Su-Fen Yang

A new nonparametric EWMA Sign Control Chart

Research highlights? A new EWMA Sign Chart is proposed for detecting deviation from the process target. ? It is suitable for data came from a process with a non-normal distribution. ? The properties of the EWMA statistics are examined. Example shows that the EWMA chart had better performance compared to Shewhart chart. Many data in practice came from a population/process with a non-normal or often unknown distribution, hence the commonly-used Shewhart control chart, which requires normality of the monitoring statistics, is not suitable. In this paper, a new nonparametric EWMA Sign Control Chart is proposed for monitoring and detecting possible deviation from the process target. The sampling properties of the new monitoring statistics are examined and the average run lengths of the proposed chart are derived for evaluating its performance. An example is used to illustrate the proposed chart and compare with other existing charts, assuming normality. Furthermore, an arcsine transformed EWMA Sign Chart is examined and proposed. The average run lengths of the Arcsine EWMA Chart are more reasonable than those of the EWMA Sign Chart. The Arcsine EWMA Sign Chart is recommended if we were concerned with the proper values of the average run length.

A new non‐parametric CUSUM mean chart

Not all data in practice came from a process with normal distribution. When the process distribution is non-normal or unknown, the commonly used Shewhart control charts are not suitable. In this paper, a new non-parametric CUSUM Mean Chart is proposed to monitor the possible small mean shifts in the process. The sampling properties of the new monitoring statistics are examined and the average run lengths of the proposed chart are examined. Two numerical examples are used to illustrate the proposed chart and compare with the two existing charts, assuming normality and Beta distribution, respectively. The CUSUM Mean Chart showed better detection ability than those two charts in monitoring and detecting small process mean shifts. Copyright

Using cause selecting control charts to monitor dependent process stages with attributes data

In this study, we propose cause selecting control charts to monitor two dependent process stages with attributes data. The control limits on the bivariate binomial control region can be obtained. The detection ability of the cause selecting control charts is compared to those of Shewhart attributes control charts and the bivariate binomial control region by different correlation. Numerical example and simulation study show that the cause selecting control charts perform better than Shewhart attributes control charts and the bivariate binomial control region.

A framework for nonparametric profile monitoring

Control charts have been widely used for monitoring the functional relationship between a response variable and some explanatory variable(s) (called profile) in various industrial applications. In this article, we propose an easy-to-implement framework for monitoring nonparametric profiles in both Phase I and Phase II of a control chart scheme. The proposed framework includes the following steps: (i) data cleaning; (ii) fitting B-spline models; (iii) resampling for dependent data using block bootstrap method; (iv) constructing the confidence band based on bootstrap curve depths; and (v) monitoring profiles online based on curve matching. It should be noted that, the proposed method does not require any structural assumptions on the data and, it can appropriately accommodate the dependence structure of the within-profile observations. We illustrate and evaluate our proposed framework by using a real data set.

The economic design of control charts when there are dependent process steps

Proposes a renewal theory approach to derive the cost model for two dependent processes. Thus, constructs the economic individual X chart and cause‐selecting chart to monitor the two processes. They may be used to maintain the process with minimum cost and effectively distinguish which component of the processes is out of control. The optimal design parameters of these control charts can be determined by minimizing the cost model using a simple grid search method. Gives an example to illustrate the design procedure and application of the economic individual X chart and cause‐selecting chart.

Economic statistical design for and S2 control charts: A markov chain approach

Over-adjustment to a process may result in shifts in process mean, process variance, or both, ultimately affecting the quality of products. A statistically constrained model is developed for the joint economic statistical design of and S2 control charts to control both process mean and variance. The objective is to determine the design parameters of the control charts, which minimize the total quality control cost. A Markov chain approach is used to derive the model. Application of the model is demonstrated through a numerical example.

Economic statistical process control for over‐adjusted process mean

An economic adjustment model of a process whose quality can be affected by multiple special causes, resulting in changes of the process mean by incorrect adjustment of the process when it is operating according to its capability. A statistically constrained adjustment model is developed for the economic statistical design of X¯ control chart to control the process mean affected by multiple special causes. The objective is to determine the design parameters of the X¯ control chart, which minimize the total quality control cost. A Markov chain approach is used to derive the model. It is demonstrated that the expressions for the expected cycle time and the expected cycle cost with multiple special causes are easier to obtain by the proposed approach than by extending or adopting that in Collani et al. Application of the model is demonstrated through a numerical example.

Economic statistical design of S control charts using Taguchi loss function

An economic statistical design approach takes statistical properties into account while designing control charts economically. It improves both statistical design and economic design. In this paper, we present a statistically constrained economic model for the optimal design of S control chart for controlling process variability. In the model, the process quality can be affected by an assignable cause resulting in a shift of the variance of the distribution of output when it is operating according to its capability. The parameters are obtained by minimizing a total cost function proposed by Lorenzen and Vance, which is embellished with Taguchi loss function, subject to additional statistical constraints on average run length or average time‐to‐signal (ATS). Sensitivity analysis of the minimum cost will be performed to depict the effect of the choice of ATS bounds.

A New Chart for Monitoring Service Process Mean

Control charts are demonstrated effective in monitoring not only manufacturing processes but also service processes. In service processes, many data came from a process with nonnormal distribution or unknown distribution. Hence, the commonly used Shewhart variable control charts are not suitable because they could not be properly constructed. In this article, we proposed a new mean chart on the basis of a simple statistic to monitor the shifts of the process mean. We explored the sampling properties of the new monitoring statistic and calculated the average run lengths of the proposed chart. Furthermore, an arcsine transformed exponentially weighted moving average chart was proposed because the average run lengths of this modified chart are more intuitive and reasonable than those of the mean chart. We would recommend the arcsine transformed exponentially weighted moving average chart if we were concerned with the proper values of the average run length. A numerical example of service times with skewed distribution from a service system of a bank branch in Taiwan is used to illustrate the proposed charts. Copyright

Multivariate extension to the economical design of control chart under Weibull shock model

This article is an extension of research conducted by Banerjee and Rahim in 1988. Their general approach is now applied to a multivariate control chart instead of a univariate control chart. A cost model for the economic-statistical design of a Hotelling T 2 control chart is derived to deal with situations involving a Weibull shock model with an increasing failure rate. Application of the proposed T 2 control chart design is demonstrated through a numerical example. A sensitivity analysis of the model is performed.