Journal of Statistical Sciences

Joint Determination of Inspection and Preventive Replacement Policy of a Parallel System Subject to Hidden Failure

Reza Ahmadi

We propose an integrated approach for decision making about repair and maintenance of deteriorating systems whose failures are detected only by inspections. Inspections at periodic times reveal the true state of the system's components and preventive and corrective maintenance actions are carried out in response to the observed system state. Assuming a threshold-type policy, the paper aims at minimizing the long-run average maintenance cost per unit time by determining appropriate inspection intervals and a maintenance threshold. Using the renewal reward theorem, the expected cost per cycle and expected cycle length emerge as solutions of equations, and a recursive scheme is devised to solve them. We demonstrate the procedure and its outperformance over specific cases when the components' lifetime conforms to a Weibull distribution. Further, a sensitivity analysis is performed to determine the impact of the model's parameters. Attention has turned to perfect repair and inspection, but the structure allows different scenarios to be explored.

Worst Allocations of Policy Layers for Independent and Identically Distributed Exponential Risks

Masoud Amiri

In this paper, the worst allocation of deductibles and limits in layer policies are discussed from the viewpoint of the insurer. It is shown that if n independent and identically distributed exponential risks are covered by the layer policies and the policy limits are equal, then the worst allocation of deductibles from the viewpoint of the insurer is (d‎, ‎0‎, ‎..., ‎0)‎.

Optimal Sample Size Based on Cost Function in Progressively Type II Censoring

Elham Basiri

‎Nowadays inference based on censored samples has been studied by many researchers‎. ‎One of the most common censoring methods is progressively type II censoring‎. ‎In this model‎, ‎n items are put on the test‎. ‎At each failure times some of the remaining items randomly withdrawn from the test‎. ‎This process continues until for a pre-fixed value as m, ‎failure times of m items are observed‎. ‎For determining the best number for the items on the test different criteria can be considered‎. ‎One of the most important factors that can be considered is the cost criterion‎. ‎In this paper‎, ‎by considering cost function and Weibull distribution for the lifetime of items‎, ‎we find the optimal value for the sample size‎, ‎i.e‎. n‎. ‎In order to evaluate‎, ‎the obtained results one example based on real data is given‎.

A Discrete Time Run Shock Model

Mohammad hossein Poursaeed

A system in discrete time periods is exposed to a sequence of shocks so that shocks occur randomly and independently in each period with a probability p. Considering k(≥1) as a critical level, we assume that the system does not fail when the number of successive shocks is less than k, the system fails with probability Ө, if the number of successive shocks is equal to k and the system completely fails as soon as the number of sequential shocks reaches k+1. Therefore, this model can be considered as a version of run shock model, in which the shocks occur in discrete periods of time, and the behavior of the system is not fixed when encountering k successive shocks. In this paper, we examine the characteristics of the system according to this model, especially the first and second-order moments of the system's lifetime, and also estimate its unknown parameters. Finally, a method is proposed to calculate the mean of the generalized geometric distribution.

Maximum Likelihood Estimators for α-Stable Distribution

Mahdi Teimouri

‎The class of α-stable distributions incorporates both heavy tails and skewness and so are the most widely used class of distributions in several fields of study which incorporates both the skewness and heavy tails‎. ‎Unfortunately‎, ‎there is no closed-form expression for the density function of almost all of the members of this class‎, ‎and so finding the maximum likelihood estimator for the parameters of this distribution is a challenging problem‎. ‎In this paper‎, ‎in order to tackle this issue‎, ‎we propose some type of EM algorithm‎. ‎The performance of the proposed EM algorithm is demonstrated via simulation and analyzing three sets of real data‎.

Semiparametric Analysis of Regression Models for Zero-Inflated Power Series Responses with Missing Covariate

Ehsan Bahrami Samani

In this paper‎, ‎the analysis of count response with many zeros‎, ‎named as zero-inflated data‎, ‎is considered‎. ‎Assumes that responses follow a zero-inflated power series distribution‎. ‎Because of there is missing of the type of random in the covariate‎, ‎some of the data application‎, ‎various methods for estimating of parameters by using the score function with and without missing data for the proposed regression model are presented‎. ‎On the other hand‎, ‎known or unknown selection probability in the missing covariates results in presenting a semi-parametric method for estimating of parameters in the zero-inflated power series regression model‎. ‎To illustrate the proposed method‎, ‎simulation studies and a real example are applied‎. ‎Finally‎, ‎the performance of the semi-parametric method is compared with maximum likelihood‎, ‎complete-case and inverse probability weighted method‎.

Ageing Properties of Modified Proportional Hazard Rates Model for Discrete Lifetime Distributions

Rasool Rozegar

The modified proportional hazard rates model, as one of the flexible families of distributions in reliability and survival analysis, and stochastic comparisons of (n-k+1) -out-of- n systems comprising this model have been introduced by Balakrishnan et al. (2018). In this paper, we consider the modified proportional hazard rates model with a discrete baseline case and investigate ageing properties and preservation of the usual stochastic order, hazard rate order and likelihood ratio order in this family of distributions.

Testing Multiple Profiles for Outlier Detection

Marjan Rajabi

The advent of new technology in recent years has facilitated the production of high dimension data. In these data we need evaluating more than one assumption.  Multiple testing can be used for the collection of assumptions that are simultaneously tested and controlled the rate of family wise error that is the most critical issue in such tests. In this report, the authors apply Sidak and Stepwise strategies for controlling family wise error rate in detecting outlier profiles and comparing to each other. Considering our simulation results, the performance of such methods are compared using the parametric bootstrap snd by applying on real data in dataset illustrate the implementation of the proposed methods.

Smallest Confidence Region for the Parameters of Two-Parameter Exponential Distribution

Akbar Asgharzadeh

In this paper, the smallest confidence region is obtained for the location and scale parameters of the two-parameter exponential distribution. For this purpose, we use constrained optimization problems. We first provide some suitable pivotal quantities to obtain a balanced confidence region. We then obtain the smallest confidence region by minimizing the area of the confidence region using the Lagrangian method. Two numerical examples are presented to illustrate the proposed methods. Finally, some applications of proposed joint confidence regions in hypothesis testing and the construction of confidence bands are discussed.

Determine the Optimal Bayesian Fuzzy Membership Function Using Fuzzy Data

Shadi Saeidi Jeyberi

In this paper, Bayesian fuzzy estimator is obtained first, for the fuzzy data based on the probability prior distribution and afterward based on the possible model and the possibility of a prior distribution. Considering the effect of the membership functions on the fuzzy and possibility Bayesian estimators, a membership function that gives the optimal fuzzy and possibility Bayesian estimators will be introduced for the data. The optimality of the new triangular-gaussian membership function is denoted by using the normal and exponential data sets.

Wavelet-Based Quantile Density Estimation By Block Thresholding Method Under L2 Loss Function

Esmaeil Shirazi

In this paper, we consider an adaptive wavelet estimation for quantile density function based on block thresholding method and obtain it's convergence rate under L2 loss function over Besove function spaces. This work is an extension of results in Chesneau et. al. (2016) and shows that the block threshold estimator gets better convergence rate (Optimal) than the estimators proposed by Chesneau et. al. (2016). The performance of the proposed estimator is investigated with a simulation study.

An INAR(1) Model Based on Negative Binomial Thinning Operator with Serially Dependent Noise.

Mehrnaz Mohammadpour

‎In this paper‎, ‎we introduce a new integer-valued autoregressive model of first order based on the negative binomial thinning operator‎, ‎where the noises are serially dependent‎. ‎Some statistical properties of the model are discussed‎. ‎The model parameters are estimated by maximum likelihood and Yule-Walker methods‎. ‎By a simulation study‎, ‎the performances of the two estimation methods are studied‎. ‎This survey was carried out to study the efficiency of the new model by applying it on real data‎.

A Test for Independence in High-Dimensional Normal Data

Dariush Najarzadeh

The hypothesis of complete independence is necessary for many statistical inferences. Classical testing procedures can not be applied to test this hypothesis in high-dimensional data. In this paper, a simple test statistic is presented for testing complete independence in multivariate high dimensional normal data. Using the theory of martingales, the asymptotic normality of the test statistic is established. In order to evaluate the performance of the proposed test and compare it with existing procedures, a simulation study was conducted. The simulation results indicate that the proposed test has an empirical type-I error rate with an average relative error less than the available tests. An application of the proposed method for gene expression clinical prostate data is presented.

E-Bayesian Estimation of the Reliabilty Parameter for Inverse Rayleigh Distribution Based on Ranked Set Sampling

Shahram Yaghoobzadeh

In this study, the E-Bayesian estimation of the reliability parameter, R = P(Y < X < Z), when X, Y and Z are three independent inverse Rayleigh distribution with different parameters, were estimated based on ranked set sampling method. To assess the efﬁciency of the obtained estimates, we compute the average absolute bias and relative efficiency of the derived estimates and compare them with those based on the corresponding simple random sample through Monte Carlo simulations. Also, E-Bayesian estimation of R is compared with its maximum likelihood estimation in each method. Finally, three real data sets are used to analyze the estimation methods.