Economic Control of Quality of Manufactured Product.

In this paper, improved Shewhart control charts based on hybrid adaptive and run rule schemes are introduced to enhance the statistical performances of the traditional static scheme, designed with consideration given to the fixed values of sample size, the width of the control limits and the sampling frequency. The proposed hybrid adaptive schemes consider both variable sampling interval and variable sample size combined with run rules. The objective of this research is to develop a statistical comparison between adaptive schemes, charts with run rules and hybrid adaptive schemes with run rules to help decision-makers in the selection of the best performing chart for an expected value of shift in the mean of a controlled parameter. An extensive set of numerical results is presented to test the effectiveness of the proposed models in detecting small and moderate shifts in the process mean. The optimal statistical designs of the charts are obtained through a heuristic algorithm, properly modified to cope with the problem.

Statistical design of variable sample size and sampling interval\(\bar X\)control charts with run rulescontrol charts with run rules

In this paper, improved Shewhart control charts based on hybrid adaptive and run rule schemes are introduced to enhance the statistical performances of the traditional static scheme, designed with consideration given to the fixed values of sample size, the width of the control limits and the sam- pling frequency. The proposed hybrid adaptive schemes consider both variable sampling interval and variable sample size com- bined with run rules. The objective of this research is to develop a statistical comparison between adaptive schemes, charts with run rules and hybrid adaptive schemes with run rules to help decision-makers in the selection of the best performing chart for an expected value of shift in the mean of a controlled parame- ter. An extensive set of numerical results is presented to test the effectiveness of the proposed models in detecting small and mod- erate shifts in the process mean. The optimal statistical designs of the charts are obtained through a heuristic algorithm, properly modified to cope with the problem. Keywords Adaptive schemes �9 Average time to signal �9 Control charts �9 Optimisation �9 Run rules

http://rd.springer.com/content/pdf/10.1007%2Fs00170-004-2444-5.pdf

Statistical design of variable sample size and sampling interval , control charts with run rules

Duncan's model is a well-known procedure to build a control chart with specific reference to the production process it has to be applied to. Although many papers report true applications proving the procedure's noteworthy economic advantages over control charts set purely on the basis of standard statistical criteria, this method is often perceived only as an academic exercise. Perhaps the greater barrier preventing its practical application stems from the difficulty in making cost items explicit. In this paper a sensitivity analysis is proposed for misspecification in the cost parameters for optimal solutions of Duncan's model. While similar contributions published in the literature perform sensitivity analyses with a one-factor-at-a-time scheme, the original contribution of this paper is represented by the focus given on interactions among changes in values of different cost parameters. The results obtained here denote that all factors significantly affect optimal solutions through quite complicated interactions. This should not, in our opinion, discourage the implementation of Duncan's model, pointing conversely to its robust versions, already available in the current literature. Copyright © 2009 John Wiley & Sons, Ltd.

http://paduaresearch.cab.unipd.it/7109/1/2007_17_20090507104200.pdf

Duncan's model for X̄‐control charts: sensitivity analysis to input parameters

The Hotelling’s T ^{2} control chart with variable parameters (VP T ^{2}) has been shown to have better statistical performance than other adaptive control schemes in detecting small to moderate process mean shifts. In this paper, we investigate the statistical performance of the VP T ^{2} control chart coupled with run rules.We consider two well-known run rules schemes. Statistical performance is evaluated by using a Markov chain modeling the random shock mechanism of the monitored process. The in-control time interval of the process is assumed to followan exponential distribution. A genetic algorithm has been designed to select the optimal chart design parameters. We provide an extensive numerical analysis indicating that the VP T ^{2} control chart with run rules outperforms other charts for small sizes of the mean shift expressed through the Mahalanobis distance.

The variable parameters T^{2} chart with run rules

Duncan's economic design of Shewhart's X¯-control chart has established its optimal design for monitoring a process. Recently, there has been a renewed interest in the use of supplementary runs rules to increase the sensitivity of the chart to small shifts. This paper presents: (1) a general version of Duncan's model in that AT&T rules 1 and 2 or AT&T rules 1, 2, and 3 are used, and (2) a flexible-zone methodology in that the zone widths are not fixed a priori but are determined by economic optimization on the basis of the particular situation at work. It is observed that the use of AT&T rules with economic design can result in substantial cost savings over Duncan's design for small shifts in the process average.

Behrooz Parkhideh

Papers

The economic design of a flexible zone X¯-chart with AT&T rules