Çağatay Çetinkaya

Kirikkale University · Department of Actuarial Sciences

Let Y represents the strength variable effected by the stress variables X1 and X2. Assume that three samples are independent. Thus, R = P (X1 < Y < X2) denotes the reliability where the strength Y should not only be greater than stress X1 but also smaller than stress X2. Estimation of R has extensive applications in various areas since it provides...

In this paper, we have considered the classical and Bayesian inference of the unknown parameters of the lifetime distribution based on the observations obtained from a simple step-stress life-testing (SSLT) experiment and when more than one cause of failures are observed. We have used the Tampered Random Variable (TRV) approach. The main advantage...

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring (BJPC) scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale param...

In the case of operating conditions in a much shorter time, the accelerated life test (ALT) models are commonly used method since these models let the experimenters control the higher stress levels to be used for components or items in the life tests. Among different ALT methods , constant stress accelerated life test (CSALT) models have a relation...

This study deals with the inference of the overlapping measure for two bathtub-shaped lifetime distributions defined by Chen [1]. Among different overlapping coefficients, we use the most popular measure, Matusita's measure [2], since its simple mathematical structure and some strong properties such as consistency , unbiasedness, validity and etc....

In a life-testing experiment, the joint progressive censoring scheme for more than one exponential population was proposed by Rasouli and Balakrishnan (Commun Stat Theory Methods 39(12):2172–2191, 2010). In this paper, we focus on the joint adaptive progressive Type-II (JAPC-II) censoring scheme for two populations to reduce the experimental time a...

The fiducial inference idea was firstly proposed by Fisher (1930) as a powerful method in statistical inference. Many authors such as Weeranhandi (1993) and Hannig et. al. (2016) improved this method from different points of view. Since the Bayesian method has some deficiencies such as assuming a prior distribution when there was little or no infor...

In this paper, we studied the estimation of R=P(X>Y) based on the Burr-XII distribution under the generalized progressive hybrid censoring scheme. This censoring scheme has become quite popular depending progressive hybrid censoring scheme cannot be applied when few failures occur before pre-determined time T. In this progressive censoring plan, am...

This paper deals with the improved point estimations of the inverse power Lindley distribution. The maximum likelihood estimation method, and a simulated annealing algorithm, a heuristic alternative method, are considered. The bias-corrected estimation methods are also used to evaluate the bias reduction of the estimates. These bias-corrected estim...

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring (BJPC) scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale param...

The fiducial inference idea was firstly proposed by Fisher (1930) as a powerful method in statistical inference. Many authors such as Weeranhandi (1993) and Hannig et. al. (2006) improved this method from different points of view. Since the Bayesian method has some deficiencies such as assuming a prior distribution when there was little or no infor...

The generalized progressive hybrid censoring schemes (GPHCS) have become quite popular in the case when there are very few failures before pre-determined time T in progressive hybrid censoring schemes. Whereas the GPHCS always ensures a fixed number of failures, which makes this scheme very popular. In this paper, we introduce a new joint generaliz...

A system of k components that functions as long as at least s components survive is termed as s-out-of-k:G system, where G refers to "good". In this study, we consider the s-out-of-k:G system when X1, X2, · · · , Xk are independent and identically distributed strength components and each component is exposed to common random stress Y when the under...

This paper deals with the jointly Type-II censored length-biased exponential populations. In this study, after introducing the jointly Type-II censoring scheme, we first obtained the maximum likelihood estimations of the unknown scale parameters with their asymptotic confidence intervals. Then, the Bayesian estimations of the parameters are obtaine...

In this study, the standard two-sided power (STSP) distribution is considered with regard to statistical reliability analysis in detail. For this purpose, along with the reliability and hazard functions of the distribution, particular reliability indices that are useful in maintenance and replacement policies are obtained and they are evaluated wit...

This paper deals with the estimation of the stress-strength reliability model in the event of its strength variable is subjected to the step-stress partially accelerated life test. Inferences for the reliability of such a system are obtained under the assumption that the strength and stress components have one-parameter exponential distributions. M...

This paper deals with the jointly Type-II censored length-biased exponential populations. After introducing the jointly Type-II censoring scheme, we first consider the maximum likelihood estimators of the unknown scale parameters along with their asymptotic confidence intervals. Then, the Bayesian estimations are obtained by using the importance sa...

This paper considers a simple step stress accelerated life test for units modelled by a length-biased exponential distribution. The cumulative exposure model of time to failure holds in this accelerated life test model. The optimal test plan is constructed by determining the optimal stress change time. Parameters of the model are estimated by using...

In this study, inference for the power Lindley distribution under a step-stress partially accelerated life test based on progressive Type-II censoring scheme is studied. The maximum likelihood estimates of the parameters and acceleration factor is investigated with their corresponding approximate confidence intervals by using asymptotic theory. The...

This study deals with point and interval estimations for the scale and shape parameters of the component lifetime distribution of a k-component series system when the component lifetimes are assumed to be independently and identically Erlang-truncated exponential distributions. It is assumed that the components are exposed to progressive Type-II ce...

This article considers the estimation of the stress-strength reliability with non-identical and also jointly censored component strengths. Both stress and strength variables are assumed to follow two-parameter Weibull distribution. In this reliability model, we assume type-II censoring scheme for common stress variable and jointly type-II censoring...

Generalized progressive hybrid censoring schemes have become quite popular depending progressive hybrid censoring scheme cannot be applied when few failures occur before pre-determined time T. Otherwise, due to the necessity of more realistic stress strength models, this article considers to estimate the reliability of an s-out-of-k system with non...

The Pareto distribution takes part in life-testing experiments as a finite range distribution. In this study, inference studies for the scale and shape parameters of the Pareto distribution under type-II hybrid censoring scheme are considered. The main reason for choosing this censoring scheme is its advantage of guaranteeing at least particular fa...

The simple stress-strength reliability model contains a strength variable X and a stress variable Y which is exposed to it. Such a system will properly function when X exceeds Y and R = P(X > Y ) denotes to the system reliability. This model can be extended for the systems with two or more components and denoted by multicomponent stress-strength mo...

Statistical entropy measures the uncertainty or ignorance about the outcome of a random variable and it is a measurement of reduction in uncertainty. It is mainly useful especially in statistical mechanics. The differential entropy (continuous entropy) is a notion in information theory and is a measure of average uncertainty or ignorance of a rando...

In statistical reliability analysis, an important topic is accelerated life test (ALT) or partially accelerated life test (PALT) which let the experimenters control the higher stress levels to be used for components or units in the life tests. It is known that it is not easy to observe lifetimes of highly reliable components since very long lifetim...

In this study, we consider the standard two-sided power (STSP) distribution with regard to stress-strength reliability for a multicomponent; s-out-of-k:G system. An s-out-of-k:G system is formed by independent and identically distributed X_1,X_2,⋯,X_n strength components and each component is exposed to a common random stress Y. Such a system survi...

In statistical literature, there are many different probability distributions for modelling lifetime data. They are mostly defined over the range (0,∞) and exponential, Weibull, log-normal distributions are common probability distributions for modelling them under reliability context. In some cases, lifetime data may be considered in a finite range...

In this report the distribution for setting up a system reliability exposed to some stress is studied. The standard two-sided power distribution is assumed to be the underlying distribution. We obtained the exact expressions and estimates for the reliability by applying different methods such as maximum likelihood and Bayesian estimators. Three dif...

The standard two-sided power distribution is a flexible distribution having uniform, power function and triangular as subdistributions, and it is a reasonable alternative to the Laplace distribution in some cases. In this work, computationally efficient expressions for moments of order statistics, expressions for L-moments, and asymptotic results f...

When a component is exposed to a random stress 𝑌, the reliability of the system is defined as 𝑅 = 𝑃(𝑌 < 𝑋), where 𝑋 is the strength of the component. Estimation of 𝑅 under various parametric models has been studied extensively in the literature. In this work, we consider the standard two-sided power (STSP) distribution which is a generalization of...

In this work, moment relations for the product moments of order statistics from the standard two-sided power (STSP) distribution are obtained. Since the probability density function (pdf) of the STSP distribution is a piecewise function, we consider the pieces separately and develop certain moment relations based on these pieces. Also, the usefulne...

The standard two-sided power (STSP) distribution was introduced by Van Dorp and Kotz (2002). The STSP distribution is a beta-like distribution since it is defined on a bounded support and has a similar flexibility. It is especially useful for modeling financial data with excess kurtosis. The distribution has also applications in risk analysis such...

The standard two-sided power (STSP) distribution is introduced by Kotz and van Dorp (2002). In this paper; firstly the density function and moments of an arbitrary order statistic from the STSP distribution are obtained. Specifically, the moments of minimum and maximum order statistics are studied. Additionally, domain of minimal, maximal attractio...