Fuzzy maximum likelihood change-point algorithms for identifying the time of shifts in process data

Process data provide important information for monitoring product quality. A common problem of process readings is their deviation from in-control values due to systematic errors or instrument biases. Timely detection and modification of instrument fault is crucial for process manipulation. Monitoring changes in process mean and variance simultaneously is important because special causes can evoke changes in both at once. Many existing methods identify either the mean or variance only; some even inaccurately assumes that the in-control parameters are known. We propose a new method called fuzzy maximum likelihood change-point (FMLCP) algorithm that allows detection of the time of shifts in mean and variance simultaneously without knowing the in-control parameters. The fuzzy c-partition concept is embedded into change-point formulation to deal with the vagueness of boundaries between adjacent segments. An FMLCP procedure is constructed and suitable for processes following any distribution. The FMLCP algorithm can be applied to both phase I and II processes in quality control without any information of in-control parameters; multiple change points are allowed and the shifts in each individual segment can be estimated simultaneously. Our experimental results demonstrate the preferred utility of FMLCP over traditional statistical maximum likelihood approaches. We used real datasets to demonstrate the effectiveness of FMLCP. Using FMLCP to detect small shifts is particularly beneficial for identifying root causes quickly and correctly in phase II applications where small changes occur more often and the average run length tends to be long.