Violating the standard assumption underlying the process monitoring: Perfect measurements

The presence of the measurement errors is a rule rather than an exception in any process monitoring context. Since the observations are generally observed, in quick manner, by some measuring process and are time ordered. Moreover, their presence contributes negatively towards the performance of the usual control charting schemes. Therefore, it will be naïve and may lead to invalid conclusions to devise a control structure, without taking them into account, at first place, and then counteracting their adverse effect. This paper studies the foregoing impact on the performance of two eminent charts, for mean or average parameter of a process, namely: Crosier CUSUM and Dual CUSUM charts. With growing intensity of the error variation, a deteriorating performance of the said charts has been observed. The average run length (ARL) behaviors, zero-state, and steady-state, of both charts are studied, using Monte-Carlo simulation algorithm, under different situations for the effect of measurement errors. Also, extra quadratic loss, relative ARL and performance comparison index (abbreviated as EQL, RARL, and PCI, respectively) are used to evaluate the performance of the charts. Repeated measurements are employed, as a remedial scheme, for the effect of measurement errors. An illustrative example is incorporated to elucidate the study.