The performance of attributes control charts (such as c and np charts) is usually evaluated under the assumption of known process parameters (i.e., the nominal proportion of nonconforming units or the nominal number of nonconformities). However, in practice, these process parameters are rarely known and have to be estimated from an in-control phase I data set. In this paper, we derive the run l...

The exponentially weighted moving average (EWMA) X chart is effective in detecting small shifts. However, the EWMA X chart is not robust enough to prevent errors in estimating the process standard deviation or a changing standard deviation. To overcome this problem, Zhang et al. suggested the EWMA t chart in 2009. The existing optimal design of the EWMA t chart is based on the average run lengt...

A Bayesian wavelet estimation method for estimating parameters of a stationary I(d) process is represented as an useful alternative to the existing frequentist wavelet estimation methods. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations. The sampling from the posterior distribution is through the Markov Chain Monte Carlo (MCMC) easily implemented in the W...

this paper presents a discrete-time single-server finite buffer n threshold policy queue with renewal input and discretemarkovian service process. the server terminates service whenever the system becomes empty, and recommencesservice as soon as the number of waiting customers in the queue is n. we obtain the system-length distributionsat pre-arrival and arbitrary epochs using the supplementary...

In this paper, we follow the model of interpurchase times to achieve heterogeneity across customers. We employ a mixture model to segment customers into three states: super-active, active and inactive. The interpurchase model and mixture model are solved by the hierarchical Bayes via Markov Chain Monte Carlo method. We employ CUSUM chart based on the density of active state to monitor consumer ...

Algorithms are presented that allow the calculation of the probability of a set of sequences related by a binary tree that have evolved according to the Thorne-Kishino-Felsenstein model for a fixed set of parameters. The algorithms are based on a Markov chain generating sequences and their alignment at nodes in a tree. Depending on whether the complete realization of this Markov chain is decomp...

Methods using regeneration have been used to draw approximations to the stationary distribution of Markov Chain Monte Carlo processes. We introduce an algorithm that allows exact sampling of the stationary distribution through the use of a regeneration method and a Bernoulli Factory to select samples within each regeneration cycle that are shown to be from the desired density. We demonstrate th...

We investigate the validity of a Markov approach for the motility of kinesin. We show in detail how the various mechanochemical states and reaction rates that are experimentally measured, can be used to create a Markov-chain model. We compare the performance of this model to motility data and we find global similarities in the load and ATP-concentration dependency of speed and mean run length. ...

A fundamental algorithm for selecting ranks from a finite subset of an ordered set is Radix Selection. This algorithm requires the data to be given as strings of symbols over an ordered alphabet, e.g., binary expansions of real numbers. Its complexity is measured by the number of symbols that have to be read. In this paper the model of independent data identically generated from a Markov chain ...