Optimal design of the adaptive exponentially weighted moving average control chart over a range of mean shifts

The adaptive exponentially weighted moving average (AEWMA) control chart is a smooth combination of the Shewhart and exponentially weighted moving average (EWMA) control charts. This chart was proposed by Cappizzi and Masarotto (2003) to achieve a reasonable performance for both small and large shifts. Cappizzi and Masarotto (2003) used a pair of shifts in designing their control chart. In this study, however, the process mean shift is considered as a random variable with a certain probability distribution and the AEWMA control chart is optimized for a wide range of mean shifts according to that probability distribution and not just for a pair of shifts. Using the Markov chain technique, the results show that the new optimization design can improve the performance of the AEWMA control chart from an overall point of view relative to the various designs presented by Cappizzi and Masarotto (2003). Optimal design parameters that achieve the desired in-control average run length (ARL) are computed in several cases and formulas used to find approximately their values are given. Using these formulas, the practitioner can compute the optimal design parameters corresponding to any desired in-control ARL without the need to apply the optimization procedure. The results obtained by these formulas are very promising and would particularly facilitate the design of the AEWMA control chart for any in-control ARL value.     

Sums of weighted spacings and a test for the logistic distribution

A simple proof for a theorem of Csörgö and Révész (1981b and 1984) concerning sums of weighted spacings is given, The conditions of the theorem are relaxed. As an application, a goodness-of-fit test for the logistic distribution is proposed. The percentage points of the proposed test statistic are obtained by a simulation experiment.     

A Comparison of the Performance of Phase II Simple Linear Profile Control Charts when Parameters are Estimated

The standard deviation of the average run length (SDARL) is an important performance metric in studying the performance of control charts with estimated in-control parameters. Only a few studies in the literature, however, have considered this measure when evaluating control chart performance. The current study aims at comparing the in-control performance of three phase II simple linear profile monitoring approaches; namely, those of Kang and Albin (2000), Kim et al. (2003), and Mahmoud et al. (2010). The comparison is performed under the assumption of estimated parameters using the SDARL metric. In general, the simulation results of the current study show that the method of Kim et al. (2003) has better overall statistical performance than the competing methods in terms of SDARL values. Some of the recommended approaches based solely on the usual average run length properties can have poor SDARL performance.     

Comparing and testing order relations between percentile residual life functions

We consider the problem of comparing and testing order relations between percentile residual life functions. We introduce R-R plots and processes and develop a general approach for this problem.     

First order autoregressive time series with negative binomial and geometric marginals

In this paper we present first order autoregressive (AR(1)) time series with negative binomial and geometric marginals. These processes are the discrete analogues of the gamma and exponential processes introduced by Sim (1990). Many properties of the processes discussed here, such as autocorrelation, regression and joint distributions, are studied.     

An ANOVA-type test for multiple change points

We consider the problem of testing the null hypothesis of no change against the alternative of multiple change points in a series of independent observations. We propose an ANOVA-type test statistic and obtain its asymptotic null distribution. We also give approximations of its limiting critical values. We report the results of Monte Carlo studies conducted to compare the power of the proposed test against a number of its competitors. As illustrations we analyzed three real data sets.     

Quadratic nuisance-parameter-free goodness-of-fit tests in the presence of location and scale parameters

The asymptotic theory of a quadratic nuisance-parameter-free goodness-of-fit procedure is studied. The present techniques are applied in testing for the exponential, the logistic, the extreme value, and the Weibull distributions.     

Domestic Violence in the Second Half of Life

Providing an adequate and effective community response to women age 50 and older who experience domestic violence is complicated by the oftentimes disparate goals and expectations of service providers, emergency responders, and victims themselves. This article shares information provided by participants of focus groups designed to understand and identify what women age 50 and older want and need from agencies that provide services to enhance victim safety.