Análise do desempenho de gráficos de controle X-Bar considerando diferentes estimadores do desvio padrão

Abstract

The reference works about control charts consider the statistical parameters as known to calculate the control limits. However, in the last decades, the literature about SPC (Statistical Process Control) has indicated a difference between the theoretical and the real performance of control charts which use estimated statistical parameters, increasing the incidence of false alarms. Reference researchers in SPC, as Castagliola and Chakraborti, propose new designs of control charts, improving the performance of Shewhart’s control charts. This work aims to compare the X-bar control charts performance, using five standard deviation estimators, based on the analysis of proportion of ARL values (Average Run Length, the average number of samples until the incidence of a false alarm) in the interval between 0 and 200 of the ARL distribution and varying the sample size and the number of the samples. The five estimators are: the estimator calculated from the average sample range; the estimator calculated from the average sample standard deviation; the estimator calculated from the pooled standard deviation divided by the result of c4 (constant influenced by the sample size) in function of ν (number of degrees of freedom, resultant from the number of samples times the sample size minus one); the estimator calculated from the pooled standard deviation times the result of the constant c4 in function of ν; and the estimator based only on the pooled standard deviation. The method applied is the simulation, developing five programs to simulate productive in-control processes, each one for each standard deviation estimator. After the comparison of proportions, the third estimator is indicated for the situation with the lowest samples values tested (m=20 and n=5 and n=10), and the first estimator is indicated for the situation with the highest samples values tested (m=200 and n=5 and n=10). Only for m=100 and n=10, there is no evidence that proves an estimator has a better performance than another. This work also proved that the sample size and the number of samples influence the performance of the control charts.