A heuristic algorithm for reliability optimization of a distributed network system is developed so that the reliability of a large system can be determined efficiently. This heuristic bases on the determination of maximal reliability set of maximum node capacity, maximal link reliability and maximal node degree.

The dimensional measurement equipment, such as Coordinate Measurement Machine (CMM), Optical Coordinate Measurement Machine (OCMM), and Checking Fixture (CF), take multiple dimensional measurements for each part in an automobile industry. Measurements are also recorded under different measurement systems to see if the responses differ significantly over these systems. Each measurement system (CMM, OCMM, and CF) will be considered as different treatments. This set-up provides massive amounts of process data which are multivariate in nature. Therefore, the multivariate statistical analysis is required to analyze data that are dependent on each other. This research provides step by step methodology for the evaluation procedure of the compatibility of measurement systems and clarify a systematic analyzation among the different measurement system's compatibility followed by number of case studies for each methodologies provided.

Analysis of measurement systems is important to determine if the measurement process is adequate to measure the part-to-part variability in the process. Control chart techniques provide an effective, and easy-to-use method for performing this analysis. However, application with the real data for the evaluation procedure for multiple measurement systems have not been demonstrated. This research will provide a methodology for the evaluation of part-to-part variation and variation of different measurement systems step by step followed by number of case studies for each methodologies provided.

In this paper generalized version of the geometric distribution is introduced. This distribution can be considered as a two-parameter generalization of the discrete geometric distribution. The main statistical and reliability properties of this distribution are discussed. Two methods of estimation, namely maximum likelihood method and the method of moments are used to estimate the parameters of this distribution. Simulation is utilized to calculate these estimates and to study some of their properties. Also, asymptotic confidence limits are established for the maximum likelihood estimates. Finally, the appropriateness of this new distribution for a set of real data, compared with the geometric distribution, is shown by using the likelihood ratio test and the Kolmogorove-Smirnove test.

In this paper, we discuss the plethora of uses for the software package R, and focus specifically on its helpful applications in reliability data analyses. Examples are presented; including the R coding protocol, R code, and plots for various statistical as well as reliability analyses. We explore Kaplan-Meier estimates and maximum likelihood estimation for distributions including the Weibull. Finally, we discuss future applications of R, and usages of quantile regression in reliability.

Based on the goodness of fit approach, a new test is presented for testing exponentiality versus exponential better (worse) than used (EBU (EWU)) class of life distributions. The new test is much simpler to compute, asymptotically normal, enjoys good power and performs better than previous tests in terms of power and Pitman asymptotic efficiencies for several alternatives.

The aim of this work is to generalize reliability equivalence techniques to apply them to a system consists of two independent and non-identical components connected in series(parallel) system, that have constant failure rates. We shall improve the system by using one component only. We start by establishing two different types of reliability equivalence factors, the survival reliability equivalence (SRE) and mean reliability equivalence (MRE) factors. Our second studies, introducing some applications for our studies in airports and our life. Also, we introduced some numerical results.

This paper gives the reliability equivalence factors of a parallel system with n independent and non-identical components. It is assumed here that, the failure rates of the system's components are constants. We used three different methods to improve the system given. Two reliability characteristics (the mean time to failure and the reliability function) are used to perform the system improvement. For this purpose, the reliability functions and the mean times to failures of the original and improved systems are obtained. The results given in this paper generalize the results given in the literatures by setting n = 1, 2. An illustrative numerical example is presented to compare the different reliability factors obtained.

In this paper, we consider a periodic preventive maintenance policy in which each preventive maintenance reduces the hazard rate of amount proportional to the failure intensity, which increases since the system started to operate. And the effect of preventive maintenance at each preventive maintenance epoch is different. The expected cost rate per unit time for the proposed model is obtained. We discuss the optimal number N of the periodic preventive maintenance and the optimal period x, which minimize the expected cost rate per unit time and obtain the optimal preventive maintenance schedule for given cost structures of the model. A numerical example is given for the purpose of illustrating our results when the failure time distribution is Weibull distribution.