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Gholam Hossein Shahkar, Rahim Badamchizadeh,
Volume 1, Issue 1 (9-2007)
Abstract
In this paper we consider a single server queue with two phase arrival and two phase services. Arrival are Poison variables with different rates. For each input, the server provides private service with exponential distribution. The rates of services are different. The policy of service is FCFS, where the server changes the king of service according to the customer in the front of queue. After the completion of each service, the server either goes for a vacation with probability (1-theta), or may continue to server the next customer with probability theta, if any. Otherwise, it remains in the system until a customer arrives. Vacation times are assumed to have exponential distribution. We obtain steady-state probability generating function for queue size distribution for each input and expected busy period.
Ghobad Barmalzan, Abedin Haidari, Maryam Abdollahzade,
Volume 6, Issue 2 (2-2013)
Abstract
Suppose there are two groups of independent exponential random variables, where the first group has different hazard rates and the second group has common hazard rate. In this paper, the various stochastic orderings between their sample spacings have studied and introduced some necessary and sufficient conditions to equivalence of these stochastic ordering. Also, for the special case of sample size two, it is shown that the hazard rate function of the second sample spacing is Shcur-concave in the inverse vector of parameters.
Mohamad Bayat, Jafar Ahmadi,
Volume 6, Issue 2 (2-2013)
Abstract
Nowadays, the use of various types of censoring plan in studies of lifetime engineering systems and industrial experiment are worthwhile. In this paper, by using the idea in Cramer and Iliopoulos (2010), an adaptive progressive Type-I censoring is introduced. It is assumed that the next censoring number is random variable and depends on the previous censoring numbers, previous failure times and censoring times. General distributional results are obtained in explicit analytic forms. It is shown that maximum likelihood estimators coincide with those in deterministic progressive Type-I censoring. Finally, in order to illustrate and make a comparison, simulation study is done for one-parameter exponential distribution.
Ghobad Barmalzan, Abedin Heidari,
Volume 7, Issue 1 (9-2013)
Abstract
Suppose there are two groups of random variables, one with independent and non-identical distributed and another with independent and identical distributed. In this paper, for the case when the size of groups are not equal, and all of the underlying random variables have exponential distribution, the necessary and sufficient conditions are obtained for establishing the mean residual life, hazard rate and dispersive orders between the second order statistics of two groups. Moreover, when random variables follow the Weibull distribution, the hazard rate, dispersive and likelihood ratio order between the second order statistics from two groups are investigated.
Hamazeh Torabi, Narges Montazeri, Fatemeh Ghasemian,
Volume 7, Issue 2 (3-2014)
Abstract
In this paper, some various families constructed from the logit of the generalized Beta, Beta, Kumar, generalized Gamma, Gamma, Weibull, log gamma and Logistic distributions are reviewed. Then a general family of distributions generated from the logit of the normal distribution is proposed. A special case of this family, Normal-Uniform distribution, is defined and studied. Various properties of the distribution are also explored. The maximum likelihood and minimum spacings estimators of the parameters of this distribution are obtained. Finally, the new distribution is effectively used to analysis a real survival data set.
Fatemeh Safaei, Jafar Ahmadi,
Volume 9, Issue 1 (9-2015)
Abstract
Consider a repairable system where two types of failures occur with different rate functions. The choice of minimal repair or replacement depends on the types of failures. The length of replacement cycle becomes optimal in terms of the cost function and the concept of discounted cost. In this paper, for two repairable systems the optimal replacement cycles are compared based on failure rate functions and probability of minimal repairs. Based on our results, one can make a decision for the period of replacement times. In order to illustrate the obtained results, numerical examples and simulation study are given.
Bahareh Afhami, Mohsen Madadi, Mohsen Rezapour,
Volume 9, Issue 1 (9-2015)
Abstract
In this paper, first the Shannon entropy of k-record values is derived from the generalized Pareto distribution and propose goodness-of-fit tests based on this entropy. Finally, real data and a simulation study are used for analyzing the performance of this statistic.
Ghobad Barmalzan, Abedin Haidari, Khaled Masomifard,
Volume 9, Issue 2 (2-2016)
Abstract
In this paper, series and parallel systems, when the lifetimes of their components following the scale model are studied and different stochastic orderings between them are discussed. Moreover, we apply these results to the series and parallel systems consisting of exponentiated Weibull or generalized gamma components. The presented results in this paper complete and extend some known results in the literature.
Ali Doostmoradi, Mohammadreza Zadkarami, Aref Khanjari Idenak, Zahara Fereidooni,
Volume 10, Issue 1 (8-2016)
Abstract
In this paper we propose a new distribution based on Weibull distribution. This distribution has three parameters which displays increasing, decreasing, bathtub shaped, unimodal and increasing-decreasing-increasing failure rates. Then consider characteristics of this distribution and a real data set is used to compared proposed distribution whit some of the generalized Weibull distribution.
Shiva Akhtarian, Tahere Yaghoobi,
Volume 10, Issue 1 (8-2016)
Abstract
Given the widespread usage of software systems in all aspects of modern life, the need to produce almost error free and high quality software has become more and more important. Software reliability is considered as an important approach to software quality assessment. Software reliability modeling based on non- homogeneous Poisson process is a quite successful method in software reliability engineering. In this paper, we first study the general growth model of software reliability, and then we extend the general model by considering two types of simple and complex errors, dependency between complex errors and time delay between detecting and removing complex errors. Estimating the model parameters has been done by using two failure data sets of real software projects through MATLAB software. We compare the proposed model with two existing models using various criteria. The results show that the proposed model better fits the data, providing more accurate information about the software quality.
Fatemeh Hooti, Jafar Ahmadi,
Volume 10, Issue 1 (8-2016)
Abstract
In this paper, the quantile function is recalled and some reliability measures are rewritten in terms of quantile function. Next, quantile based dynamic cumulative residual entropy is obtained and some of its properties are presented. Then, some characterization results of uniform, exponential and Pareto distributions based on quantile based dynamic cumulative entropy are provided. A simple estimator is also proposed and its performance is studied for exponential distribution. Finally discussion and results are presented.
Eisa Mahmoudi, Somayeh Abolhosseini,
Volume 10, Issue 1 (8-2016)
Abstract
In this paper we propose a new two-parameters distribution, which is an extension of the Lindley distribution with increasing and bathtub-shaped failure rate, called as the Lindley-logarithmic (LL) distribution. The new distribution is obtained by compounding Lindley (L) and Logarithmic distributions. We obtain several properties of the new distribution such as its probability density function, its failure rate functions, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented in this paper. At the end, in order to show the flexibility and potentiality of this new class, some series of real data is used to fit.
Jafar Ahmadi, Mansoureh Razmkhah,
Volume 11, Issue 1 (9-2017)
Abstract
Consider a repairable system which starts operating at t=0. Once the system fails, it is immediately replaced by another one of the same type or it is repaired and back to its working functions. In this paper, the system's activity is studied from t>0 for a fixed period of time w. Different replacement policies are considered. In each cases, for a fixed period of time w, the probability model and likelihood function of repair process, say window censored, are obtained. The obtained results depend on the lifetime distribution of the original system, so, expression for the maximum likelihood estimator and Fisher information are derived, by assuming the lifetime follows an exponential distribution.
Eisa Mahmoudi, Reyhaneh Lalehzari, Ghahraman Roughani,
Volume 11, Issue 1 (9-2017)
Abstract
We consider the purely sequential procedure for estimating the scale parameter of an exponential distribution, when the risk function is bounded by the known preassigned number. In this paper, we provide explicit formulas for the expectation of the total sample size. Also, we propose how to adjust the stopping variable so that the risk is uniformly bounded by a known preassigned number. In the end, the performances of the proposed methodology are investigated with the help of simulations.
Shahrokh Hashemi-Bosra, Ebrahim Salehi,
Volume 11, Issue 1 (9-2017)
Abstract
The (n-k+1)-out-of-n systems are important types of coherent systems and have many applications in various areas of engineering. In this paper, the general inactivity time of failed components of (n-k+1)-out-of-n system is studied when the system fails at time t>0. First we consider a parallel system including two exchangeable components and then using Farlie-Gumbel-Morgenstern copula, investigate the behavior of mean inactivity time of failed components of the system. In the next part, (n-k+1)-out-of-n systems with exchangeable components are considered and then, some stochastic ordering properties of the general inactivity time of the systems are presented based on one sample or two samples.
Fatemeh Iranmanesh, Mohsen Rezapour, Reza Pourmousa,
Volume 12, Issue 1 (9-2018)
Abstract
In this paper, we study the maintenance method in a system. We also consider a system that begin at time zero with most efficienty. After the first failure it is repaired, but we assume that the lifetime of the system is stochastically less than its lifetime at time zero. It is repaired after the second failure and after the third failur it is checked whether the system should be dismanteld or completly repaired. During the performance of the system preventive maintenance could be used to increase the lifetime of the system. Because these actions are costly, we discuss a method for optimizing the cost of preventive maintenance. Finally, we provide some illustrative examples.
Ebrahim Amini-Seresht, Majid Sadeghifar, Mona Shiri,
Volume 12, Issue 1 (9-2018)
Abstract
In this paper, we further investigate stochastic comparisons of the lifetime of parallel systems with heterogeneous independent Pareto components in term of the star order and convex order. It will be proved that the lifetime of a parallel system with heterogeneous independent components from Pareto model is always smaller than from the lifetime of another parallel system with homogeneous independent components from Pareto model in the sense of convex order. Also, under a general condition on the scale parameters, it is proved a result involving with star order.
Afsaneh Shokrani, Mohammad Khorashadizadeh,
Volume 12, Issue 2 (3-2019)
Abstract
This paper first introduces the Kerridge inaccuracy measure as an extension of the Shannon entropy and then the measure of past inaccuracy has been rewritten based on the concept of quantile function. Then, some characterizations results for lifetimes with proportional reversed hazard model property based on quantile past inaccuracy measure are obtained. Also, the class of lifetimes with increasing (decreasing) quantile past inaccuracy property and some of its properties are studied. In addition, via an example of real data, the application of quantile inaccuracy measure is illustrated.
Rabeeollah Rahmani, Muhyiddin Izadi,
Volume 12, Issue 2 (3-2019)
Abstract
Consider a system consisting of n independent binary components. Suppose that each component has a random weight and the system works, at time t, if the sum of the weight of all working components at time t, is above a pre-specified value k. We call such a system as random-weighted-k-out-of-n system. In this paper, we investigate the effect of the component weights and reliabilities on the system performance and show that the larger weights and reliabilities, the larger lifetime (with respect to the usual stochastic order). We also show that the best random-weighted-k-out-of-n system is obtaind when the components with the more weights have simultaneously more reliability. The reliability function and mean time to failure of a random-weighted-k-out-of-n system are stated based on the reliability function of coherent systems. Furthermore, a simulation algorithm is presented to observe the mean time to failure of random-weighted-k-out-of-n system.
Vahideh Ahrari, Simindokht Baratpour, Arezo Habibirad,
Volume 12, Issue 2 (3-2019)
Abstract
Entropy plays a fundamental role in reliability and system lifetesting areas. In the recent studies, much attentions have been paid to use quantile functions properties and their applications as an alternate approac in distinguishing statistical models and analysis of data. In the present paper, quantile based residual Tsallis entropy is introduced and its properties in continuous models are investigated. Considering distributions of certain lifetime, explicit versions for quantile based residual Tsallis entropy are obtained and their properties monotonicity are studied and characterization based on this entropy is investigated. Also quantile based Tsallis divergence is introduced and quantile based residual Tsallis divergence is obtained. Finally, an estimator for the quantile based residual Tsallis entropy is introduced and its performance is investigate by study simulation.
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