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The quality of a measurement or estimation procedure for the value of a parameter of interest refers to its reliability and its precision. The reliability of a measurement procedures is quantified in a straightforward way by the probability of the event of a correct measurement result. However, the quantification of the precision of a measurement procedure is not at all evident and the related problems are not satisfactorily solved so far. This paper presents and discusses several possibilities for a quantification of the measurement precision. Among others, a minmax-regret approach is introduced which takes into account the “unavoidable imprecision”. Realistically, it is assumed here that the parameter space is bounded. Moreover, it is shown how prior information can be utilized without applying the Bayesian way which considers the parameter of interest as a random variable. The theory is illustrated by the example of the measurement of the first moment of a normally distributed random variable.

In this paper some reliability concepts in the telescopic family of distributions are compared. The telescopic family is named after the telescopic series in mathematics and represents an interesting class of discrete life time distributions. The telescopic family is introduced and also some conditions being equivalent to the IFR property are presented.

In many practical situations, we observe that the residual life gets independent of age after some shift. For example, at the of operation the life time of a component cannot be described sufficiently well by an exponential distribution as many internal sources of failure are existing. However, once the component has reached, let us say, the full operative status after some time, the component enters a stable state without any essential internal failure modes. During this state the assumption of exponential distribution is justified. We extend the multivariate loss of memory property of Marshall-Olkin (Journal of the American Statistical Association 62: 30–44, 1967) by admitting some shift in the lifetimes of the components. Furthermore, we present four examples of bivariate exponential models that satisfy the here considered generalized loss of memory property.

We investigate historically troublesome threshold autoregressive (TAR) model specification in the context of epidemiologic surveillance with meta-models of log likelihood arising from reasonable combinations of TAR parameter values. In this research, a system for intelligently specifying TAR with influenza activity data has lead to a valuable new model-based chart: The threshold autoregressive individuals control (TARIC) chart.

In this paper, a group acceptance sampling plan is developed based on truncated lifetimes when the lifetime of an item follows a generalized exponential distribution. For a given group size, the minimum number of groups and the acceptance number required are determined for specified consumer's risk and the test termination time. The values of operating characteristic function for various quality levels are calculated and the minimum ratios of the true average life to the specified life at given producer's risk are obtained. The results are illustrated by an examples.

In this paper we introduce a new class of life distribution called the new better (worse) than used renewal failure rate at specified time t 0 NBURFR- t 0 (NWURFR- t 0 ). Some closure properties, such as closure under convolution, arbitrary and general mixture, and Shock model are discussed. Furthermore, a nonparametric test is proposed to test exponentiality against the NBURFR- t 0 class. The critical values, the powers and Pitman efficiencies are calculated for t 0 = 0 : 25.

System reliability is considered as an important performance index. Performance of engineering systems can be assessed by various techniques. The traditional analytical approach consists of developing a mathematical model that represents the system and to evaluate its reliability indices. There have been attempts in the literature to derive more realistic approaches for the reliability analysis of systems, for example, based on simulations. This paper proposes a hybrid approach called Markov System Dynamics (MSD) approach which combines the Markov approach with system dynamics simulation approach for performing a reliability analysis and for studying the dynamic behavior of systems. This approach will have the advantages of both the methodologies that of Markov processes as well as system dynamics. The proposed framework is illustrated by a numerical example for a single component system with increasing failure rates. The results of the simulation when compared with those obtained by the traditional Markov analysis clearly validate the Markov System Dynamics (MSD) approach as an alternative for reliability analysis.

A cumulative sum (CUSUM) control chart referred to as the SS-CUSUM chart is proposed that is capable of simultaneously detecting changes in both mean and standard deviation. The construction of this chart is based on the sum of squares of the maximum standard CUSUM statistics. The average run sengths (ARLs) are computed for comparison with other charts particularly with some recently developed single charts. The SS-CUSUM chart has an advantage over its competitors since it quickly detects both small and large shifts in the process parameters. The chart is also easy to implement and to interpret the given signals.

In this article following the approach of Lorenzen and Vance, an economic design of moving average control chart is developed for ceased as well for continued production during control actions. The performance of the control charts is compared for the two production modes by means of the loss cost per time unit. The ceased production mode yields about 30% saving in the loss cost when compared to that of the continued production. The example given provides some insight to the sensitivity of the model.

This paper deals with the estimation of reliability of either parallel or series systems with two components. We assume that the strengths of the components follow a bivariate Rayleigh distribution. The two components are subjected to either two independent stresses or a common stress which are (is) independent of the strengths of two components. We also assume that the stresses are Rayleigh distributed. Under these assumptions, the asymptotic distributions of the estimators are obtained and used for constructing asymptotic confidence intervals.