement of a back propagation algorithm by the extended Kalman filter and demand forecasting by layered neural networks

Recently, Watanabe et al. proposed a back propagation algorithm via the extended Kalman filter, in which the learning rate was time-varying. In their algorithm the weights and biases are treated as independent variables. It is, however, natural that the weights and biases are not always independent, and generally have mutual correlation. In this paper, we improve the back propagation algorithm by considering that there is mutual correlation among the weights and bias directly connected to the unit. Through some numerical examples, our improved learning algorithm is compared with Watanabe et al.s algorithm in learning ability. Furthermore, we consider demand forecasting as a kind of pattern recognition, and propose a demand forecasting method using layered neural networks with the improved learning algorithm. The effectiveness of this demand forecasting method is also discussed through some simulations.