Monitoring of Fuzzy Quality Profiles via Fuzzy I-MR Control Chart

In some statistical process control applications in the real world, quality of a process or a product is characterized by a relationship between two or more variables, which is referred to as profile. Understanding and checking the stability of process over time can be facilitated by monitoring the quality profile in phase I. Sometimes the quality characteristics may be linguistic, imprecise, vague, ambiguous or deficient that leads to the quality profile represented adequately by a fuzzy linear regression model. In this article, a new methodology in phase I is proposed for monitoring quality profiles in fuzzy environment. In the proposed method, a model in fuzzy linear regression is developed to build the quality profiles by means of multi-objective linear programming and then fuzzy individuals and moving-range (I-MR) control charts are developed to monitor the process fuzzy profiles with the aim of achieving an in-control process. Through a simulation study we investigated the performance of introduced approach on the basis of signal probability in various out-of-control scenarios. The results indicated a good performance of our monitoring approach in detecting medium and large shifts in process profiles. To show the applicability of our approach, a real case in tourism industry is studied and sensibility analysis of parameters in constructing a fuzzy profile is discussed.