Klasik kontrol diyagramları, W.A. Shewhart tarafından 1920’lerde geliştirilmiş olmasına rağmen yeni uygulama alanları ile günümüzde hala gelişimini sürdürmektedir. Verilerin tam ve kesin olduğu durumlarda klasik kontrol diyagramlarının kullanılması uygundur; ancak subjektifliğin önemli bir rol oynadığı bazı durumlarda bu kadar kesin verilere sahip olmak neredeyse imkânsızdır. Belirsizlik altındaki durumlarda karar analizleri genellikle olasılık teorisi ve/veya bulanık kümeler teorisi kullanılarak yapılmaktadır. Bunlardan birincisi karar vermenin stokastik yapısını diğeri ise insanın düşüncesinin subjektifliğini temsil eder. Bulanık kümeler teorisi, ne rassal ne de stokastik olan insanın zihinsel yapısından kaynaklanan belirsizliğin modellenmesinde mükemmeldir. Belirsiz, kesin olmayan veya dilsel anlatımlar içeren durumlarda bulanık kümeler teorisinin kullanılması kaçınılmazdır. Bu çalışmada, bulanık kümeler teorisi kullanılarak belirsizlik içeren dilsel verilerle kontrol diyagramlarına yeni yaklaşımlar geliştirilmiştir. Belirsizlik içeren dilsel veriler, bulanık sayılarla ifade edilmiştir. Dilsel veriler için bulanık kontrol diyagramları α-kesim yaklaşımı kullanılarak geliştirilmiş ve bu suretle muayene sıklığı tanımlanmıştır. Veri ve kontrol limitlerinin temsili değerler ile klasik biçime (nümerik değerlere) dönüştürülmesi sonucu taşıdığı bilgiler yitirilmektedir. Bulanık kontrol diyagramlarının oluşturulmasında, bulanık verilerin taşıdığı bilgilerin kaybolmasını önlemek amacıyla “Direkt Bulanık Yaklaşım” geliştirilmiştir. Bu yaklaşımda veriler bulanık sayılarla ifade edilmiş ve temsili değerler kullanılmadan kontrol limitleri de bulanık sayılar olarak hesaplanmıştır. Kontrol altında, kontrol dışında kararlarına ek olarak kısmen kontrol altında, kısmen kontrol dışında gibi ara kararlar geliştirilmiştir. Anahtar Kelimeler: Bulanık proses kontrol diyagramları, bulanık kümeler, dilsel veriler, normal olmayan davranış analizi, belirsizlik. Control charts have been widely used for monitoring process stability and capability. Control charts are based on data representing one or several quality-related characteristics of the product or service. If these characteristics are measurable on numerical scales, then variable control charts are used. If the quality-related characteristics cannot be easily represented in numerical form, then attribute control charts are useful. Even though the first classical control chart was proposed during the 1920's by W.A. Shewhart, today they are still subject to new application areas that deserve further attention. Classical process control charts are suitable when the data are exactly known and precise; but in some cases, it is nearly impossible to have such strict data if human subjectivity plays an important role. It is not surprising that uncertainty exists in the human world. To survive in our world, we are engaged in making decisions, managing and analyzing information, as well as predicting future events. All of these activities utilize information that is available and help us try to cope with information that is not. A rational approach toward decision-making should take human subjectivity into account, rather than employing only objective probability measures. A research work incorporating uncertainty into decision analysis is basically done through the probability theory and/or the fuzzy set theory. The former represents the stochastic nature of decision analysis while the latter captures the subjectivity of human behavior. The fuzzy set theory is a perfect means for modeling uncertainty (or imprecision) arising from mental phenomena which is neither random nor stochastic. Many problems in scientific investigation generate nonprecise data incorporating nonstatistical uncertainty. A nonprecise observation of a quantitative variable can be described by a special type of membership function defined on the set of all real numbers called a fuzzy number or a fuzzy interval. A methodology for constructing control charts is proposed when the quality characteristics are vague, uncertain, incomplete or linguistically defined. The binary classification into conforming and nonconforming used in the p-chart might not be appropriate in many situations where product quality does not change abruptly from satisfactory to worthless, and there might be a number of intermediate levels. Without fully utilizing such intermediate information, the use of the p-chart usually results in poorer performance than that of the x-chart. This is evidenced by weaker detectability of process shifts and other abnormal conditions such as unnatural patterns. To supplement the binary classification, several intermediate levels may be expressed by using linguistic terms. For example, the quality of a product can be classified into the following terms: 'perfect', 'good', 'medium', 'poor', or 'bad' depending on its deviation from specifications. Then, the continuous functions selected appropriately can be used to describe the quality characteristic associated with each linguistic term. In this study, the control charts for number of nonconformities are handled. The type of available data is the imprecise number of nonconformities such as "between 5 and 8" or "approximately 6". The statistical model is based on the classical Shewhart control charts. In the literature, there exist few papers on fuzzy control charts, which use defuzziffication methods such as fuzzy mod, fuzzy midrange, fuzzy median, and fuzzy average in the early steps of their algorithms. The use of defuzziffication methods in the early steps of the algorithm makes it too similar to the classical analysis. Linguistic data in those works are transformed into numeric values before control limits are calculated. Thus both control limits as well as sample values become numeric. This transformation may cause biased results due to the loss of information included by the samples. For example, two fuzzy samples with the equal fuzzy mod may explain very different characteristics. A new approach called direct fuzzy approach to fuzzy control charts is modeled in order to prevent the loss of information of the fuzzy data during the construction of control charts. In this approach, linguistic or uncertain data are represented by means of triangular and/or trapezoidal fuzzy numbers. Using fuzzy arithmetics, control limits based on the fuzzy data are also determined as fuzzy numbers. The decision about the process control is based on the area measurement method. The proposed approach directly compares the linguistic data in fuzzy space without making any transformation. The percentage area of the fuzzy sample behind the fuzzy control limits is used in the decision and intermediate decision levels are defined. Keywords: Fuzzy control charts, fuzzy sets, linguistic data, unnatural pattern analysis, uncertainty.
