A CUSUM control chart for gamma distribution with guaranteed performance

Abstract

Even though most control chart developments have revolved around the normal distribution, productive operations, in fact, often use non‐normal data, and some even use skewed distributions. This occurs with cycle times and many processes with a single specification limit. Under these conditions, gamma distributions often offer a better characterization where CUSUM schemes provide optimal performance to detect changes of a known in‐control (IC) parameter. In practice, gamma parameters have to be estimated, and limited phase I samples have undesirable effects on the phase II average run length (ARL) that has not been examined. To address this situation, this study uses Markovian models to assess the ARL of a CUSUM developed to monitor scale changes when IC parameters are estimated. This paper discusses the conditional ARL performance and proposes an adaptation of a stochastic estimation algorithm to guarantee a minimum performance. IC and out‐of‐control performance is compared with the conditional performance of a traditional approach where no corrections are made to guarantee a specific behavior. To demonstrate the practical application of this new approach, an implementation was made in a packaging process using multihead weighing machines. Practitioners interested in using reliable monitoring schemes will find, in this proposal, several implementation guidelines such as algorithms and look up tables to facilitate their implementations.