Xiaolong Pu

Mixed Variables-Attributes Test Plans for Single and Double Acceptance Sampling under Exponential Distribution

The mixed variables-attributes test plans for single acceptance sampling are proposed to protect “good lots” from attributes aspect and to optimize sample sizes from variables aspect. For the single and double mixed plans, exact formulas of the operating characteristic and average sample number are developed for the exponential distribution. Numerical illustrations show that the mixed sampling plans have some advantages over the variables plans or attributes plans alone.

Adaptive charting schemes based on double sequential probability ratio tests

Sequential probability ratio test (SPRT) control charts are shown to be able to detect most shifts in the mean or proportion substantially faster than conventional charts such as CUSUM charts. However, they are limited in applications because of the absence of the upper bound on the sample size and possibly large sample numbers during implementation. The double SPRT (2-SPRT) control chart, which applies a 2-SPRT at each sampling point, is proposed in this paper to solve some of the limitations of SPRT charts. Approximate performance measures of the 2-SPRT control chart are obtained by the backward method with the Gaussian quadrature in a computer program. On the basis of two industrial examples and simulation comparisons, we conclude that the 2-SPRT chart is competitive in that it is more sensitive and economical for small shifts and has advantages in administration because of fixed sampling points and a proper upper bound on the sample size. Copyright

On the Performance of Two-sided Control Charts for Short Production Runs

In this paper, statistical performance measures for short-run production are summarized and proposed. Evaluation and computation based on these performance measures were developed for the two-sided Shewhart, cumulative sum, and exponentially weighted moving average control charts. Applying these measures, we provided numerical illustrations to compare the efficiency of the three charts and the corresponding Q charts in the cases of known and unknown nominal values of process parameters. Copyright

A robust self-starting spatial rank multivariate EWMA chart based on forward variable selection

A robust self-starting control chart based on forward variable selection is proposed.The proposed chart does not need prior knowledge of the IC distribution and is robust to non-normally distributed data.The need to gather extensive data before monitoring is overcome.The sensitivity to small and moderate sparse shifts in mean vectors is remarkable. Shifts in one or a few components of process mean vectors, called sparse shifts, are monitored in many applications. To monitor sparse shifts, several control charts have recently been proposed based on the variable selection technique. These charts assume either that the in-control (IC) distribution is completely known or that a sufficiently large reference dataset is available. However, this assumption is not always valid in practice. This paper develops a self-starting control chart that integrates a multivariate spatial rank test with the EWMA charting scheme based on forward variable selection for monitoring sparse mean shifts. Both the theoretical and numerical results show that the proposed chart is robust to non-normally distributed data, fast to compute, easy to construct, and can efficiently detect sparse shifts, especially when the process distribution is heavy-tailed or skewed. The proposed control chart does not need prior knowledge of the IC distribution and can start monitoring even before considerable reference data have been collected. A real-data example from a white wine production process illustrates the effectiveness of the proposed control chart.

Hypothesis Designs for Three-Hypothesis Test Problems

As a helpful guide for applications, the alternative hypotheses of the three-hypothesis test problems are designed under the required error probabilities and average sample number in this paper. The asymptotic formulas and the proposed numerical quadrature formulas are adopted, respectively, to obtain the hypothesis designs and the corresponding sequential test schemes under the Koopman-Darmois distributions. The example of the normal mean test shows that our methods are quite efficient and satisfactory for practical uses.

A Robust Multivariate EWMA Control Chart for Detecting Sparse Mean Shifts

In multivariate statistical process control (MSPC) applications, process mean shifts sometimes occur in only a few components. To solve this MSPC problem, many control charts were proposed in the literature. Most of these charts assumed that the multivariate quality characteristics are normally distributed. Among them, the control chart proposed by Zou and Qiu (2009), incorporating the least absolute shrinkage and selection operator (LASSO) method into the EWMA scheme, has the best overall performance. In this paper, we extend the classical multivariate LASSO control chart to a robust version that has an affine-invariance property and is distribution free under the family of elliptical direction distributions, indicating that the in-control run-length distribution is the same for any continuous distribution in this family and the control limit can be acquired from the multivariate standard normal distribution. Our simulation results show that the proposed method is very efficient in detecting various sparse shifts under heavy-tailed and skewed multivariate distributions. In addition, it is easy to implement with an iterative algorithm and the least angle regression (LARS) algorithm. White-wine data illustrates that the proposed control chart performs quite well in applications.

A New EWMA Chart Based on Weighted Loss Function for Monitoring the Process Mean and Variance

With the weighted loss function, a new single Exponential Weighted Moving Average (EWMA) chart (WLE chart hereafter for short) is proposed to detect both mean and variance shifts simultaneously. It includes the EWMA control chart based on the semicircle statistic and weighted-loss-function control chart as special cases. Numerical studies show that the WLE chart is superior to the weighted-loss-function Cumulative Sum (CUSUM) chart when the mean and standard deviation shifts are both small, and offers at least comparable detection ability with the WLC chart in other cases. Compared with the Shiryaev–Roberts chart, the WLE chart has a better or comparable performance except for small and moderate mean shifts. Furthermore, an equivalent form of the WLE chart is developed to diagnose the source and direction of a process change. Copyright

A Method for Designing Three-Hypothesis Test Problems and Sequential Schemes

In applications, a two-sided hypothesis test problem sometimes needs to be changed to a three-hypothesis one with the two alternative hypotheses properly selected. In this article, we obtain the hypothesis design and the three-hypothesis sequential test scheme under the Koopman–Darmois distribution by solving a system of equations that meet requirements on the error rates and average sample number. This method provides a useful guide for practitioners to design hypotheses in multihypothesis test problems with controlled error rates and sampling cost. Formulas of the schemes error rates and average sample number are obtained using numerical quadrature for the discrete-time situation.

Monitoring individuals with irregular semiparametric longitudinal behaviour

In our daily life, identifying individuals whose longitudinal behaviour differs from the behaviour of those well-functioning individuals is often necessary to avoid some unpleasant consequences. For such purposes, this paper proposes a new charting scheme called semiparametric screening system in cases when the longitudinal behaviour is semiparametric, using SPC and longitudinal data analysis techniques. Various cases, including those with equally spaced data points, unequally spaced data points, temporal correlated data, non-normal data, are discussed by simulations. Also our proposed method is demonstrated using two real data examples about the SHARe Framingham Heart Study of the National Heart, Lung and Blood Institute, and the moisture content of cut tobacco at the outlet collected in Shanghai tobacco group co., LTD of China, respectively. All the numerical results show that the proposed method works well in practice.

A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions

Abstract Most existing control charts monitoring the covariance matrix of multiple variables were restricted to multivariate normal distribution. When the process distribution is non-normal, the performance of these control charts could potentially be (highly) affected, especially for heavy-tail distributions. To construct a robust multivariate control chart for monitoring the covariance matrix, we applied spatial sign covariance matrix and maximum norm to the exponentially weighted moving average (EWMA) scheme and proposed a Phase II control chart. The novel chart is distribution-free under the family of elliptical directions distributions. Comparison studies demonstrate that the novel method is very powerful in detecting various shifts, especially for heavy-tailed distributions. The implementation of the proposed control chart is demonstrated by a white wine data.