Qin Su

Robust algorithms for economic designing of a nonparametric control chart for abrupt shift in location

The existing statistical process control procedures typically rely on the fundamental assumption of a parametric distribution of the quality characteristic. However, when there is a lack of knowledge about the underlying distribution (as full knowledge is not available in practice), the performance of these parametric charts is very likely to be heavily degraded. Motivated by this problem, a one-sided nonparametric monitoring procedure using the single sample sign statistic is proposed for detecting a shift in the location parameter of a continuous distribution. An economic model of the control chart is developed to optimize the sample size, sampling interval, and control limits. Three data-dependent estimation approaches for the unknown parameter are evaluated and discussed. Simulation results exhibit that our proposed procedure generally performs well under a great variety of continuous distributions and hence it is recommended as an alternative scheme especially when the knowledge of the underlying distribution is imperfect. Furthermore, beneficial recommendations of estimation approach selection are provided for practical implementation of the control chart.

Design and Implementation of Two CUSUM Schemes for Simultaneously Monitoring the Process Mean and Variance with Unknown Parameters

Designing joint monitoring schemes for the mean and variance of a Gaussian process (normal distribution) using a single combined statistic instead of the traditional approach of using two separate statistics has gained many attention in recent years. Most of the existing one-chart schemes, however, assume that the true process parameters (standards) are known which is usually not practical and will lead to problems because of improper choices of statistic and control limits. In this paper, we propose two CUSUM control schemes that instinctively work well for the joint monitoring in the case of the unknown parameters by correcting the influence of the reference sample on the plotting statistic. We provide the control limits of the proposed control charts for practical implementation and also offer follow-up procedures for post-signal detection of the nature of shifts. We carry out a comprehensive simulation study to examine the performance of the schemes. When the true population parameters are unknown, we observe clear and distinct performance advantages of the proposed schemes. The empirical design issues regarding the optimal choice of the reference value of the proposed CUSUM schemes are systematically investigated. We provide beneficial recommendations for the practitioners. We also provide an example to illustrate the practical relevance of the proposed schemes. Copyright

Optimal design of a distribution-free quality control scheme for cost-efficient monitoring of unknown location

Traditionally, a cost-efficient control chart for monitoring product quality characteristic is designed using prior knowledge regarding the process distribution. In practice, however, the functional form of the underlying process distribution is rarely known a priori. Therefore, the nonparametric (distribution-free) charts have gained more attention in the recent years. These nonparametric schemes are statistically designed either with a fixed in-control average run length or a fixed false alarm rate. Robust and cost-efficient designs of nonparametric control charts especially when the true process location parameter is unknown are not adequately addressed in literature. For this purpose, we develop an economically designed nonparametric control chart for monitoring unknown location parameter. This work is based on the Wilcoxon rank sum (hereafter WRS) statistic. Some exact and approximate procedures for evaluation of the optimal design parameters are extensively discussed. Simulation results show that overall performance of the exact procedure based on bootstrapping is highly encouraging and robust for various continuous distributions. An approximate and simplified procedure may be used in some situations. We offer some illustration and concluding remarks.

An economically designed Sequential Probability Ratio Test control chart for short-run production

We propose an economic model for the SPRT chart in short-run production.A simple algorithm is proposed for the model.It is worth designing an SPRT scheme specifically for short-run production only if the out-of-control probability is relatively large.In some cases, it is possible that no process control may be the most economical policy. This paper proposes an economic model for the design of an SPRT (Sequential Probability Ratio Test) chart for monitoring the process mean in short-run production. The model expresses the short-run cost per unit of operating the SPRT chart as a function of the cost parameters associated with the operation. A simple algorithm capable of optimizing the charting parameters is also proposed. The model can be used to quantify cost reductions achievable by substituting a traditional control policy by SPRT control. Numerical examples illustrate the effectiveness of the proposed procedure. It is shown that the resulting cost reduction can range from modest to substantial as the out-of-control probability of the process increases.

A univariate procedure for monitoring location and dispersion with ordered categorical data

ABSTRACT The quality characteristic is usually measured by ordered attribute levels, such as good, general, and poor, which describe different magnitudes of the characteristic. The ordinal levels are determined by a continuous latent variable, the shifts of which are reflected by the observed counts in each level. This article devises a control procedure based on the discrepancy between observed average cumulative counts and their expected ones. Simulation results are shown to demonstrate its superior sensitivity in simultaneously detecting location and dispersion shifts of the latent variable. Flexibility in assigning the weight for each level can allow the chart to be more powerful.

Multivariate Ordinal Categorical Process Control Based on Log-Linear Modeling

In many applications, the quality of products or services tends to be measured by multiple categorical characteristics, each of which is classified into attribute levels such as good, marginal, and bad. Here there is usually natural order among these attribute levels. However, traditional monitoring techniques ignore such order among them. By assuming that each ordinal categorical quality characteristic is determined by a latent continuous variable, this paper incorporates the ordinal information into an extended log-linear model and proposes a multivariate ordinal categorical control chart based on a generalized likelihood-ratio test. The proposed chart is efficient in detecting location shifts and dependence shifts in the corresponding latent continuous variables of ordinal categorical characteristics based on merely the attribute-level counts of the ordinal characteristics.

Economic modelling for statistical process control subject to a general quality deterioration

The applications of control chart have traditionally focused on the detection of step shifts in process mean. However, changes are usually gradual, not as perfect step shifts. The common consideration of a shift as a step function does not always adequately describe what actually happens in practice. Hence, there is a need for more realistic assumptions to be incorporated. This paper employs a Markov chain approach and provides a way to quantitatively measure the economic performance of control charts in the presence of a more general quality deterioration mechanism. The finite production run is considered in the model as it has become a very important production mode at present and the process failure mechanism is described by geometric distribution. The chart properties, particularly on the issues of the quality deterioration mechanism, are investigated. The findings provide critical insights on the use of step shift assumption when designing control charts.

Economic Design of a Nonparametric Control Chart for Shift in Location

Most economically designed control charts rely on the assumption of normality or some specific process distribution. However, when identifying a specific distribution is not possible or unlikely (as full knowledge is not available in practice), the economic effectiveness of conventional charts is very likely to be heavily discounted. In this paper, we first consider an economic model based on the Duncan-type cost function for designing a nonparametric sign chart for monitoring the location parameter of a univariate process. Numerical results show that the proposed design performs well for various continuous distributions.

A multivariate sign chart for monitoring dependence among mixed-type data

Abstract Statistical process control (SPC) has been widely utilised for quality improvement and surveillance in industrial engineering. Modern industrial applications have witnessed more and more mixed-type quality characteristics such as those consisting of ordinal categorical and continuous ones. However, traditional charting techniques consider the dependence in either categorical or continuous data and hardly combine the two in quality control. Under the assumption that the ordinal attribute levels of a factor are determined by a latent continuous variable, there exists an order among categorical observations of this factor, which is similar to that among continuous observations. Then mixed-type observations can be transformed into a unified framework of standardized ranks, based on directions of which with respect to their centre parameter, the spatial-sign covariance matrix can be calculated for statistical surveillance of cross-dependence among mixed-type factors. The affine invariant property of consequent charting statistic helps improve the efficiency of detecting dependence shifts in mixed-type data. Simulation results demonstrate the superiority of proposed control chart and an additive manufacturing (3D printing) example shows that it can perform excellently well in practice.