A natural multivariate extension of the two-sided cumulative sum chart is proposed via projection pursuit. A modification is given for improving its performance for the special situation in which the process mean is already shifted at the time the charting begins. Simulation studies show that the new charts have slightly better performance than the competing charts (MC1, MEWMA1 and MEWMA2) in t...

Nonparametric control charts do not require knowledge about the shape of the underlying distribution and can thus be attractive in certain situations. Two new Shewharttype nonparametric control charts are proposed for monitoring the unknown location parameter of a continuous population in Phase II (prospective) applications. The charts are based on control limits given by two specified order st...

The control chart based on geometric distribution (geometric chart) has been shown to be competitive to por npcharts for monitoring proportion nonconforming, especially for applications in high quality manufacturing environment. However, implementing a geometric chart often assumes the process parameter to be known or accurately estimated. For a high quality process, an accurate parameter estim...

A simple algorithm is introduced for computing the run length distribution of a monitoring scheme combining a Shewhart chart with an Exponentially Weighted Moving Average control chart. The algorithm is based on the numerical approximation of the integral equations and integral recurrence relations related to the run-length distribution. In particular, a modified Clenshaw-Curtis quadrature rule...

In this article, we introduce a method for monitoring the Weibull shape parameter β with type II (failure) censored data. The control limits depend on the sample size, the number of censored observations, the target average run length, and the stable value of β. The method assumes that the scale parameter α is constant during each sampling period, which is true under rational subgrouping. The p...

Designs of the double sampling (DS) X chart are traditionally based on the average run length (ARL) criterion. However, the shape of the run length distribution changes with the process mean shifts, ranging from highly skewed when the process is in-control to almost symmetric when the mean shift is large. Therefore, we show that the ARL is a complicated performance measure and that the median r...

We prove a number of results on the structure and enumeration of palindromes and antipalindromes. In particular, we study conjugates of palindromes, palindromic pairs, rich words, and the counterparts of these notions for antipalindromes.