Abstract
This paper proposes a minimum loss cost model for the joint economic design of an x-bar chart and an s-control chart for monitoring both the process mean and process variance simultaneously. The process is subject to the occurrences of two independent Weibull shocks each having increasing failure rates. One shock shifts the process mean and the other shock changes the process variance. When the failure mechanism obeys a Weibull shock model, the length of the sampling interval should vary with the age of the system. This approach is more appropriate than the traditional uniform sampling approach to keep the length of sampling intervals constant. The loss cost model, including an asymmetric quadratic loss function, emphasises the importance of continuously reducing performance variation and overcomes the difficulty in estimating various quality costs. Application of the proposed model is demonstrated through numerical examples.
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