Arden Miller

On Proper Choice of Variability Control Chart for Normal and Non-normal Processes

Control charts are an important statistical process control tool used to monitor changes in process location and variability. This study addresses issues regarding the proper choice of control chart for efficient monitoring of process variability. The choice of the best estimator to be used for variability charts has not been made clear in literature. We have analyzed the performance of eight control chart structures, based on different estimates of process standard deviation. The performance of control charts is investigated under the existence and violation of ideal assumptions of normality. Control chart constants and factors required for computing probability limits, considering normal and different non-normal parent distributions, are provided for all variability charts. This study aims at providing guidance to quality practitioners in choosing the appropriate variability control chart for normal and non-normal processes. Copyright

Using the Folded-Over 12-Run Plackett—Burman Design to Consider Interactions

This article demonstrates that the folded-over 12-run Plackett–Burman design is useful for considering up to 12 factors in 24 runs, even if one anticipates that some two-factor interactions may be significant. The properties of this design are investigated, and a sequential procedure for analyzing the data from such a design is proposed. The performance of the procedure is investigated through the analysis of real and constructed examples and through a small simulation study. Applications to other folded-over Plackett–Burman designs are also briefly discussed.

Strip-plot configurations of fractional factorials

Running industrial experiments in strip-plot configurations can be a useful method of reducing cost. This article presents an effective procedure for constructing strip-plot arrangements of fractional factorial designs that can be used for m-level or mixed-level designs. The procedure consists of three steps: (1) Identify a suitable row design, (2) identify a suitable column design, and (3) select a latin-square fraction of the product of the designs in (1) and (2). Several examples are used to demonstrate the procedure.

MDEWMA chart: an efficient and robust alternative to monitor process dispersion

Control chart is the most important statistical process control tool used to monitor changes in process location and dispersion. In this study, an EWMA control chart is proposed for efficient and robust monitoring of process dispersion. The proposed chart, namely the MDEWMA chart, is based on estimating the process standard deviation (σ) using the mean absolute deviations (MD), taken from the sample median. The performance of the proposed chart has been compared with the EWMASR chart (a dispersion EWMA chart based on sample range) and MD chart (a Shewhart-type dispersion chart based on MD), under the existence and violation of normality assumption. It has been observed that the proposed MDEWMA chart is more efficient and robust when compared with both EWMASR and MD charts in terms of run length (RL) characteristics such as average RL, median RL and standard deviation of the RL distribution.

Analysis of Parameter Design Experiments for Signal-Response Systems

Robust parameter design experiments for signal-response systems (Taguchis dynamic characteristics) have received an increasing amount of interest over the last few years. The development of methodology to analyze data from such experiments is still in the formative stages. This paper covers three approaches for analysis, including the use of Taguchis dynamic signal-to-noise ratio. A new graphical technique, the joint effects plot, is introduced, and its usefulness is demonstrated.

The rotating spot method of timing subjective events

The rotating spot method of timing subjective events involves the subjects watching a rotating spot on a computer and reporting the position of the spot at the instant when the subjective event of interest occurs. We conducted an experiment to investigate factors that may impact on the results produced by this method, using the subjects perception of when they made a simple finger movement as the subjective event to be timed. Seven aspects of the rotating spot method were investigated, using a factorial experiment. Four of these aspects altered the physical characteristics of the computer generated spot or clock face and the remaining three altered the instructions given to the participant. We found compelling evidence that one factor, whether the subject was instructed to report the instant when the finger movement was initiated or the instant when it was completed, resulted in a systematic shift in the response. Evidence that three other factors affect the observed variability in the response was also found. In addition, we observed that there are substantial systematic differences in the responses made by different subjects. We discuss the implications of our findings and make recommendations about the optimal way of conducting future experiments using the rotating spot method. Our overall conclusion is that our results strongly validate the rotating spot method of timing at least the studied variety of subjective event.

Enhancing the performance of CUSUM scale chart

Control charts act as the most important statistical process monitoring tool, widely used for the purpose of identifying unusual variations in process parameters. Researchers have implemented different rules to increase the sensitivity of Shewhart, CUSUM and EWMA control charts for the detection of small shifts in process location. However, for the monitoring of process scale, the use of such rules has been limited to Shewhart charts. This study proposes the implementation of sensitizing rules in CUSUM scale charts to enhance their ability to detect smaller changes in process variability. The performance of the proposed schemes is evaluated and compared with the simple scale CUSUM scheme, the EWMS chart, the M-EWMS chart and the COMB chart, in terms of run length characteristics such as average run length (ARL) and standard deviation of the run length distribution (SDRL). Control chart coefficients to set the ARL at the desired level are also provided. Two numerical examples are given to illustrate the application of the proposed schemes on practical data sets.

Using Folded-Over Nonorthogonal Designs

This article demonstrates advantages of using nonorthogonal resolution IV designs for running small screening experiments when the primary goal is identification of important main effects (MEs) with a secondary goal of entertaining a small number of potentially important second-order interactions. This is accomplished by evaluating the structure and performance of designs obtained by folding over small efficient nonorthogonal resolution III designs and comparing them with more commonly used orthogonal resolution III designs of comparable size, such as fractional factorials and Plackett–Burman designs. The folded-over designs are available for a wider class of run sizes and perform as well as or better than resolution III competitors in selecting the correct model when a few active two-factor interactions are present and significantly outperform resolution III competitors in terms of correctly identifying MEs. A simple two-step procedure is proposed for analyzing data from such designs that separates the goals and is well suited for sorting through likely models quickly.

The Analysis of Unreplicated Factorial Experiments Using All Possible Comparisons

This article proposes a new procedure for analyzing small unreplicated factorial experiments. This procedure is based on using likelihood ratio tests to compare competing models. An easy method of implementing the procedure is presented and then demonstrated on a real set of data. Results of a simulation study are presented that indicate that the new procedure compares favorably with Lenths method. Tables of constants are supplied that allow the new procedure to be easily applied to the analysis of 8-run, 12-run, and 16-run experiments.

Nonparametric Progressive Mean Control Chart for Monitoring Process Target

Nonparametric control charts are widely used when the parametric distribution of the quality characteristic of interest is questionable. In this study, we proposed a nonparametric progressive mean control chart, namely the nonparametric progressive mean chart, for efficient detection of disturbances in process location or target. The proposed chart is compared with the recently proposed nonparametric exponentially weighted moving average and nonparametric cumulative sum charts using different run length characteristics such as the average run length, standard deviation of the run length, and the percentile points of the run length distribution. The comparisons revealed that the proposed chart outperformed recent nonparametric exponentially weighted moving average and nonparametric cumulative sum charts, in terms of detecting the shifts in process target. A real life example concerning the fill heights of soft drink beverage bottles is also provided to illustrate the application of the proposed nonparametric control chart. Copyright