![]() ![]() Collani, Sheil, and Yang proposed the ESD of charts, considering the importance of the error Type I and II for minimization of costs. In this case the or control charts are more suitable. To keep control in both the mean and variability of a process the control chart has been used, although the chart loses reliability when 10. Variability is an important factor to control in a process because raw material, operators skills, machine calibration, etc., increase variability without affecting the process mean. Other works extended the ED to ESD and covered other control charts:, , and control charts were proposed to monitor variability – and control charts were proposed to monitor proportion or number of nonconforming units within samples. It had the following assumptions: the failure mechanism of the process had an Exponential probability distribution, there was only one assignable cause, and the sampling interval was constant. The ED of control charts was introduced in 1956 by Duncan for X-bar ( ) charts that monitor the mean of the quality characteristic of produced items. On the other hand, the Economic Statistical Design (ESD) additionally considers the statistical requirements, such as the probabilities of error Type I (detecting an out-of-control state when the process is fine) and II (not detecting an out-of-control state when the process is not fine) in the estimation of the parameters. The Economic Design (ED) of control charts (the estimation of the parameters) considers the costs (in time and money) associated with sampling and searching/repairing of assignable causes. The chart parameters must be selected following a methodology in order to minimize the “cost of quality”. Also, close control limits would increase the frequency of failure alarms and rejection of products which not necessarily would be of low quality. These parameters are selected based on economic and statistical restrictions because there are costs and times associated with sampling and searching of assignable causes: high sampling frequency would take more time from the process cycle time, and depending on the nature of the item, product loss. In such case, is necessary to find and correct the assignable cause that originated this state (failure).Ī control chart is defined by three main parameters: the size of the sample ( ), the sampling interval between samples ( ), and the coefficient of the control limits ( ). ![]() If the attribute (i.e., weight, length, dimensions, etc.) is not within these limits, then the process is in an “out-of-control” state. The concept of “control” is related to the quality attribute that is within specified limits (control limits) to ensure production stability and quality of products. Experiments showed statistically significant reductions in costs when PM is performed on processes with high failure rates and reductions in the sampling frequency of units for testing under SPC.Ĭontrol charts are tools of Statistical Process Control (SPC) that monitor the state of a production process, identifying when the quality attributes of a product change. Hence, this paper covers these points, presenting the Economic Statistical Design (ESD) of joint X-bar-S control charts with a cost model that integrates PM with general failure distribution. Third, the effect of PM on processes with different failure probability distributions has not been studied. ![]() Second, many studies of design of control charts consider just the economic aspect while statistical restrictions must be considered to achieve charts with low probabilities of false detection of failures. First, most SPC is performed with the X-bar control chart which does not fully consider the variability of the production process. However there are some points that have not been explored in depth about its joint application. The application of Preventive Maintenance (PM) and Statistical Process Control (SPC) are important practices to achieve high product quality, small frequency of failures, and cost reduction in a production process.
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