Maria E. Calzada

THE ROBUSTNESS OF THE SYNTHETIC CONTROL CHART TO NON-NORMALITY

The Synthetic control chart has recently been introduced as an improvement over the standard Shewhart control chart for detecting changes in the mean of a normally distributed process. The salient features of the Shewhart chart and the Conforming Run Length chart are integrated to produce the Synthetic control chart. In many practical instances, the Synthetic chart is superior to the Shewhart chart in terms of quicker detection of out-of-control status when the process data are normally distributed. The robustness of the Synthetic chart to violations of the normality assumption is the central theme of this study. We find that in-control average run lengths for the Synthetic chart are reasonably close to the normal theory values when there is moderate nonnormality or when the sample size n is large. Additionally, out-of-control average run lengths are comparable to the corresponding normal theory values for a variety of non-normal distributions.

The Generalized Synthetic Chart

Abstract The Generalized Synthetic chart is presented and mathematical expressions for its average run length and variance of the run length are developed. The methodology is applied to the EWMA and CUSUM charts and near-optimization procedures are discussed. The synthetic EWMA and CUSUM charts are compared with their standard counterparts, the original synthetic chart, and the Shewhart chart. Significant improvements in detecting power are reported.

A Note on the Lower-Sided Synthetic Chart for Exponentials

The synthetic control chart for exponential data is discussed and an expression is derived for its average run length, as well as its design parameters. The synthetic control chart for exponentials is shown analytically to be a two-in-a-row rule. This chart is compared with the Shewhart chart for individuals and with the worst-case, lower-sided exponential EWMA and CUSUM charts. While the synthetic control chart for exponentials outperforms the Shewhart chart for individuals, the EWMA and CUSUM charts are shown to be far superior in detecting decreases in the exponential mean.

Pulsed quantum cascade laser-based CRDS substance detection: real-time detection of TNT

This paper presents experimental results from a pulsed quantum cascade laser based cavity ringdown spectrometer used as a high-throughput detection system. The results were obtained from an optical cavity with 99.8% input and output coupling mirrors that was rapidly swept (0.2s to 7s sweep times) between 1582.25 cm(-1) (6.3201μm) and 1697.00 cm(-1) (5.8928μm). The spectrometer was able to monitor gas species over the pressure range 585 torr to 1μtorr, and the analysis involves a new digital data processing system that optimises the processing speed and minimises the data storage requirements. In this approach we show that is it not necessary to make direct measurements of the ringdown time of the cavity to obtain the system dynamics. Furthermore, we show that correct data processing is crucial for the ultimate implementation of a wideband IR spectrometer that covers a range similar to that of commercial Fourier transform infrared instruments.

The Synthetic t and Synthetic EWMA t Charts

Abstract The t and the exponentially weighted moving average (EWMA) t charts were introduced in quality control literature for cases when users are not able to accurately estimate the process standard deviation. In this paper we present the synthetic versions of the t and the EWMA-1 charts, and determine near-optimized control limits for these charts. The new charts are shown to have improved performance properties over the original t and EWMA-t charts, while maintaining the desirable feature that the process standard deviation does not need to be estimated.

Reconciling the Integral Equation and Markov Chain Approaches for Computing EWMA Average Run Lengths

Abstract The integral equation and Markov chain approaches for computing average run lengths for two-sided exponentially weighted moving average control charts are studied. For the integral equation approach, the choice of numerical method can greatly ease the burden of computation. Gaussian quadrature is recommended when the underlying process data arise from a distribution whose support is the entire real line; however, the Collocation method is to be preferred when the support is finite or semi-infinite. Results for EWMA average run length calculations are given for process data following normal, gamma, t, and uniform distributions. Ultimately, the Markov chain approach is shown to be equivalent to a special case of the integral equation method.

Frequency domain analysis for laser-locked cavity ringdown spectroscopy

In this paper we report on the development of a Fourier-transform based signal processing method for laser-locked Continuous Wave Cavity Ringdown Spectroscopy (CWCRDS). Rather than analysing single ringdowns, as is the norm in traditional methods, we amplitude modulate the incident light, and analyse the entire waveform output of the optical cavity; our method has more in common with Cavity Attenuated Phase Shift Spectroscopy than with traditional data analysis methods. We have compared our method to Levenburg-Marquardt non linear least squares fitting, and have found that, for signals with a noise level typical of that from a locked CWCRDS instrument, our method has a comparable accuracy and comparable or higher precision. Moreover, the analysis time is approximately 500 times faster (normalised to the same number of time domain points). Our method allows us to analyse any number of periods of the ringdown waveform at once: this allows the method to be optimised for speed and precision for a given spectrometer.

Joint Monitoring of the Mean and Variance of Combined Control Charts with Estimated Parameters

Joint , two-sided (CUSUM, S2), and (EWMA, S2) control charts are numerically compared when (i) process parameters are known and (ii) process parameters are estimated from retrospective data. In both cases, equations for the conditional and unconditional run length distributions are developed, and expressions for the average run lengths (ARL), the second moment of the run length (SMRL), and the standard deviation of the run lengths (SDRL) are derived for these charts. In-control and out-of-control ARLs and SDRLs are tabulated and compared for a variety of design parameters for each chart. Numerical results and practical recommendations are given.

Real-time FPGA data collection of pulsed-laser cavity ringdown signals

This paper presents results from a pulsed-laser cavity ring-down spectrometer with novel field programable gate array real-time data collection. We show both theoretically and experimentally that the data extraction can be achieved from a single cavity ringdown event, and that the absorbance can be determined without the need to fit the ringdown time explicitly. This methodology could potentially provide data acquisition rate up to 1 MHz, with the accuracy and precision comparable to nonlinear least squares fitting algorithms.

Computing Average Run Lengths for the MaxEWMA Chart

Abstract The MaxEWMA chart has recently been introduced as an alternative to control charting procedures that are designed to jointly detect changes in the mean and standard deviation of a normally distributed process. Here, a method for computing both in-control and out-of-control average run lengths for purposes of effectively designing this chart is offered. Design strategies are considered, numerical results to aid the design effort are given, and examples are discussed.