JOURNAL OF STATISTICAL RESEARCH OF IRAN (JSRI)
Year:2018 | Volume:15 | Issue:1|Papers Count:6

A proper method of monitoring a stochastic system is to utilize the control charts of statistical process control in which a drift in characteristics of output may be due to one or several assignable causes. In the establishment of X charts, an assumption is made that there is no correlation within the samples. However, in practice, there are many industrial cases in which the correlation does exist within the samples. It would be more appropriate to assume that each sample is a realization of a multivariate normal random vector. Although some research works have been done on the economic design of control charts with single assignable cause with correlated data, the economic statistical design of X control chart for correlated data under Weibull shock model with modified Taguchi loss function have not been presented yet. Using modified Taguchi loss function in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Based on the optimization of the average cost per unit of time and different combination values of Weibull distribution parameters, optimal design values of sample size, sampling interval and control limit coefficient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with correlated samples with non-uniform sampling has a lower cost than that with uniform sampling.

We propose a new class of continuous models called the Weibull Generalized G family with two extra positive shape parameters, which extends several well-known models. We obtain some of its mathematical properties including ordinary and incomplete moments, generating function, order statistics, probability weighted moments, entropies, residual, and reversed residual life functions. Characterizations based on a ratio of two truncated moments, in terms of hazard function and based on certain functions of the random variable are presented. We estimate the model parameters by the maximum likelihood method. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of two simulation studies. The usefulness of the proposed models is illustrated via three real data sets.

In this paper we study the Tsallis relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the Tsallis relative entropy between two finite subsequences of above mentioned chains with the help of the definition of Tsallis relative entropy between two random variables then we define the Tsallis relative entropy rate between these stochastic processes. Finally, we calculate Tsallis relative entropy rate for some hidden Markov models.

In this paper, it is assumed that the mean of a normal process is monitored by a CUSUM control chart. When the control chart triggers a signal and declares that the process has gone out of control, a search process is started to find the time of change and the causes of going the process out of control. Several methods (plans) for finding the true (real) change point is proposed. It is shown that the plans which are based on the likelihood of the points in time perform better.

A new generalized version of the mixed Poisson distribution, called the Poisson-beta exponential (PBE) distribution, is obtained by mixing the Poisson and the beta exponential (BE) distributions. Estimation of the parameters, using the method of moments and maximum likelihood estimators, is discussed. We show the consistency of the new model parameters using simulation study. Examples are given for fitting the PBE distribution to data, and the fit model is compared with that obtained using other distributions.

Shirakura et al. (1996) has been introduced and calculated the search probability (SP) for normal search model. However, in practical situations the normality assumption may fail. In this study, we consider a more realistic underlying skew-normal/independent (SNI) model and obtain the SP. This is a general case, in a sense that the result in Shirakura et al. (1996) is its special case. The proposed SP carries some reliable properties and can be used as a design comparison criterion to compare and rank the search designs (SD).