Dependent Process Steps Research Articles

Using Adaptive Scheme to Monitoring Dependent Steps with Attributes Data

The article considers the dependent process steps with attributes data. We explore the monitoring of the dependent process steps with attributes data by using two designed variable sample size and sampling interval cause selecting control charts, and then evaluate their performance by the adjusted average time to signal. Numerical example and simulation study illustrated that the proposed VSSI charts have better performance than the fixed parameters control charts. The proposed VSSI cause selecting charts are thus recommended.

Dynamic scheduling of maintenance measures in complex production systems

In complex production systems, involving multiple, mutually dependent process steps, the unplanned failure of even a single machine can have significant consequences (e.g. loss of production) for upstream and downstream process steps and equipment. In order to detect maintenance needs before the machine components fail, condition monitoring systems are increasingly applied in practice.However, the main requirement for short-term scheduling of planned maintenance measures is to predict the impact of the ensuing downtime of the machine on the productivity of the whole production system. This is hardly possible for the production planner due to the dynamic and stochastic interactions (e.g. variation of buffer levels over time) of production processes. As a consequence, high production and maintenance costs tend to occur.Hence, a model-based planning approach which enables the dynamic short-term scheduling of planned maintenance measures has been developed. Instead of focusing separately on production and maintenance, this integrated approach allows a forecasting of the most cost-effective period of necessary maintenance measures for machines which are part of a complex production system. In contrast to existing, static approaches which fail at accurately representing the dynamic of production states and information, this approach aims to determine the various failure-related costs and to evaluate the impact of the maintenance measures on the production processes by means of event-driven simulation. The prediction accuracy is ensured by integrating the dynamic and stochastic correlations characteristic of real production systems into the simulation model.A concluding evaluation of the approach based on real application scenarios of an industrial company illustrates the need for a dynamic planning to lastingly reduce the production and maintenance costs of production systems compared to a purely static evaluation and planning based on average values (e.g. for transport time).

Monitoring Two Dependent Process Steps Using Special Variable Sample Sizes and Sampling Intervals Cause‐Selecting Control Charts

Cause‐selecting control charts are effective statistical process control tools for monitoring multistage processes. In this article, an adaptive statistical process control scheme to monitor a process with two dependent steps is proposed. Two different policies based on a combination of two different sample sizes and sampling intervals are utilized. Adjusted average time to signal measure, calculated through Markov chain approach, is applied to evaluate performance of the proposed control scheme. Numerical results indicate that the proposed scheme has improved performance over the fixed sample sizes at fixed sampling intervals scheme. Finally, the optimal parameters of the proposed scheme with two different policies are recommended, and comparisons between the minimum adjusted average time to signal of the proposed charts and variable sample sizes and sampling intervals cause‐selecting control charts with three different sample sizes and sampling intervals are performed. It is shown that performance of the proposed scheme with four variable parameters is similar and even somewhat better than that of the scheme with six variable parameters. Copyright © 2011 John Wiley & Sons, Ltd.

Monitoring and diagnosing dependent process steps using VSI control charts

The paper proposes the variables sampling interval (VSI) scheme to monitor the means and the variances in two dependent process steps. The performance of the considered VSI control charts is measured by the adjusted average time to signal derived by a Markov chain approach. An example of the process control for the metallic film thickness of the computer connectors system shows the application and performance of the proposed VSI control charts in detecting shifts. Furthermore, the performance of the VSI control charts and the fixed sampling interval control charts are compared via the numerical analysis results. These demonstrate that the former is much faster in detecting shifts. Whenever quality engineers cannot specify the values of variable sampling intervals, the optimal VSI control charts are recommended. Furthermore, the impacts of misusing Shewhart charts to monitoring the process mean and variance in the second process step are also investigated.

Process control using VSI cause selecting control charts

The article considers the variable process control scheme for two dependent process steps with incorrect adjustment. Incorrect adjustment of a process may result in shifts in process mean, process variance, or both, ultimately affecting the quality of products. We construct the variable sampling interval (VSI) $${Z_{\overline{X}}-Z_{S_X^2}}$$ and $${Z_{\bar{{e}}}-Z_{S_e^2}}$$ control charts to effectively monitor the quality variable produced by the first process step with incorrect adjustment and the quality variable produced by the second process step with incorrect adjustment, respectively. The performance of the proposed VSI control charts is measured by the adjusted average time to signal derived using a Markov chain approach. An example of the cotton yarn producing system shows the application and performance of the proposed joint VSI $${Z_{\overline{X}} -Z_{S_X^2 }}$$ and $${Z_{\bar{{e}}} -Z_{S_e^2 }}$$ control charts in detecting shifts in mean and variance for the two dependent process steps with incorrect adjustment. Furthermore, the performance of the VSI $${Z_{\overline{X}}-Z_{S_X^2 }}$$ and $${Z_{\bar{{e}}} -Z_{S_e^2 }}$$ control charts and the fixed sampling interval $${Z_{\overline{X}} -Z_{S_X^2 }}$$ and $${Z_{\bar{{e}}} -Z_{S_e^2 }}$$ control charts are compared by numerical analysis results. These demonstrate that the former is much faster in detecting small and median shifts in mean and variance. When quality engineers cannot specify the values of variable sampling intervals, the optimum VSI $${Z_{\overline{X}}-Z_{S_X^2 }}$$ and $${Z_{\bar{{e}}} -Z_{S_e^2 }}$$ control charts are also proposed by using the Quasi-Newton optimization technique.

Monitoring dependent process steps using robust cause‐selecting control charts

AbstractCause‐selecting control charts are believed to be invaluable for monitoring and diagnosing multistage processes where the output quality of some stages is significantly impacted by the output quality of preceding stages. To establish a relationship between input and output variables, a standard procedure uses historical data, which are often prone to hold outliers. The presence of outliers tends to decrease the effectiveness of monitoring procedures because the regression model is distorted and the control limits become stretched. To dampen the negative repercussions of outliers, robust fitting techniques based on M‐estimators are implemented instead of the ordinary least‐squares method and two robust monitoring approaches are presented. An example is given to illustrate the application and performance of the proposed control charts. Furthermore, a simulation‐based study is included to investigate and compare the average run length of robust and non‐robust schemes. The results reveal that the robust procedure far outperforms the non‐robust counterpart due to its prompt detection of out‐of‐control conditions when outliers exist. Copyright © 2009 John Wiley & Sons, Ltd.

Controlling over-adjusted process means and variances using VSI cause selecting control charts

Process adjusted unnecessarily is a common problem in statistical process control. Incorrect adjustment of a process may result in shifts in process mean, process variance, or both, ultimately affecting the quality of products. The article considers the variable process control scheme for two dependent process steps with incorrect adjustment. We construct the variable sampling interval (VSI) Z X ¯ - Z S 2 and Z e ¯ - Z S e 2 control charts in order to effectively monitor the quality variable produced by the first process step with incorrect adjustment and the quality variable produced by the second process step with incorrect adjustment, respectively. The performance of the proposed VSI control charts is measured by the adjusted average time to signal (AATS) derived using a Markov chain approach. An example of process control for automobile braking system shows the application and performance of the proposed joint VSI Z X ¯ - Z S 2 and Z e ¯ - Z S e 2 control charts in detecting small and median shifts in mean and variance for the two dependent process steps with incorrect adjustment. The performance of the VSI Z X ¯ - Z S 2 and Z e ¯ - Z S e 2 control charts and the fixed sampling interval (FSI) Z X ¯ - Z S 2 and Z e ¯ - Z S e 2 control charts are compared via the numerical analysis results. These demonstrate that the former is much faster in detecting shifts in mean and variance. Whenever quality engineers cannot specify the values of variable sampling intervals, the optimal VSI Z X ¯ - Z S 2 and Z e ¯ - Z S e 2 control charts are suggested. Furthermore, the impacts of misusing Z Y ¯ - Z S y 2 charts to monitoring the process mean and variance in the second step are also investigated.

Using VSI EWMA charts to monitor dependent process steps with incorrect adjustment

The article considers the variable process control scheme for two dependent process steps with incorrect adjustment. Incorrect adjustment of a process may result in shifts in process mean, ultimately affecting the quality of products. We construct variable sampling interval (VSI) EWMAZX and EWMAZe control charts to effectively monitor the quality variable produced by the first process step with incorrect adjustment and the quality variable produced by the second process step with incorrect adjustment. The performance of the proposed VSI control charts is measured by the adjusted average time to signal (AATS) derived using a Markov chain approach. An example of the automobile braking system with incorrect adjustment shows the application and performance of the proposed VSI EWMAZX and EWMAZe control charts in detecting shifts in process mean. Furthermore, the performance of the proposed VSI EWMAZX and EWMAZe control charts and the fixed sampling interval (FSI) EWMAZX and EWMAZe control charts are compared by numerical analysis results. These demonstrate that the former is much faster in detecting small and median shifts in mean. The optimum VSI EWMAZX and EWMAZe control charts are also proposed using optimization technique to minimize AATS when quality engineers cannot specify the values of variable sampling intervals. It has been found that the optimum VSI EWMAZX and EWMAZe control charts always work better than the VSI EWMAZX and EWMAZe control charts.

Effects of Measurement Error on Controlling Two Dependent Process Steps

Imprecise measurements may seriously affect the efficiency of process control and production cost. For two dependent processes, the in-coming quality variable in the first process may influence the out-going quality variable in the second process. To effectively monitor and distinguish the state of the two dependent process steps with imprecise measurements, the EWMA control chart and cause-selecting control chart are constructed by taking account of the measurement errors. The EWMA control chart for imprecise measurements is constructed to monitor small shifts in the process mean on the first step, and the cause-selecting control chart for imprecise measurements, is constructed to monitor small shifts in the process mean in the second step. The effects of imprecise measurements on the performance of the two proposed control charts are examined for the case, where the mean of each process may be changed by the occurrence of a special cause. The performance of the proposed control charts is measured by the average run length. A sensitivity analysis indicates that a larger variation of imprecise measurements leads to a larger average run length for the out-of-control process and a larger average loss.

Adaptive control schemes for two dependent process steps

The article considers the statistical adaptive process control for two dependent process steps. We construct adaptive sample size and sampling interval (ASSI) Z X ¯ and Z e ¯ control charts to monitor the quality variables produced by the first process step and the second process step at the end of the second process step and effectively distinguish which process step is out-of-control. The performance of the proposed ASSI control charts is measured by adjusted average time to signal (AATS) using Markov chain approach. An example of automobile braking system shows the application and performance of the proposed ASSI Z X ¯ and Z e ¯ control charts in detecting shifts in process mean. Furthermore, the performance of the ASSI Z X ¯ and Z e ¯ control charts and the nonadaptive sample size and sampling interval Z X ¯ and Z e ¯ control charts are compared by some numerical analysis results. It demonstrates that the former is much faster than the latter in detecting small shifts in mean.

Controlling‐dependent process steps using variable sample size control charts

AbstractThe article considers the variable process control scheme for two dependent process steps. We construct variable sample size (VSS) ZX̄ and Zē control charts to effectively monitor the quality variable produced by the first process step and the quality variable produced by the second process step 2, respectively. The performance of the proposed VSS control charts is measured by the adjusted average time to signal (AATS) using a Markov chain approach. An example of producing cotton yarn system shows the application and performance of the proposed VSS ZX̄ and Zē control charts in detecting shifts in process mean. Furthermore, the performance of the VSS ZX̄ and Zē control charts and the fixed sample size (FSS) ZX̄ and Zē control charts are compared by numerical analysis results. These demonstrate that the former is much faster in detecting small shifts in mean. Copyright © 2006 John Wiley & Sons, Ltd.

Adaptive sampling interval cause-selecting control charts

This article considers the statistical adaptive process control for two dependent process steps. We construct an adaptive sampling interval Z X control chart to monitor the quality variable produced by the first process step, and use the adaptive sampling interval Z e control chart to monitor the specific quality variable produced by the second process step. By using the proposed adaptive sampling interval control charts, we can quickly detect and distinguish which process step is out of control. The performance of the proposed adaptive sampling interval control charts is measured by the adjusted average time to signal (AATS), which was derived by a Markov chain approach, for an out-of-control process. An empirical automobile braking system example shows the application and the performance of the proposed adaptive sampling control charts in detecting shifts in process means. Some numerical results obtained demonstrated that the performance of the proposed adaptive sampling cause-selecting control charts outperforms the fixed sampling interval cause-selecting control charts.

Optimal control policy for dependent process steps with over-adjusted means and variances

Over-adjustment to processes may result in shifts in process mean and variance, ultimately affecting the quality of products. An economic adjustment model is developed for the joint design of X-S2 control charts and ē-Se2 cause-selecting control charts to control both means and variances of two dependent process steps using the Markov chain approach. The objective is to determine the optimal control policy of the proposed control charts, which effectively detect and distinguish the shifts of means and variances on the dependent process steps and minimize the total quality control cost. Application of the proposed control charts is illustrated through a numerical example.

An approach to controlling two dependent process steps with autocorrelated observations

The observations from the process output are always assumed independent when using a control chart to monitor a process. However, for many processes the process observations are autocorrelated. This autocorrelation can have a significant effect on the performance of the control chart. This paper considers the problem of monitoring the mean of a quality characteristic X on the first process step and the mean of a quality characteristic Y on the second process step, in which the observations X can be modeled as an AR(1) model and observations Y can be modeled as a transfer function of X since the state of the second process step is dependent on the state of the first process step. To effectively distinguish and maintain the state of the two dependent process steps, the Shewhart control chart of residual and the cause-selecting control chart are proposed. The proposed control charts’ performance is measured by the rate of alarm on the proposed charts. From numerical analysis, it shows that the performance of the proposed control charts is much better than the misused Hotelling T2 control chart and the individual Shewhart X and Y control charts.

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.