Loss-Based Control Charts for Monitoring Non-Normal Process Data

Abstract

Quality and loss of products are crucial factors in competitive companies, and firms widely adopt a loss function to measure the loss caused by a deviation in the quality variable from the target value. From Taguchi's view point, it is important to monitor any deviation from the process target value. While most existing studies assume the quality variable follows a normal distribution, the distribution can in fact be skewed or deviate from normal in practice. This paper thus proposes loss-based control charts for monitoring the quality loss location or equivalently the deviation of the quality variable from the target value under a skew-normal distribution. We consider the exponentially weighted moving average (EWMA) average loss control chart, which illustrates the best performance in detecting an out-of-control loss location for a process with a left-skewed distribution. Numerical analysis demonstrates that the proposed EWMA average loss chart always performs better than the existing median loss chart for both left-skewed and right-skewed distributions. A numerical example illustrates the application of the proposed EWMA average loss control chart.

Keywords

• Control chart
• loss function
• process control
• run length
• skew-normal distribution