Comparison of statistical and fuzzy quantitative quality control using with simulation data

Statistical Quality Control (SQC) is a collection of statistical methods that check whether the services or products obtained from the process comply with standards, customer expectations and specifications. The most known SQC method is quality control charts (QCC). QCCs are a graphical method that checks whether the quality characteristic (average, standard deviation, etc.) of a product remains within acceptable limits and gives a warning if it exceeds these limits. QCCs are divided into two as quantitative and qualitative. The main difference between these two categories is that while quantitative QCCs take into account the measurable features of the product, such as standard deviation, average and range, qualitative QCCs also take into account features that cannot be measured. The main statistical assumption in both categories is that the samples obtained from the process fit into the normal distribution. However, in real applications it is quite difficult for the examples to provide this assumption. Apart from this, observations in the examples must be precise for these graphics to be available. To eliminate such disadvantages of statistical QCCs, fuzzy QCCs have been used recently. Fuzzy QCCs are based on the fuzzy set theory that has the ability to handle ambiguous and incomplete data. The basic logic in fuzzy SBCs is that it allows control limits to be obtained as fuzzy numbers. Fuzzy QCCs have been used in many studies so far. However, there is no study comparing the performance of statistical and fuzzy QCCs through simulation study. This study aims to compare the performances of qualitative statistical and fuzzy QCCs through simulation study. For this purpose, a simulation study was carried out that takes into account the situations in which the process is under control and out of control. As a result of the analyzes, it was seen that qualitative fuzzy QCCs provide the best performance.