Adaptive EWMA Control Charts with a Time Varying Smoothing Parameter

It is known that time-weighted charts like EWMA or CUSUM are designed to be optimal to detect a specific shift. If they are designed to detect, for instance, a very small shift, they can be inefficient to detect moderate or large shifts. In the literature, several alternatives have been proposed to circumvent this limitation, like the use of control charts with variable parameters or adaptive control charts. This paper has as main goal to propose some adaptive EWMA control charts (AEWMA) based on the assessment of a potential misadjustment, which is translated into a time-varying smoothing parameter. The resulting control charts can be seen as a smooth combination between Shewhart and EWMA control charts that can be efficient for a wide range of shifts. Markov chain procedures are established to analyze and design the proposed charts. Comparisons with other adaptive and traditional control charts show the advantages of the proposals.Acknowledgements: financial support from the Spanish Ministry of Education and Science, research project ECO2012-38442

Method of lines and runge-kutta method in solving partial differential equation for heat equation

Solving the differential equation for Newton’s cooling law mostly consists of several fragments formed during a long time to solve the equation. However, the stiff type problems seem cannot be solved efficiently via some of these methods. This research will try to overcome such problems and compare results from two classes of numerical methods for heat equation problems. The heat or diffusion equation, an example of parabolic equations, is classified into Partial Differential Equations. Two classes of numerical methods which are Method of Lines and Runge-Kutta will be performed and discussed. The development, analysis and implementation have been made using the Matlab language, which the graphs exhibited to highlight the accuracy and efficiency of the numerical methods. From the solution of the equations, it showed that better accuracy is achieved through the new combined method by Method of Lines and Runge-Kutta method

Economic Design of a Single CUSUM Chart with Combined One-sided Monitoring of Process Mean

A single, two-sided CUSUM chart utilizing continuously variable sampling intervals and continuously variable sample sizes monitors a process mean and is optimized through an economic design metric. The combined CUSUM statistic is capable of detecting positive and negative shifts simultaneously in one chart, which relies on consecutive indications of either an increase or decrease in mean. A family of polynomial shapes define the rate at which the minimum sample size/maximum sampling interval sweeps to the maximum sample size/minimum sampling interval as the combined CUSUM statistic approaches the boundary. All possible transition probabilities are derived and nine parameters are optimized by minimizing a long-run hourly cost function using 16 different scenarios, varying costs and times spent in/out of control

Optimal Designs Of The Double Sampling X Chart Based On Parameter Estimation

Control charts, viewed as the most powerful and simplest tool in Statistical Process Control (SPC), are widely used in manufacturing and service industries. The double sampling (DS) X chart detects small to moderate process mean shifts effectively, while reduces the sample size. The conventional application of the DS X chart is usually investigated assuming that the process parameters are known. Nevertheless, the process parameters are usually unknown in practical applications; thus, they are estimated from an in-control Phase-I dataset. In this thesis, the effects of parameter estimation on the DS X chart’s performance are examined. By taking into consideration of the parameter estimation, the run length properties of the DS X chart are derived. Since the shape and the skewness of the run length distribution change with the magnitude of the process mean shift, the number of Phase-I samples and sample size, the widely applicable performance measure, i.e. the average run length (ARL) should not be used as a sole measure of a chart’s performance. For this reason, the ARL, the standard deviation of the run length (SDRL), the median run length (MRL), the percentiles of the run length distributions and the average sample size (ASS) are recommended to effectively evaluate the proposed DS X chart with estimated parameters

Optimal Designs Of The Double Sampling X Chart Based On Parameter Estimation

Control charts, viewed as the most powerful and simplest tool in Statistical Process Control (SPC), are widely used in manufacturing and service industries. The double sampling (DS) X chart detects small to moderate process mean shifts effectively, while reduces the sample size. The conventional application of the DS X chart is usually investigated assuming that the process parameters are known. Nevertheless, the process parameters are usually unknown in practical applications; thus, they are estimated from an in-control Phase-I dataset. In this thesis, the effects of parameter estimation on the DS X chart’s performance are examined. By taking into consideration of the parameter estimation, the run length properties of the DS X chart are derived. Since the shape and the skewness of the run length distribution change with the magnitude of the process mean shift, the number of Phase-I samples and sample size, the widely applicable performance measure, i.e. the average run length (ARL) should not be used as a sole measure of a chart’s performance. For this reason, the ARL, the standard deviation of the run length (SDRL), the median run length (MRL), the percentiles of the run length distributions and the average sample size (ASS) are recommended to effectively evaluate the proposed DS X chart with estimated parameters

Economic Design of X-bar Control Chart Using Gravitational Search Algorithm

Control chart is a major and one of most widely used statistical process control (SPC) tools. It is used to statistically monitor the process through sampling inspection. Control chart tells us when to allow the process to continue or avoid unnecessary adjustments with machine and when to take the corrective action. On to same problem either on the material side or from the operator side it is quite possible that either targeted value X-bar has changed or process dispersion has changed. These changes must be reflected on the control chart so that the corrective action can be taken. The use of control chart requires selection of three parameters namely sample size n, sampling interval h, and width of control limits k for the chart. Duncan developed a loss cost function for X-bar control chart with single assignable cause. The function has to be optimized using metaheuristic optimization technique. In the present project, the economic design of the X-bar control chart using Gravitational Search Algorithm (GSA) has been developed MATLAB software to determine the three parameters i.e. n , h and k such that the expected total cost per hour is minimized. The results obtained are found to be better than that reported in literature

Economic Design of X-bar Control Chart Using Gravitational Search Algorithm

Control chart is a major and one of most widely used statistical process control (SPC) tools. It is used to statistically monitor the process through sampling inspection. Control chart tells us when to allow the process to continue or avoid unnecessary adjustments with machine and when to take the corrective action. On to same problem either on the material side or from the operator side it is quite possible that either targeted value X-bar has changed or process dispersion has changed. These changes must be reflected on the control chart so that the corrective action can be taken. The use of control chart requires selection of three parameters namely sample size n, sampling interval h, and width of control limits k for the chart. Duncan developed a loss cost function for X-bar control chart with single assignable cause. The function has to be optimized using metaheuristic optimization technique. In the present project, the economic design of the X-bar control chart using Gravitational Search Algorithm (GSA) has been developed MATLAB software to determine the three parameters i.e. n , h and k such that the expected total cost per hour is minimized. The results obtained are found to be better than that reported in literature