Serkan Eryilmaz

A Nonparametric Shewhart-Type Signed-Rank Control Chart Based on Runs

Shewhart-type distribution-free control charts are considered for the known in-control median of a continuous process distribution based on the Wilcoxon signed-rank statistic and some runs type rules. The new charts are more attractive to the practitioner than a basic Shewhart-type signed-rank chart proposed by Bakir (2004), as they offer more desirable (smaller) false alarm rates and (larger) in-control average run-lengths, and can be easily implemented. In addition to being nonparametric, that is with a known and stable in-control performance for all continuous distributions, a simulation study indicates that the proposed charts can have better out-of-control performance than the Shewhart X-bar chart and the basic signed-rank chart for the normal distribution and for some heavy-tailed distributions such as the double exponential and the Cauchy. A numerical example is provided.

RELIABILITY PROPERTIES OF CONSECUTIVE K-OUT-OF-N SYSTEMS OF ARBITRARILY DEPENDENT COMPONENTS

Abstract In this paper, the reliability properties of consecutive k-out-of-n systems with arbitrarily dependent components are studied. For 2 k ⩾ n we present efficient formulas to compute the reliability characteristics such as meantime to failure, failure rate, and mean residual lifetime. Approximations for the survival functions when 1 ⩽ k ⩽ n are also provided. The results are illustrated for the multivariate survival distribution generated by a Weibull and Inverse-Gaussian mixture.

Reliability of a K-Out-of-n System Equipped With a Single Warm Standby Component

A k-out-of-n:G system consists of n components, and operates if at least k of its components operate. Its reliability properties have been widely studied in the literature from different perspectives. This paper is concerned with the reliability analysis of a k-out-of-n:G system equipped with a single warm standby unit. We obtain an explicit expression for the reliability function of the system for arbitrary lifetime distributions. Two different mean residual life functions are also studied for the system.

Computing and Applying the Signature of a System With Two Common Failure Criteria

The signature of a system is a useful tool in a variety of applications including the evaluation of the reliability characteristics of systems, and the comparison of the performance of competing systems. We study the evaluation and application of signatures of systems involving two common failure criteria which are common in real life applications. The failure or survival of these systems generally depends on the number of consecutively failed or working components, or total number of failed or working components in the whole system. We provide a method for obtaining the signatures of such systems. Applications of the results are also presented.

On the mean residual life of a k-out-of-n:G system with a single cold standby component

The concept of mean residual life is one of the most important characteristics that has been widely used in dynamic reliability analysis. It is a useful tool for investigating ageing properties of technical systems. In this paper, we define and study three different mean residual life functions for k-out-of-n:G system with a single cold standby component. In particular, we obtain explicit expressions for the corresponding functions using distributions of order statistics. We also provide some stochastic ordering results associated with the lifetime of a system. We illustrate the results for various lifetime distributions.

Mixture representations for the reliability of consecutive-k systems

In this paper, we obtain representations for the reliability of consecutive type systems as a mixture of the reliability of order statistics whenever the systems consist of exchangeable components. The representations enable us to compute the reliability of linear and circular consecutive systems in a simple way. Furthermore the limiting behaviour of these systems can be evaluated and stochastic ordering results can be established with the help of these mixture representations.

Consecutive k-Out-of-n : G System in Stress-Strength Setup

A consecutive k-out-of-n: G system consists of n linearly ordered components functions if and only if at least k consecutive components function. In this article we investigate the consecutive k-out-of-n: G system in a setup of multicomponent stress-strength model. Under this setup, a system consists of n components functions if and only if there are at least k consecutive components survive a common random stress. We consider reliability and its estimation of such a system whenever there is a change and no change in strength. We provide minimum variance unbiased estimation of system reliability when the stress and strength distributions are exponential with unknown scale parameters. A nonparametric minimum variance unbiased estimator is also provided.

On the distribution and expectation of success runs in nonhomogeneous Markov dependent trials

The number of success runs for nonhomogeneous markov dependent trials are represented as the sum of Bernoulli trials and the expected value of runs are obtained by using this representation. The distribution and bounds for the distribution of the longest run are derived for markov dependent trials.

An algorithmic approach for the dynamic reliability analysis of non-repairable multi-state weighted k-out-of-n:G system

Abstract In this paper, we study a multi-state weighted k -out-of- n :G system model in a dynamic setup. In particular, we study the random time spent by the system with a minimum performance level of k . Our method is based on ordering the lifetimes of the system׳s components in different state subsets. Using this ordering along with the Monte-Carlo simulation algorithm, we obtain estimates of the mean and survival function of the time spent by the system in state k or above. We present illustrative computational results when the degradation in the components follows a Markov process.

The Number of Failed Components in a Coherent System With Exchangeable Components

This paper is concerned with the number of components that are failed at the time of system failure. We study the corresponding quantity for a coherent structure via the system signature. Furthermore, we study the distribution of the number of failures after a specified time until the system failure. We illustrate the results for well-known general classes of coherent systems such as linear consecutive -within- -out-of- :F, and -consecutive- -out-of- :F.