Efeitos da estimação de parâmetros no desempenho do gráfico modificado considerando os índices de capacidade

Abstract

The modified and the acceptance control charts are indicated for monitoring highly capable processes, whose natural dispersion is significantly lower than the specification limits. This affirmation is based on the fact that these charts allow the process mean to vary over a range (specified by the tolerable non-conforming items rate,) remaining its in in-control (IC) condition and, from a practical point of view, highly capable processes support some shifts on their mean without affect the production of non-conforming items (cause there is a considerable room between the nominal mean and the specification limits). As the modified and acceptance charts do not require a rigid stability on the process mean, detecting just practical importance shifts, the number of process halts are minimized, which can save time and resources, making their use even more relevant. This work studies the effect of the parameter estimation and the influence of the capability indexes on the performance measures of the modified chart. We chose to detail the study only for this chart because the focus of this chart is on the control of the probability of type I error (which is the most common on the industry). To understand the effect of the standard deviation estimation on the modified chart performance, there were proposed some statistical models to calculate the False Alarm Rate (FAR) and the Average Run Length (ARL), considering the cases where the standard deviation is known and the one in which it is unknown. The results showed that when the standard deviation is estimated, both FAR and ARL become random variables, what compromise the performance of the chart. To amply the knowledge about this damage it was done some graphical and numerical tests, which showed that it is necessary to collected a big number of data (many large samples) from the process on Phase I to get closer the results of the unknown case to the desired value. However, this high number of m and n makes the use of the chart unfeasible in many manufacture industries. Some solutions were proposed to reduce this high number of data needed on Phase I. Finally, it was evaluated the influence of the capability indexes on FAR and ARL, and it was attested that the modified chart is really appropriated for high capable processes, because while the mean vary inside the allowed range, the maximum false alarm rates remains bellow or equal to the nominal value.