The Poisson distribution assumption often arises in several industrial applications for modeling defects or nonconformities. In this work, we investigate the one- and two-sided performance of a new adaptive EWMA (exponentially weighted moving average)-type chart monitoring count data. An appropriate discrete-state Markov chain technique is provided to compute exact ARL (average run length) prop...

Given a sequence of letters generated independently from a finite alphabet, we consider the case when more than one, but not all, letters are generated with the highest probability. The length of the longest run of any of these letters is shown to be one greater than the length of the longest run in a particular state of an associated Markov chain. Using results of Foulser and Karlin (19...

Mukherjee and Chakraborti 1 proposed a single distribution-free (nonparametric) Shewhart-type chart based on the Lepage 2 statistic for simultaneously monitoring both the location and the scale parameters of a continuous distribution when both of these parameters are unknown. In the present work, we consider a single distribution-free CUSUM chart, based on the Lepage 2 statistic, referred to as...

We study asymptotic properties (as A →∞) of the first exit time from the interval [0, A] of a non-negative Harris-recurrent Markov process. It is shown that under certain fairly general conditions the limiting distribution of the suitably normalized first exit time is exponential E(1) and that the moment generating function converges to that of E(1). The method of proof is based on considering ...

Abstract: In this paper, we present a performance analysis of a system with two multiplexers in tandem. Each multiplexer is fed by an external arrival process that consists of the superposition of the traffic generated by independent binary Markov sources. Further, the output of the first multiplexer is fed into the second multiplexer according to an independent Bernoulli process. The probabili...

The global navigation satellite system (GNSS), as a high-time resolution and high-precision measurement technology, has been widely used in the field of deformation monitoring. Owing to influence uncontrollable factors, there are inevitably some abnormal data GNSS monitoring series. Thus, it is necessary detect identify series improve accuracy reliability disaster law analysis warning. Many met...

For many years, copolymerization has been studied using mathematical and statistical models. Here, we present new Markov chain models for copolymerization kinetics: the Bernoulli and Geometric models. They model copolymer synthesis as a random process and are based on a basic reaction scheme. In contrast to previous Markov chain approaches to copolymerization, both models take variable chain le...