Economic statistical design for x-bar control charts under non-normal distributed data with Weibull in-control time

Abstract

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 (α₃) results in a slight decrease for sample size (n), but is robust to the control limit width (L). Also, an increase of kurtosis coefficient (α₄) leads to a wider control limit width.

Keywords:

• control charts
• variable sampling
• non-normal distribution
• economic design
• Burr distribution