A review of statistical process control techniques for short run manufacturing systems

Because manufacturing lot sizes continue to shrink, statistical process control methods for short production runs are increasingly important. We review and comment on the assumptions, advantages and disadvantages of alternatives, Traditional methods well as more recent developments are described and contrasted.     

Modified S-charts for controlling process variability

To help in the detection of variance increases and decreases, three modified versions of traditional Shewhart S-charts are evaluated in terms of their average run length values. One scheme uses control limits based on equal tail chi-square distribution probabilities. The second uses control limits based on unequal tail probabilities. The third uses warning limits based on equal tail probabilities, but requires two successive points beyond the warning limit to give an out-of-control signal. They all result in better average run length values than the traditional S-chart. Also, if the only concern is the detection of variance increases, then both S-charts and warning limit charts without lower control limits are shown to have better average run length values than those of the traditional charts.     

A new synthetic control chart for monitoring process mean using auxiliary information

ABSTRACT

Quality control charts have been widely recognized as a potentially powerful statistical process monitoring tool in statistical process control because of their superior ability in detecting shifts in the process parameters. Recently, auxiliary-information-based control charts have been proposed and shown to have excellent speed in detecting process shifts than those based without it. In this paper, we design a new synthetic control chart that is based on a statistic that utilizes information from both the study and auxiliary variables. The proposed synthetic chart encompasses the classical synthetic chart. The construction, optimal design, run length profiles, and the performance evaluation of the new chart are discussed in detail. It turns out that the proposed synthetic chart performs uniformly better than the classical synthetic chart when detecting different kinds of shifts in the process mean under both zero-state and steady-state run length performances. Moreover, with reasonable assumptions, the proposed chart also surpasses the exponentially weighted moving average control chart. An application with a simulated data set is also presented to explain the implementation of the proposed control chart.     

Statistical control charts for monitoring the mean of a stationary process

Recently statistical process control (SPC) methodologies have been developed to accommodate autocorrelated data. A primary method to deal with autocorrelated data is the use of residual charts. Although this methodology has the advantage that it can be applied to any autocorrelated data it needs time series modeling efforts. In addition for a X residual chart the detection capability is sometimes small compared to the X chart and EWMA chart. Zhang (1998) proposed the EWMAST chart which is constructed by charting the EWMA statistic for stationary processes to monitor the process mean. The performance of the EWMAST chart the X chart the X residual chart and other charts were compared in Zhang (1998). In this paper comparisons are made among the EWMAST chart the CUSUM residual chart and EWMA residual chart as well as the X residual chart and X chart via the average run length.     

A weighted likelihood ratio test-based chart for monitoring process mean and variability

In this paper, a new single exponentially weighted moving average (EWMA) control chart based on the weighted likelihood ratio test, referred to as the WLRT chart, is proposed for the problem of monitoring the mean and variance of a normally distributed process variable. It is easy to design, fast to compute, and quite effective for diverse cases including the detection of the decrease in variability and individual observation case. The optimal parameters that can be used as a design aid in selecting specific parameter values based on the average run length (ARL) and the sample size are provided. The in-control (IC) and out-of-control (OC) performance properties of the new chart are compared with some other existing EWMA-type charts. Our simulation results show that the IC run length distribution of the proposed chart is similar to that of a geometric distribution, and it provides quite a robust and satisfactory overall performance for detecting a wide range of shifts in the process mean and/or variability.     

Average run lengths for cusum control charts applied to residuals

A common approach to building control charts for autocorrelated data is to apply classical SPC to the residuals from a time series model of the process. However, Shewhart charts and even CUSUM charts are less sensitive to small shifts in the process mean when applied to residuals than when applied to independent data. Using an approximate analytical model, we show that the average run length of a CUSUM chart for residuals can be reduced substantially by modifying traditional chart design guidelines to account for the degree of autocorrelation in the data.     

New cumulative sum control charts for monitoring process variability

In this article, we propose new cumulative sum (CUSUM) control charts using the ordered ranked set sampling (RSS) and ordered double RSS schemes, with the perfect and imperfect rankings, for monitoring the variability of a normally distributed process. The run length characteristics of the proposed CUSUM charts are computed using the Monte Carlo simulations. The proposed CUSUM charts are compared in terms of the average and standard deviation of run lengths with their existing competitor CUSUM charts based on simple random sampling. It turns out that the proposed CUSUM charts with the perfect and imperfect rankings are more sensitive than the existing CUSUM charts based on the sample range and standard deviation. A similar trend is present when these CUSUM charts are compared with the fast initial response features. An example is also used to demonstrate the implementation and working of the proposed CUSUM charts.     

A new non-parametric multivariate EWMA sign control chart for monitoring process dispersion

In this paper, a new non-parametric multivariate exponentially weighted moving average (NMEWMA) sign chart is proposed for monitoring the process dispersion. The run length characteristics of the NMEWMA sign chart are computed with the help of Markov chain and Monte Carlo simulations. Moreover, the NMEWMA sign chart is also used to detect changes in the process mean and dispersion simultaneously. An illustrative example is also used to explain the implementation of proposed control chart.     

A synthetic control chart for monitoring the small shifts in a process mean based on an attribute inspection

Abstract

In this paper, a synthetic control chart is proposed by integrating the salient features of the np_x chart and the CRL chart. The synthetic chart achieves higher detection effectiveness on both small and large mean shifts while retaining the operational simplicity of the attribute charts owing to only using attribute inspection. Both statistical and economic design of the synthetic chart are considered and numerical tests have indicated that the synthetic chart has a higher power for detecting mean shifts than the np_x chart, MON chart and CUSUM chart. In addition, sensitivity analyses are also performed under both the statistical and economic design model.     

Performance of the zone control chart

Average run lengths of the zone control chart are presented, The performance of this chart is compared with that of several Shewhart charts with and without runs rules, It is shown that the standard zone control chart has performance similar to some even simpler charts and a much higher false alarm rate than the Shewhart chart with all of the common runs rules. It is also shown that a slightly modified zone control chart outperforms the Shewhart chart with the common runs rules.     

A new nonparametric synthetic EWMA control chart for monitoring process mean

The exponentially weighted moving average (EWMA) control charts are widely used in chemical and process industries because of their excellent speed in catching small to moderate shifts in the process target. In usual practice, many data come from a process where the monitoring statistic is non-normally distributed or it follows an unknown probability distribution. This necessitates the use of distribution-free/nonparametric control charts for monitoring the deviations from the process target. In this paper, we integrate the existing EWMA sign chart with the conforming run length chart to propose a new synthetic EWMA (SynEWMA) sign chart for monitoring the process mean. The SynEWMA sign chart encompasses the synthetic sign and EWMA sign charts. Monte Carlo simulations are used to compute the run length profiles of the SynEWMA sign chart. Based on a comprehensive comparison, it turns out that the SynEWMA sign chart is able to perform substantially better than the existing EWMA sign chart. Both real and simulated data sets are used to explain the working and implementation of existing and proposed control charts.     

Short run spc based upon the second order dynamic linear model for trend detection

Recently, several new applications of control chart procedures for short production runs have been introduced. Bothe (1989) and Burr (1989) proposed the use of control chart statistics which are obtained by scaling the quality characteristic by target values or process estimates of a location and scale parameter. The performance of these control charts can be significantly affected by the use of incorrect scaling parameters, resulting in either an excessive "false alarm rate," or insensitivity to the detection of moderate shifts in the process. To correct for these deficiencies, Quesenberry (1990, 1991) has developed the Q-Chart which is formed from running process estimates of the sample mean and variance. For the case where both the process mean and variance are unknown, the Q-chaxt statistic is formed from the standard inverse Z-transformation of a t-statistic. Q-charts do not perform correctly, however, in the presence of special cause disturbances at process startup. This has recently been supported by results published by Del Castillo and Montgomery (1992), who recommend the use of an alternative control chart procedure which is based upon a first-order adaptive Kalman filter model Consistent with the recommendations by Castillo and Montgomery, we propose an alternative short run control chart procedure which is based upon the second order dynamic linear model (DLM). The control chart is shown to be useful for the early detection of unwanted process trends. Model and control chart parameters are updated sequentially in a Bayesian estimation framework, providing the greatest degree of flexibility in the level of prior information which is incorporated into the model. The result is a weighted moving average control chart statistic which can be used to provide running estimates of process capability. The average run length performance of the control chart is compared to the optimal performance of the exponentially weighted moving average (EWMA) chart, as reported by Gan (1991). Using a simulation approach, the second order DLM control chart is shown to provide better overall performance than the EWMA for short production run applications     

Interpreting out-of-control signals using instance-based bayesian classifier in multivariate statistical process control

In this article, an instance-based naive Bayes (INB) method is proposed to interpret out-of-control signals. By training one for one classifier, this method considers the similar features between test instance and training instances. For three benchmark examples with small number of variables, the experimental results show that INB outperforms all techniques in overall average performance; in cases of more than two variables, INB performs better in most scenarios. For two examples with large number of variables, the experimental results show that INB can be applied to practical problems. This research indicates that INB is very encouraging for interpreting the out-of-control signals in multivariate statistical process control.     

A rational sequential probability ratio test control chart for monitoring process shifts in mean and variance

The sequential probability ratio test (SPRT) chart is a very effective tool for monitoring manufacturing processes. This paper proposes a rational SPRT chart to monitor both process mean and variance. This SPRT chart determines the sampling interval d based on the rational subgroup concept according to the process conditions and administrative considerations. Since the rational subgrouping is widely adopted in the design and implementation of control charts, the studies of the rational SPRT have a practical significance. The rational SPRT chart is designed optimally in order to minimize the index average extra quadratic loss for the best overall performance. A systematic performance study has also been conducted. From an overall viewpoint, the rational SPRT chart is more effective than the cumulative sum chart by more than 63%. Furthermore, this article provides a design table, which contains the optimal values of the parameters of the rational SPRT charts for different specifications. This will greatly facilitate the potential users to select an appropriate SPRT chart for their applications. The users can also justify the application of the rational SPRT chart according to the achievable enhancement in detection effectiveness.     

The computation of average run length and average time to signal: an overview

Control charts are widely used in industries to monitor a process for quality improvement. Evaluation of the average run length (ARL) or average time to signal (ATS) plays an important role in the design of control charts and performance comparison. In this paper, we review several basic and popular procedures, including the Markov chain and integral equation methods for computing ARL, ATS and associated run length distributions for cumulative sum charts, exponentially weighted moving average charts and combined control charts, respectively. Some important references and key formulations are provided for practitioners.     

A new adaptive EWMA control chart using auxiliary information for monitoring the process mean

The adaptive memory-type control charts, including the adaptive exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, have gained considerable attention because of their excellent speed in providing overall good detection over a range of mean shift sizes. In this paper, we propose a new adaptive EWMA (AEWMA) chart using the auxiliary information for efficiently monitoring the infrequent changes in the process mean. The idea is to first estimate the unknown process mean shift using an auxiliary information based mean estimator, and then adaptively update the smoothing constant of the EWMA chart. Using extensive Monte Carlo simulations, the run length profiles of the AEWMA chart are computed and explored. The AEWMA chart is compared with the existing control charts, including the classical EWMA, CUSUM, synthetic EWMA and synthetic CUSUM charts, in terms of the run length characteristics. It turns out that the AEWMA chart performs uniformly better than these control charts when detecting a range of mean shift sizes. An illustrative example is also presented to demonstrate the working and implementation of the proposed and existing control charts.     

Improving the performance of the zone control chart

A general model for the zone control chart is presented. Using this model, it is shown that there are score vectors for zone control charts which result in superior average run length performance in comparison to Shewhart charts with common runs rules.

A fast initial response (FIR) feature for the zone control chart is also proposed. Average run lengths of the zone control chart with this feature are calculated. It is shown that the FIR feature improves zone control chart performance by providing significantly earlier signals when the process is out of control.     

Moving range EWMA control charts for monitoring the Weibull shape parameter

In this article, we propose an exponentially weighted moving average (EWMA) control chart for the shape parameter β of Weibull processes. The chart is based on a moving range when a single measurement is taken per sampling period. We consider both one-sided (lower-sided and upper-sided) and two-sided control charts. We perform simulations to estimate control limits that achieve a specified average run length (ARL) when the process is in control. The control limits we derive are ARL unbiased in that they result in ARL that is shorter than the stable-process ARL when β has shifted. We also perform simulations to determine Phase I sample size requirements if control limits are based on an estimate of β. We compare the ARL performance of the proposed chart to that of the moving range chart proposed in the literature.     

New tests for stochastic order with application to case control studies

It is shown that if a binary regression function is increasing then retrospective sampling induces a stochastic ordering of the covariate distributions among the responders, which we call cases, and the non-responders, which we call controls. We also show that if the covariate distributions are stochastically ordered then the regression function must be increasing. This means that testing whether the regression function is monotone is equivalent to testing whether the covariate distributions are stochastically ordered. Capitalizing on these new probabilistic observations we proceed to develop two new non-parametric tests for stochastic order. The new tests are based on either the maximally selected, or integrated, chi-bar statistic of order one. The tests are easy to compute and interpret and their large sampling distributions are easily found. Numerical comparisons show that they compare favorably with existing methods in both small and large samples. We emphasize that the new tests are applicable to any testing problem involving two stochastically ordered distributions.