MONITORING MEAN SHIFT OF SKEWED DISTRIBUTION USING MODIFIED ONE-STEP M-ESTIMATOR WITH EWMA CONTROL STRUCTURE

摘要

A generalized form of Shewhart chart, known as Exponentially Weighted Moving Average (EWMA) control chart is frequently exercised to monitor small shift in the process mean. Aptly tune, it is claimed to be robust to slight deviation in normality. For that to be successful, the weighting constant (λ) shall be set quite small. However, too small of the value may reduce the effectiveness of the chart in shift detection, a phenomenon known as the inertia effect. Thus, meticulous approach ought to be exerted to tune the traditional EWMA chart under non-normality. Recurrent use of robust control charts is now seen in quality control literature as one of the few solutions to cope with non-normality. In line with this, a novel EWMA control chart was proposed in this paper. The proposed chart was constructed using a highly robust breakdown point location estimator, known as modified one-step M-estimator (MOM). Monte Carlo simulation approach was used to model and evaluate performance of the proposed chart when process data was subjected to non-normality using skewed distributions. Two separate cases were considered: (i) when both mean and standard deviation of the process were known and (ii) when the mean was unknown and estimated from an in-control Phase I sample. While demonstrating a mediocre power to detect shift in the first case, an outcome on simultaneous effect of parameter estimation and non-normality for the proposed chart indicated a reversal. Besides equipped to regulate false alarm rate following an increase in the level of skewness of the distribution, the proposed chart also possessed the best-shift detecting ability in extreme non-normal cases as observed in this paper. This was demonstrated using average run length (ARL) when the underlying distribution of Phase I and Phase II data were matched.