This paper proposes an approach which simultaneously considers the properties of cost and quality based on the Burr distribution to determine three parameters (including sample size, sampling interval between successive samples, and the control limits) when an x-bar chart monitors a manufacturing process with Weibull failure characteristic and non-normal data. Also, the cost model of Banerjee and Rahim (1988) is used as the objective function, and the probability density function of the Burr distribution is applied to derive the statistical constraints of economic statistical design of the x-bar control charts for non-normal data. The example of Banerjee and Rahim (1988) is adopted to indicate the solution procedure and sensitivity analyses. Meanwhile, the design parameters of the x-bar control charts can be obtained through the grid search method. The results show that an increase of skewness coefficient ( 3 ) results in a slight decrease for sample size (n), but is robust to the control limit width (L). Also, an increase of kurtosis coefficient ( 4 ) leads to a wider control limit width.
When the x bar chart is applied to monitor a manufacturing process, three parameters should be determined: sample size, sampling interval between successive samples, and the control limits for the chart. In 1988, Banerjee and Rahim presented the cost model that used variable sampling intervals as opposed to sampling intervals of fixed length under the process-failure mechanism which follows a Weibull model or some other models having an increased hazard rate. However, when designing control charts, one usually assumes that the measurements in the subgroup are normally distributed. This assumption may not be tenable. This paper develops the economic design of x bar control charts for non-normal data under Weibull shock models. An example is presented to illustrate the solution procedure.
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