Economic process control for multivariate quality characteristics with Hotelling's T<sup>2</sup> charts under Gamma shock model

Abstract

This study is an extension of research conducted by Rahim and Banerjee (Journal of Naval Research Logistics 40 (1993), pp.787–809) to construct an economic design approach of control chart for simultaneously monitoring several quality characteristics under a Gamma shock model with an increasing failure rate. Furthermore, measure the advantage of the Hotelling's T2 control chart with a variable sampling interval (VSI) versus a fixed-length sampling interval (FSI) and a standard Shewhart sampling interval (SSI) under Gamma (λ, 2) shock models based on an economic aspect. This primary contribution of this study is to find an optimal sampling interval to improve the traditional Hotelling's T2 control chart under a non - exponential failure mechanism detecting the small process shift from considering the cost viewpoint. As a result in earlier investigations most control chart economic designs assumed the occurrence time of an assignable cause, which belongs to a random variable of exponential distribution with constant hazard rates because of their administrative simplicity. However, it may not be appropriate for some processes which deteriorate over time. Hence, this study employs a numerical example to indicate the solution procedure and to implement the sensitivity analysis while comparing the results of using various sampling interval approaches.