Sevil Şentürk

Fuzzy exponentially weighted moving average control chart for univariate data with a real case application

Statistical process control (SPC) is an approach to evaluate processes whether they are in statistical control or not. For this aim, control charts are generally used. Since sample data may include uncertainties coming from measurement systems and environmental conditions, fuzzy numbers and/or linguistic variables can be used to capture these uncertainties. In this paper, one of the most popular control charts, exponentially weighted moving average control chart (EWMA) for univariate data are developed under fuzzy environment. The fuzzy EWMA control charts (FEWMA) can be used for detecting small shifts in the data represented by fuzzy numbers. FEWMA decreases number of false decisions by providing flexibility on the control limits. The production process of plastic buttons is monitored with FEWMA in Turkey as a real application.

Fuzzy Statistical Process Control Techniques in Production Systems

Crisp Shewhart control charts monitor and evaluate a process as “in control” or “out of control” whereas the fuzzy control charts do it by using suitable linguistic or fuzzy numbers by offering flexibility for control limits. In this chapter, fuzzy attribute control charts and fuzzy variable control charts are developed and some numeric examples are given.

Modeling attribute control charts by interval type-2 fuzzy sets

Fuzzy attribute control charts, where data are classified into conforming/nonconforming product units, are used to monitor fuzzy fractions of nonconforming units for variable sample sizes and the fuzzy number of nonconforming units for constant sample sizes. Data defined as quality characteristics can be imprecise due to the subjective decisions of the quality control operator. Type-2 fuzzy set theory deals with ambiguity associated with the uncertainty of membership functions by incorporating footprints and modeling high-level uncertainty. In this paper, the structure of an interval type-2 fuzzy p-control chart and interval type-2 fuzzy np-control chart with constant sample size are developed and applied to real data. The main advantage in using interval type-2 fuzzy sets in control charts is the flexibility allowed in determining control limits for process monitoring by incorporating fuzzy set theory. Therefore, fuzzy control charts with interval type-2 fuzzy numbers afford the decision maker the opportunity to see and detect process defects.

Estimating Fuzzy Life Time with a Fuzzy Reliability Function in the Appliance Sector.

Reliability is defined as the length of time a component works without failing. The reliability function shows an estimate for the probable amount of time a component should work without experiencing failure. Fuzzy set theory is rather useful for evaluating ambiguity and vagueness that exists within reliability parameters. Fuzzy reliability can model more appropriately a components lifetime if the inputs on the system are fuzzy numbers. Also fuzzy parameters of function can be estimated as fuzzy numbers in a reliability analysis. In this study, the fuzzy lifetime of a component in a refrigerator with censored data is estimated via a fuzzy reliability function for modeling the uncertainty of the process.

Monitoring Fraction Nonconforming in Process with Interval Type-2 Fuzzy Control Chart

Fuzzy set theory is particularly appropriate approach when data include imprecise. Type-2 fuzzy set theory captures ambiguity that associates the uncertainty of membership functions by incorporating footprints and models high level uncertainty. If the quality characteristic is a binary classification into conforming/non-conforming of product, this decision depends on human subjectivity that have ambiguity or vague. In this situation, monitoring the process with statistical control charts based on interval type-2 fuzzy sets, a special case of type-2 fuzzy sets, is more suitable due to the human imprecise judgments on quality characteristics. In this paper, interval type-2 fuzzy p-control chart is developed into the literature for the first time. Due to the interval type-2 fuzzy sets modelled more uncertainty for defining membership functions, in this paper interval type-2 fuzzy fraction nonconforming numbers used for handling more uncertainty in process. Real word application is implemented with developed fuzzy control chart.

Fuzzy EWMA and Fuzzy CUSUM Control Charts

Exponentially Weighted Moving-Averages (EWMA) and Cumulative-Sum (CUSUM) control charts have the ability of detecting small shifts in the process mean. Classical EWMA and CUSUM charts are not capable to capture the uncertainty in case of incomplete data. Fuzzy EWMA and CUSUM control charts are developed in this chapter and numerical illustrations are given.

Intelligent Systems in Total Quality Management

Total Quality Management (TQM) is a widely known and applied concept by organizations for continuous improvement in the workplace. This philosophy is based on eight main principles: customer focus, leadership, involvement of employee, system approach, continuous improvement, process approach, and facts based decision making, and mutually beneficial supplier relationship. TQM includes statistical analysis of data, implementation of corrective and preventive actions, measurement of performance indicators of process and also advancement on actions for continuous improvement. The aim of Statistical Process Control (SPC) is to detect the variation and nonconforming units for improvement in the quality of process. While manually collecting data, the ambiguity or vagueness exists in the data which are called fuzzy data from measurement system or human experts. Fuzzy data can be analyzed by fuzzy control charts in SPC. Fuzzy control charts are implemented for monitoring and analyzing process, and reducing the variability of process. Also, an intelligent system is developed to eliminate or reduce uncertainty on data by using a fuzzy approach.