One-sided Cusum Chart with V-mask for Weighted Weibull Distribution Parameter Shifts
Shei Baba Sayibu
*
Department of Statistics, Faculty of Physical Sciences, University for Development Studies, Tamale, West Africa, Ghana.
Sualihu Mohammed Muntaka
Department of Statistics, Faculty of Physical Sciences, University for Development Studies, Tamale, West Africa, Ghana.
Alhassan Mubarika
Department of Statistical Science, Tamale Technical University, Tamale, West Africa, Ghana.
*Author to whom correspondence should be addressed.
Abstract
In our research, we have developed a cumulative sum control chart to identify changes in the parameter of the weighted Weibull distribution. This chart incorporates the V-mask technique and a sequential ratio test. Our analysis of the V-mask revealed that even minor shifts in the weighted Weibull distribution's parameters led to significant variations in the mask's angle, lead distance, and average run length. A change in the V-mask parameters has the following importance: it can lead to an increase in false alarms, decreased detection of true signals, change in process capability, indicates the need for process adjustments, increased security from regulatory bodies, impact on supply chain and customer relationships, and the need for re-training or re-certification. Finally, we applied the cumulative sum chart to real data from the Kabsad Scientific Hospital to illustrate the sensitivity of the proposed cumulative sum control chart. The V-mask plot showed a shift in the process mean of the dataset.
Keywords: Deviations, flexibility, inadequacy, sensitivity, variability