Interval Type-2 Fuzzy Standardized Cumulative Sum Control Charts in Production of Fertilizers

Abstract

Statistical process control is a method used for controlling processes in which causes of variations and correction actions can be observed. Control chart is one of the powerful tools of statistical process control that are used to control nonconforming products. Previous literature suggests that fuzzy charts are more sensitive than conventional control charts, and hence, they provide better quality and conformance of products. Nevertheless, some of the data used are more suitable to be presented in interval type-2 fuzzy numbers compared to type-1 fuzzy numbers as interval type-2 fuzzy numbers have more ability to capture uncertain and vague information. In this paper, we develop an interval type-2 fuzzy standardized cumulative sum (IT2F-SCUSUM) control chart and apply it to data of fertilizer production. This new approach combines the advantages of interval type-2 fuzzy numbers and standardized sample means which can control the variability. Twenty samples with a sample size of six were examined for testing the conformance. The proposed IT2F-SCUSUM control chart unveils that 15 samples are “out of control.” The results are also compared to the conventional CUSUM chart and type-1 fuzzy CUSUM chart. The conventional chart shows that 13 samples are “out of control.” In contrast, the type-1 fuzzy CUSUM chart shows that the process is “out of control” for 14 samples. In the analysis of average run length, the proposed IT2F-SCUSUM chart outperforms the other two CUSUM charts. Thus, we can conclude that the IT2F-SCUSUM chart is more sensitive and takes lesser number of observations to identify the shift in the process. The analyses suggest that the IT2F-SCUSUM chart is a promising tool in examining conformance of the quality of the fertilizer production.

WITHDRAWN: Interval type-2 fuzzy moving average control charts considering explicit formula of average run length and their application

“…Previous research indicated that there are various kind of research that had been explored on interval type-2 fuzzy control charts other than interval type-2 fuzzy 𝑋 ̅ and R control charts. For instance, Mohd Razali et al (2021) conclude that the interval type-2 fuzzy Cumulative Sum (CUSUM) chart is more sensitive and accurate in monitoring the analysis by comparing the proposed method with the type-1 fuzzy CUSUM chart and conventional chart.…”

Reading between the (Spectral) Lines: Magellan/IMACS Spectroscopy of the Ultrafaint Dwarf Galaxies Eridanus IV and Centaurus I

“…The Anderson-Darling test was chosen over other similar statistical tests like a Kolmogorov-Smirnov test because it gives more weight to the tails of the distributions and has greater statistical power at small sample sizes while remaining flexible (Mohd Razali & Yap 2011). The data are standardized and compared to a reference distribution, 0, 1…”

Investigating the trend of road traffic fatalities in Malawi using Mann-Kendall statistic

“…Intervention analysis can be performed using the Cumulative Sum [CUSUM] method given in Hipel and McLeod [ 21 ] to determine the likely date/time of intervention in a given time series, or changes in environmental regime [ 22 ], if any. Razali, Abdullah [ 23 ] also used CUSUM methodology in examining conformance of the quality of the fertilizer production and even the method has been used in psychometric research to detect aberrant responses in a response sequence, e.g., test speediness, inattentiveness, or cheating [ 24 ]. On the whole, CUSUM is a well-established statistical process control method to detect changes in a sequence [ 24 ], hence has been used for determining the impact of intervention measures such as on road fatalities, if any.…”