Early warning CUSUM plans for surveillance of negative binomial daily disease counts

Automated public health surveillance of disease counts for rapid outbreak, epidemic or bioterrorism detection using conventional control chart methods can be hampered by over-dispersion and background (‘in-control’) mean counts that vary over time. An adaptive cumulative sum (CUSUM) plan is developed for signalling unusually high incidence in prospectively monitored time series of over-dispersed daily disease counts with a non-homogeneous mean. Negative binomial transitional regression is used to prospectively model background counts and provide ‘one-step-ahead’ forecasts of the next day's count. A CUSUM plan then accumulates departures of observed counts from an offset (reference value) that is dynamically updated using the modelled forecasts. The CUSUM signals whenever the accumulated departures exceed a threshold. The amount of memory of past observations retained by the CUSUM plan is determined by the offset value; a smaller offset retains more memory and is efficient at detecting smaller shifts. Our approach optimises early outbreak detection by dynamically adjusting the offset value. We demonstrate the practical application of the ‘optimal’ CUSUM plans to daily counts of laboratory-notified influenza and Ross River virus diagnoses, with particular emphasis on the steady-state situation (i.e. changes that occur after the CUSUM statistic has run through several in-control counts).     

Minimum aberration blocking schemes for 128-run designs

Several criteria have been proposed for ranking blocked fractional factorial designs. For large fractional factorial designs, the most appropriate minimum aberration criterion was one proposed by Cheng and Wu (2002). We justify this assertion and propose a novel construction method to overcome the computational challenge encountered in large fractional factorial designs. Tables of minimum aberration blocked designs are presented for N=128 runs and n=8–64 factors.     

The influence of parameter estimation on the ARL of Shewhart type charts for time series

In this paper we discuss the behavior of the Shewhart residual chart and the modified Shewhart chart if the parameters of the underlying process are unknown and thus have to be estimated. We focus on the estimation of the variance. For AR models we also consider the estimation of the AR coefficients. The average run length (ARL) of the control chart with estimated parameters is compared with the ARL of the scheme for known parameters and with the ARL for independent variables. Additionally, we give recommendations on the choice of the estimators in the context of Shewhart control schemes.     

Evaluation of control charts under linear trend

The performance of several control charting schemes is studied when the process mean changes as a linear trend. The control charts considered include the Shewhart chart, the Shewhart chart supplemented with runs rules, the cumulative sum (CUSUM) chart, the exponentially weighted moving average (EWMA) chart, and a generalized control chart.     

Improving the performance of the zone control chart

A general model for the zone control chart is presented. Using this model, it is shown that there are score vectors for zone control charts which result in superior average run length performance in comparison to Shewhart charts with common runs rules.

A fast initial response (FIR) feature for the zone control chart is also proposed. Average run lengths of the zone control chart with this feature are calculated. It is shown that the FIR feature improves zone control chart performance by providing significantly earlier signals when the process is out of control.     

Asymptotics of the run lengths of two control charts

The CUSUM control chart proposed by Page is a widely used in monitoring the quality of manufacturing processes. The Shiryayev-Roberts (S-R) control chart due to Shiryayev (1963) and Roberts (1988) is one of its competitors, This paper is concerned with the distribution properties of the run lengths of these two control charts. In context of continuous time, we first give the expansions of the higher moments of these run lengths. Then, we show that the asymptotic distributions of these run lengths are either some exponential distributions, or the distribution of the suprema of a standard Brownian motion, or some normal distributions, according to whether the μ<δ/2,μ =δ/2 and μ>δ/2. Here δ is the reference value of the above charts. Some similar results are also obtained in the context of discrete time.     

A review of statistical process control techniques for short run manufacturing systems

Because manufacturing lot sizes continue to shrink, statistical process control methods for short production runs are increasingly important. We review and comment on the assumptions, advantages and disadvantages of alternatives, Traditional methods well as more recent developments are described and contrasted.     

DECOMPOSITIONS OF THE QUEUE LENGTH DISTRIBUTIONS IN THE MAP/G/1 QUEUE UNDER MULTIPLE AND SINGLE VACATIONS WITH N-POLICY

In this paper, we establish an explicit form of matrix decompositions for the queue length distributions of the MAP/G/1 queues under multiple and single vacations with N-policy. We show that the vector generating function Y (z) of the queue length at an arbitrary time and X (z) at departures are decomposed into Y (z) = p _idle (z)ζ _Y (z) and X (z) = p _idle (z)ζ _X (z) where p _idle (z) is the vector generating function of the queue length at an arbitrary epoch at which the server is not in service, and ζ _Y (z) and ζ _X (z) are unidentified matrix generating functions.     

BMAP/G/1 Queue Under D-Policy: Queue Length Analysis

ABSTRACT

We study the queue length distribution of a queueing system with BMAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths are derived and a numerical example is presented.     

Comments on the Mixture Detection Rule Used in SPC Control Charts

When calculating independently the false alarm rate of the eight usual runs rules used in SPC control chart, it appears that the proposed rule designed to detect mixture patterns corresponds to a Type-I error strongly lower than the seven other rules. This discrepancy is underlined and the mixture rule is showed to be useless both for in-control and out-of-control processes. Thus a modification of the mixture detection rule is proposed and the impact of this new mixture rule is then illustrated and discussed using Monte Carlo calculations.