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The main purpose of this paper is to use fuzzy logic to provide a systematic approach for designing fuzzy control charts and compare the average run length type 2 of these charts in three different modes: Gaussian fuzzy, triangular fuzzy, and crisp cases. The process of solving and presenting the research results is by calculating the fuzzy control chart conditions and fuzzy descriptive capability indices through theoretical calculations and a project-based organizational case study and comparing the average run length type 2, which represents the expected interval between out-of-control events. Average run length type 2 illustrates that Gaussian and triangular quality control charts are able to detect an out-of-control signal more quickly. The main contributions of this paper are to use Gaussian fuzzy numbers in order to provide a systematic approach for designing fuzzy control charts, estimating descriptive capability indices, and analyzing the results of their estimation under fuzzy logic. [ABSTRACT FROM AUTHOR]

The important and common applications of process capability indices (PCI’s) is the process capability ratio and the process capability index , and the use of these measures in practical applications is based on the assumption that the process is under statistical control and that the outputs of that process follow the normal distribution. In practice, however, there are many cases in which the outputs of the process are not follow normal distribution, in such cases, calculating PCI’s will lead to misleading results. In this paper, the non-normal production process capability was evaluated. The evaluation process was conducted using four methods: The first method involved the use of Box-Cox power transformation to normal distribution of data and then calculating indicators of the capability process by traditional methods. The second method is by using the weighted variance method, and the third method is by using the Clements’ method based on the percentiles calculation of data, and the fourth method is based on the use of the Darling-Anderson goodness of fit test to accommodate some of the probability distributions of the original data, this test shows that the log-normal distribution is the most appropriate distribution for the data The results showed that although the process is stable and under statistical control, it is not capable based on the value of the process capability index that did not exceed (65%), as the percentage defect units, which is outside the specifications, is large and located between (3.6%) and (13.4%). The results also showed that there is a convergence in the results of the PCI’s calculated by all methods, and that the Clements’ method is the best method as it gives the highest values ​​for the PCI’s. The research recommended studying and calculating other PCI’s like, , , and CMA(τ,v). One of the recommendations for future research and studies is to do a theoretical study to compare the mentioned methods and choose the best ones based on some statistical criteria.

The capability analysis of a process against requirements is often an instrument of change. The traditional and fuzzy process capability approaches are the most useful statistical techniques for determining the intrinsic spread of a controlled process for establishing realistic specifications and use for comparative processes. In the industry, the traditional approach is the most commonly used instrument to assess the impact of continuous improvement projects. However, these methods used to evaluate process capability indices could give misleading results because the dataset employed corresponds to the final product/service measures. This paper reviews an alternative procedure to assess the fuzzy process capability indices based on the statistical methodology involved in the modeling and design of experiments. Firstly, a model with reasonable accuracy is developed using a neural network approach. This model is embedded in a graphic user interface (GUI). Using the GUI, an experimental design is carried out, first to know the membership function of the process variability and then include this variability in the model. Again, an experimental design identifies the improved operating conditions for the significative independent variables. A new dataset is generated with these operating conditions, including the minimum error reached for each independent variable. Finally, the GUI is used to get a new prediction for the response variable. The fuzzy process capability indices are determined using the triangular membership function and the predicted response values. The feasibility of the proposed method was validated using a random data set corresponding to the basis weight of a papermaking process. The results indicate that the proposed method provides a better overview of the process performance, showing its true potential. The proposed method can be considered non-invasive.

Process capability analysis (PCA) is a completely effective statistical tool for ability of a process to meet predetermined specification limits (SLs). Unfortunately, especially the real case problems include many uncertainties, it is one of the critical necessities to define the parameters of PCIs by using crisp numbers. So, the results obtained may be incorrect, if the PCIs are calculated without taking into account the uncertainty. To overcome this problem, the fuzzy set theory (FST) has been successfully used to design of PCA. We also know that fuzzy set extensions have an important role in modelling the case that include uncertainty, incomplete and inconsistent information and they are more powerful than traditional FST to model uncertainty. Defining of main parameters of PCIs such as SLs, mean (µ) and variance (σ²) by using the flexible of fuzzy set extensions rather than precise values due to uncertainty, time, cost, inspectors hesitancy and the results based on fuzzy sets for PCIs contain more, flexible and sensitive information. In this study, two of well-known PCIs called Cp and Cpk have been re-designed at the first time by using one of fuzzy set extensions named Pythagorean fuzzy sets (PFSs). Defining PCIs with more than one membership function instead of an only one membership function is enabling to evaluate the process more broadly more flexibility. For this aim, the main parameters of PCIs have been defined and analyzed by using PFSs. Finally, four new PCIs based on PFSs such as ...sp, ...spk, ...fp and ...fpk have been derived. The proposed new PCIs based on PFSs have been also applied on manufacturing process and capability for gears have been analyzed. It is shown that the flexibility of the PFSs on PCIs enables the PCA to give more realistic, more sensitive, and more comprehensive results. [ABSTRACT FROM AUTHOR]

Process capability indices (PCIs) can be used as an effective tool for measuring product quality and process performance. In classic quality control there are some limitations which prevent a deep and flexible analysis because of the crisp definition of PCA‟s parameters. Fuzzy set theory can be used to add more flexibility to process capability analyses. In this study, the fuzzy X ba and MRx ba control charts are introduced to monitor continuous production process in triangular fuzzy state. Also, fuzzy PCIs are produced when SLs and measurements are triangular fuzzy numbers (TFN). For this aim, a computer program is coded in Matlab software. The fuzzy control charts is applied in Yazd fiber production plant. The results show that in continuous production processes, the better analysis will be performed by using fuzzy measurements. Also, based on the fuzzy capability indices, we can have a flexible analysis of the process performance.

In process capability indices, the generalized confidence interval (GCI) method has been used many times in several research articles. In this article, we have considered the supplier's selection problems by using the GCI of difference between two process capability indices δ ′ . We have considered two classical methods of estimation, viz. maximum likelihood estimation (MLE), and maximum product spacing estimation (MPSE) to estimate δ ′ . By using Monte Carlo simulation, we have obtained the biases and corresponding mean squared errors (MSEs) of δ ′ . Here, we also find the lower confidence limit (L), upper confidence limit (U), and their corresponding average width (AW) for both classical methods MLE and MPSE. Three real data sets have been reanalyzed to illustrate the methodology of the supplier's selection problem by utilizing the generalized confidence interval method. [ABSTRACT FROM AUTHOR]

Statistical Quality Control is a valuable strategy that applies to the statistical technique for monitoring a manufacturing system under particular situations. On the other hand, the fuzzy set theory is an ideal instrument to cope with an unclear situation. The existing studies are restricted, and there is still mystery behind the unclear data. This paper deals with technique: namely, the fuzzy control chart based on fuzzy process capability indices (FCPI) using triangular fuzzy numbers (TFNs). Alpha cut theory is applied in statistical quality control for fuzzy process control industrial application. This is a five-phase study that deals with the control chart using capability indices. The numerical example is also performed using the proposed technique. This paper would help to better assess/understand the manufacturing system data and would explore the application of the fuzzy control techniques.