Usual Control Chart Research Articles

Shewhart-Type Charts for Masked Data: A Strategy for Handling the Privacy Issue

Data privacy is a serious issue and therefore needs our attention. In this study, we propose masking through randomized response techniques (RRTs) to ensure the privacy and thus to avoid falsification. We assume that the process characteristic is of sensitive nature, and due to privacy issue, the actual measurements cannot be shared with the monitoring team. In such situations, the producer is very likely to falsify the measurements. Consequently, the usual control charting techniques will mislead about the process status. We discuss different data masking strategies to be used with Shewhart-type control charts. The usual Shewhart-type control chart appears to be a subchart of the proposed charts. Average run length (ARL) is used as a performance measure of the study proposals. We have evaluated the performance of the proposed charts for different shift sizes and under different intensities of masking. We have also carried out a comparative analysis for various models under varying sensitivity parameters. We have also compared the performance of the proposals with the traditional Shewhart chart. It is observed that the B-L control chart under the RRT model performs better for smaller shifts and for larger shift sizes, the G-B chart under an unrelated question model tperforms better. A real-life application of the study proposal is also considered where monitoring of thickness of paint on refrigerators is of interest.

A control chart to monitor the process mean based on inspecting attributes using control limits of the traditional X-bar chart

ABSTRACTThis paper proposes a new control chart, denoted by , for evaluating the stability of a process mean, which is based on attribute inspection. In the control chart, the mean of the quality characteristic of interest is controlled by a go-no-go gauge device that generates five categorizations. In equally-spaced times, samples of n items are collected, their categories are determined, and random values are generated according to a truncated normal distribution that corresponds to their categories. With these random values, the averages are estimated and the control charts are built. Extensive computational experiments shown that the newly introduced control charts perform similarly to the usual control chart in terms of average run length, provided that the sample sizes are raised by approximately three additional sample units. Because the control charts use attributes, they can be considered a viable alternative to the traditional control chart.

Shewhart control chart for monitoring the mean of Poisson mixed integer autoregressive processes via Monte Carlo simulation

Most control charts for process monitoring assume independence among observations and that the nature of the characteristics of interest is continuous. However, these assumptions are often violated in practice, include industrial engineering applications. For integer-valued autocorrelated processes, usual control charts have a poor performance. Time-series modeling and modified control limits play a fundamental role in such circumstances. In this paper, we propose a Shewhart control chart for monitoring the mean when observations can be modeled as a first order Poisson mixed integer autoregressive model - POMINAR(1) process. The performance of the proposed approach is investigated based on in-control and out-of-control average run lengths (ARL0 and ARL1, respectively) in different scenarios. Both the determination of the control limits and the evaluation of the chart are done through computational studies using Monte Carlo simulations. Practical use of the proposed approach is illustrated with two real examples for monitoring crime data and network traffic.

Monitoring of serially correlated processes using residual control charts

Control charts act as the most important tool for monitoring of process parameters. The assumption of independence that underpins the implementation of the charts is violated when process observations are correlated. The e ect of this issue can lead to the malfunctioning of the usual control charts by causing a large number of false alarms or slowing the detection ability of the chart in unstable situations. In this paper, weinvestigated the performance of the Mixed EWMA-CUSUM and Mixed CUSUM-EWMA charts for the ecient monitoring of autocorrelated data. The charts are applied to the residuals obtained from tting an autoregressive (AR) model to the autocorrelated observations. The performance of these charts is compared with the performances of the residual Shewhart, EWMA, CUSUM, combined Shewhart-CUSUM, and combinedShewhart-EWMA charts. Performance criteria such as Average Run Length (ARL) and Extra Quadratic Loss (EQL) are used for the evaluation and comparison of the charts. Illustrative examples are presented to demonstrate the application of the charts to serially correlated observations

Shewhart and EWMA t control charts for short production runs

AbstractShort‐run productions are common in manufacturing environments like job shops, which are characterized by a high degree of flexibility and production variety. Owing to the limited number of possible inspections during a short run, often the Phase I control chart cannot be performed and correct estimates for the population mean and standard deviation are not available. Thus, the hypothesis of known in‐control population parameters cannot be assumed and the usual control chart statistics to monitor the sample mean are not applicable. t‐charts have been recently proposed in the literature to protect against errors in population standard deviation estimation due to the limitation of available sampling measures. In this paper the t‐charts are tested for implementation in short production runs to monitor the process mean and their statistical properties are evaluated. Statistical performance measures properly designed to test the chart sensitivity during short runs have been considered to compare the performance of Shewhart and EWMA t‐charts. Two initial setup conditions for the short run fixing the population mean exactly equal to the process target or, alternatively, introducing an initial setup error influencing the statistic distribution have been modelled. The numerical study considers several out‐of‐control process operating conditions including one‐step shifts for the population mean and/or standard deviation. The obtained results show that the t‐charts can be successfully implemented to monitor a short run. Finally, an illustrative example is presented to show the use of the investigated t charts. Copyright © 2010 John Wiley & Sons, Ltd.

Control charts for attributes with maxima nominated samples

We develop quality control charts for attributes using the maxima nomination sampling (MNS) method and compare them with the usual control charts based on simple random sampling (SRS) method, using average run length (ARL) performance, the required sample size in detecting quality improvement, and non-existence region for control limits. We study the effect of the sample size, the set size, and nonconformity proportion on the performance of MNS control charts using ARL curve. We show that MNS control chart can be used as a better benchmark for indicating quality improvement or quality deterioration relative to its SRS counterpart. We consider MNS charts from a cost perspective. We also develop MNS attribute control charts using randomized tests. A computer program is designed to determine the optimal control limits for an MNS p-chart such that, assuming known parameter values, the absolute deviation between the ARL and a specific nominal value is minimized. We provide good approximations for the optimal MNS control limits using regression analysis. Theoretical results are augmented with numerical evaluations. These show that MNS based control charts can yield substantial improvement over the usual control charts based on SRS.

Monitoring roundness profiles based on an unsupervised neural network algorithm

In modern manufacturing, approaches for profile monitoring can be adopted to detect unnatural behaviors of production processes, i.e. to signal when the relationship used to represent the profiles changes with time. Most of the literature concerned with profile monitoring deals with the problem of model identification and multivariate charting of parameters vector. In this paper, a different approach, which is based on an unsupervised neural network, is presented for profile monitoring. The neural network allows a computer to automatically learn from data the relationship to represent in-control profiles. Then, the algorithm may produce a signal when an input profile does not fit to the prototype learned from the in-control ones. The neural network does not require an analytical model for the statistical description of profiles faced (model-free approach). A comparison study is provided in this paper, in which the Phase II performance of the neural network is compared to that of approaches representative of the industrial practice. Performance is assessed by computer simulation, with reference to a case study related to profiles measured on machined items subject to geometrical specification (roundness). The results indicate that the neural network may outperform usual control charts in signaling out-of-control conditions, due to spindle-motion errors in several production scenarios. The proposed approach can be considered a valuable option for profile monitoring in industrial applications.

A robust alternative to Hotelling's T2 control chart using trimmed estimators

AbstractA control chart is one of the primary techniques used in statistical process control. In phase I, historical observations are analysed in order to construct a control chart with which to determine whether the process has been in control over the period of time in which the data were collected. The presence of multiple outliers may go undetected by the usual control charts, such as Hotelling's T2 due to the masking effect. In this paper we propose a robust alternative to Hotelling's T2 control chart with estimators defined using trimming. Simulation studies show that the proposed control chart is more effective than T2 in detecting outliers. Copyright © 2008 John Wiley & Sons, Ltd.

Monitoring Multivariate Process Variability for Individual Observations

Most of the existing control charts for monitoring multivariate process variability are based on subgroup sizes greater than one. In many practical applications, however, only individual observations are available and the usual control charts are not applicable in these cases. In this paper, two new control charts are proposed to monitor multivariate process variability for individual observations. The proposed control charts are constructed based on the traces of the estimated covariance matrices derived from the individual observations. When there is only one quality characteristic, these two charts respectively reduce to the exponentially weighted mean squared deviation and exponentially weighted moving variance charts. It is shown based on the simulation studies that the proposed charts are superior to the existing ones in detecting increases in variance and changes in correlation. An example from the semiconductor industry is also presented to illustrate the applicability of the proposed charts.

Statistical quality control based on ranked set sampling

Different quality control charts for the sample mean are developed using ranked set sampling (RSS), and two of its modifications, namely median ranked set sampling (MRSS) and extreme ranked set sampling (ERSS). These new charts are compared to the usual control charts based on simple random sampling (SRS) data. The charts based on RSS or one of its modifications are shown to have smaller average run length (ARL) than the classical chart when there is a sustained shift in the process mean. The MRSS and ERSS methods are compared with RSS and SRS data, it turns out that MRSS dominates all other methods in terms of the out-of-control ARL performance. Real data are collected using the RSS, MRSS, and ERSS in cases of perfect and imperfect ranking. These data sets are used to construct the corresponding control charts. These charts are compared to usual SRS chart. Throughout this study we are assuming that the underlying distribution is normal. A check of the normality for our example data set indicated that the normality assumption is reasonable.

A note on maximum Z-scores for control charts for individuals

Control chart limits are often constructed retrospectively based on a sequence of individual measurements. It is shown that the usual control chart limits cannot be crossed for small numbers of measurements.

Exact Statistical Tolerance Limits for Sample Variances

Exact statistical tolerance limits on the population of sample variances and standard dewtions arising from a normal (μ, σ2) distribution are derived. The use of tolerance limits on the variance or standard deviation is motivated by a number of applied problems which we describe. These tolerance limits are discussed in relation to the usual control chart limits.

Exact Statistical Tolerance Limits for Sample Variances

Exact statistical tolerance limits on the population of sample variances and standard dewtions arising from a normal (μ, σ2) distribution are derived. The use of tolerance limits on the variance or standard deviation is motivated by a number of applied problems which we describe. These tolerance limits are discussed in relation to the usual control chart limits.