Browsing by Subject "Control charts"

Now showing 1 - 3 of 3

Open Access
Economic design of EWMA control charts based on loss function
(Elsevier, 2009) Serel, D. A.
For monitoring the stability of a process, various control charts based on exponentially weighted moving average (EWMA) statistics have been proposed in the literature. We study the economic design of EWMA-based mean and dispersion charts when a linear, quadratic, or exponential loss function is used for computing the costs arising from poor quality. The chart parameters (sample size, sampling interval, control limits and smoothing constant) minimizing the overall cost of the control scheme are determined via computational methods. Using numerical examples, we compare the performances of the EWMA charts with Shewhart over(X, -) and S charts, and investigate the sensitivity of the chart parameters to changes in process parameters and loss functions. Numerical results imply that rather than sample size or control limits, the users need to adjust the sampling interval in response to changes in the cost of poor quality.
Open Access
Quality control chart design under jidoka
(John Wiley & Sons, Inc., 2009) Berk, E.; Toy, A. Ö.
We consider design of control charts in the presence of machine stoppages that are exogenously imposed (as under jidoka practices). Each stoppage creates an opportunity for inspection/repair at reduced cost. We first model a single machine facing opportunities arriving according to a Poisson process, develop the expressions for its operating characteristics and construct the optimization problem for economic design of a control chart. We, then, consider the multiple machine setting where individual machine stoppages may create inspection/repair opportunities for other machines. We develop exact expressions for the cases when all machines are either opportunity-takers or not. On the basis of an approximation for the all-taker case, we then propose an approximate model for the mixed case. In a numerical study, we examine the opportunity taking behavior of machines in both single and multiple machine settings and the impact of such practices on the design of an X̄ - Q C chart. Our findings indicate that incorporating inspection/repair opportunities into QC chart design may provide considerable cost savings.
Open Access
Univariate X̄ control charts for individual characteristics in a multinormal model
(Taylor & Francis, 2000) Serel, D. A.; Moskowitz, H.; Tang, J.
The early work on multivariate statistical process control was built upon Hotelling's T2 control chart which was developed to simultaneously monitor the means of correlated quality variables. This chart, however, has a drawback, namely, the problem of identifying the responsible variable(s) when an out-of-control signal occurs. One alternative is to use a separate X̄ control chart for each individual characteristic with equal risks, based on Bonferroni inequality. In this study, we show that, from an economic perspective, it may be desirable to have unequal type I risks for the individual charts, because of different inspection and restoration costs associated with each variable. We obtain their risk ratios, which are measures of relative importance of the variables monitored. Then, based on these risk ratios, we develop computer algorithms for finding the exact control limits for individual variables from a multinormal distribution, in the sense that the overall type I risk of the charts is equal to the desired value. Numerical studies show that the proposed methods give optimal or near-optimal results from an economic as well as statistical point of view.