Monitoring Oral Cancer Survival Using Non-Normal Control Charts: An Application of the Transmuted Kumaraswamy Distribution

Conventional statistical process control (SPC) charts, which are normality given, do not tend to monitor processes whose distributions are heavily skewed, especially where medical survival monitoring and reliability engineering are concerned. This paper presents a new research strategy which involves the use of the Transmuted Kumaraswamy Distribution (TKD) to derive control charts that will be specifically used to monitor skewed data of oral cancer survival. The TKD is a three-parameter generalization of the Kumaraswamy distribution which provides increased flexibility to modeling the appearance of asymmetric patterns of data with the addition of a transmutation parameter. Our theoretical model of the TKD-based control limits is the upper control limit (UCL), lower control limit (LCL), and center line (CL) derived with the help of the percentile-based approach that applies to non-normal distributions. The proposed methodology is confirmed by a comprehensive case study based on oral cancer survival data of 20 patients. The empirical outcomes show that there is no special cause variation in the sample values since all of them lie within the control limits (LCL = 0, CL = 58.47, UCL = 130.67) showing statistical stability. After comparing the two charts, it is clear that the TKD-based charts are more performant as compared to the traditional Shewhart charts when the data is highly skewed (skewness coefficient > 1.5). The suggested framework will be useful to generalize the conventional SPC methodology by supporting complex distributional environments to provide more effective process monitoring, higher sensitivity in assignable causes detection and a better Type I and Type II error rates in skewed data environments. The development has enormous implications on quality control of healthcare, biomedical research, analysis of reliability and manufacture of pharmaceuticals that have non-normal distributions.