TY - EJOU
AU - Zaka, Azam
AU - Akhter, Ahmad Saeed
AU - Jabeen, Riffat
AU - Sanaullah, Aamir
TI - Control Charts for the Shape Parameter of Power Function Distribution under Different Classical Estimators
T2 - Computer Modeling in Engineering \& Sciences
PY - 2021
VL - 127
IS - 3
SN - 1526-1506
AB - In practice, the control charts for monitoring of process mean are based on the normality assumption. But
the performance of the control charts is seriously affected if the process of quality characteristics departs from
normality. For such situations, we have modified the already existing control charts such as Shewhart control
chart, exponentially weighted moving average (EWMA) control chart and hybrid exponentially weighted moving
average (HEWMA) control chart by assuming that the distribution of underlying process follows Power function
distribution (PFD). By considering the situation that the parameters of PFD are unknown, we estimate them by
using three classical estimation methods, i.e., percentile estimator (P.E), maximum likelihood estimator (MLE)
and modified maximum likelihood estimator (MMLE). We construct Shewhart, EWMA and HEWMA control
charts based on P.E, MLE and MMLE. We have compared all these control charts using Monte Carlo simulation
studies and concluded that HEWMA control chart under MLE is more sensitive to detect an early shift in the shape
parameter when the distribution of the underlying process follows power function distribution.
KW - Average run length; control chart; percentile estimator; power function distribution
DO - 10.32604/cmes.2021.014477