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Control charts for monitoring the time between events can be applied in various areas. In this study, we focus on the exponential control chart and consider the phase II problem (when process parameters are known) as well as the phase I problem (when process parameters are unknown). An exponential chart designed with the conventional approach has the disadvantage that the Average Run Length (ARL) value may increase when the process deviates from the nominal state. An ARL-unbiased design approach is therefore proposed for both phase II and phase I exponential charts. A sequential sampling scheme is adopted for the phase I exponential chart. The proposed ARL-unbiased design approach has several advantages over the conventional one, as it provides a self-starting feature and can significantly improve the ARL performance. Specific guidelines are suggested regarding the time to stop updating the estimates of parameters and control limits based on the actual false alarm rate. The phase I exponential chart can be calibrated to a constant in-control ARL value for each successive event accumulated to date. Simulated and real data examples are given to demonstrate the use and efficiency of the proposed design approach., 1. Introduction Control charts based on monitoring the time between events have been studied and applied in various areas. Besides applications to traditional manufacturing processes (see Chan et al. (2000)), [...]

This paper considers software systems consisting of fault-tolerant components built from functionally equivalent but independently developed modules (versions) characterized by different reliability and execution times. The components are designed using either the N-version programming method or the recovery block scheme. In our general model, we also allow the number of versions that can run simultaneously to be limited because of hardware or computation time constraints. An analytical algorithm and a numerical procedure to evaluate system execution-time distributions are presented. This algorithm takes into account the positive correlation among failures in different versions by introducing common-cause failures (mutually exclusive and independent common causes are considered). Illustrative examples are presented., 1. Introduction The reliability and performance of computing systems can be improved by the incorporation of redundancy or fault tolerance into the system. Two of the best known fault-tolerant software [...]

An inspection scheme is an integral part of any maintenance policy and we usually have to determine the time points at which the system should be inspected to make sure that the system availability requirement is met satisfactorily. There are many optimal policies for the determination of inspection times. This paper deals with periodic inspection with the emphasis on meeting the availability requirement. Five models for assigning the inspection times are studied. For these models, limiting average availability, long-run inspection rate, instantaneous availability and instantaneous inspection rate, are all derived. The relationships among the models are also discussed. A numerical example is presented to illustrate the differences for the cases of steady-state availability and instantaneous availability., 1. Introduction Component failures are often observed through inspections as continuous observation may not always be possible. For periodic inspection, the system is tested or inspected after a certain period [...]

A goal attainment approach to optimize multiresponse systems is presented. This approach aims to identify the settings of control factors to minimize the overall weighted maximal distance measure with respect to individual response targets. Based on a nonlinear programming technique, a sequential quadratic programming algorithm, the method is proved to be robust and can achieve good performance for multiresponse optimization problems with multiple conflicting goals. Moreover, the optimization formulation may include some prior work as special cases by assigning proper response targets and weights. Fewer assumptions are needed when using the approach as compared to other techniques. Furthermore, the decision-maker's preference and the model's predictive ability can easily be incorporated into the weights' adjustment schemes with explicit physical interpretation. The proposed approach is investigated and compared with other techniques through various classical examples in the literature., 1. Introduction Response Surface Methodology (RSM) (Box and Draper, 1987; Khuri and Cornell, 1996; Myers and Montgomery, 2002) is increasingly being used in various industries (semiconductor, chemical, food industry, etc.) [...]

Parallel redundancy is a common approach to increase system reliability and mean time to failure. When studying systems with redundant components, it is usually assumed that the components are independent; however, this assumption is seldom valid in practice. In the case of dependent components, the effectiveness of adding a component may be quite different from the case of independent components. In this paper we investigate how the degree of correlation affects the increase in the mean lifetime for parallel redundancy when the two components are positively quadrant dependent. A number of bivariate distributions that can be used in the modeling of dependent components are compared. Various bounds are also derived. The results are useful in reliability analysis as well as for designers who are required to take into account the possible dependence among the components., Nomenclature [F.sub.X] = cumulative distribution function (cdf) of X; F = common cdf when X and Y are identically distributed; [F.sub.X](t) = 1 - [F.sub.X](t); [F.sub.X,Y](x,y) = P(X > x, [...]