Abstract
The control chart and the maintenance management need to control process quality and reduce out-of-control cost. They are two key tools in the production process; however, they have usually been analyzed separately in the literature. Moreover, the existing studies integrating these two concepts suffer from three significant drawbacks as follows: (1) using control charts with fixed parameters to monitor the process, so that the small and middle shifts are detected slowly; (2) monitoring the mean and standard deviation separately, whereas, in real condition, the mean and standard deviation should be monitored simultaneously; (3) quality loss function is not usually used to design economic model, which leads to a large social quality loss in the monitoring process of control chart. To eliminate these weaknesses, the economic design of the exponential weighted moving average (EWMA) control chart with variable sampling intervals (VSI) for monitoring the mean and standard deviation under preventive maintenance and Taguchi’s loss functions is proposed. The optimal values of the parameters are determined to minimize the loss-per-item in an average cycle process. In addition, a genetic algorithm is used in a numerical example to search for the optimal values of the parameters. According to the sensitivity analysis, the effect of the model parameters on the solution of the economic model is obtained. Finally, the comparison study shows that the VSI EWMA control charts designed by the joint economic model are expected to reduce loss.
Highlights
Academic Editor: Kauko Leiviska e control chart and the maintenance management need to control process quality and reduce out-of-control cost. ey are two key tools in the production process; they have usually been analyzed separately in the literature
We obtain the optimal values of n, h1, h2, k, w, λ as follows: n 1, h 0.681, k 2.764, r 0.305, ETL 18.852. e result shows that the variable sampling intervals (VSI) exponential weighted moving average (EWMA) control charts designed by the joint economic model have a less expected loss and are superior to the FSI EWMA control charts designed by the joint economic model
When the process is in control μ μ0, σ σ0, and when the process is out of control μ μ0 + δ1σ0, σ δ2σ0, where δ1 and δ2 are two constants, and typically δ2 is larger than 1. is process can be monitored by the VSI EWMA control charts. e optimality of the joint economic model of the VSI EWMA control chart for monitoring the process mean and standard deviation is verified by comparing the following three control charts: (1) VSI EWMA control chart that is designed based on the economic model (23); (2) FSI EWMA control chart that considers quality loss and preventive maintenance; (3) VSI EWMA control chart, which is designed by using the average time to signal (ATS) as the evaluation criterion
Summary
Before the economic model of VSI EWMA control charts is established, we first introduce the VSI EWMA control charts for monitoring the mean and standard deviation. e details of the approach are shown as follows. When the process is on out-of control, μ μ0+δ1σ0, or, σ δ2σ0, where δ1 and δ2 are constants, and typically δ2 is larger than the sample. Let T∗i (n/σ20)Ti. When the process is in control, T∗i ∼ χ2n, so we can get the mean and variance of T∗i as follows:. En, the ith sample statistic of EWMA chart for monitoring the mean and standard deviation is defined as [49]. If the sample statistic falls in the safe region (i.e., 0 ≤ Qi ≤ UWL), take the sample using the sampling interval h1. If the sample statistic falls in the warning region (i.e., UWL < Qi ≤ UCL), take the sample using the sampling interval h2. If the sample statistic falls outside the control limits (i.e., Qi > UCL), we will find the assignable cause
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