Reliability computation for an uncertain PVC window production system using a modified bayesian estimation

Nowadays, Industries have been receiving much attention in Failure modelling and reliability assessment of repairable systems due to the fact that it plays a crucial role in risk and safety management of process. The primary purpose of this article is to present a methodology for discussing uncertainty in the reliability assessment if the production system. In fact, we discuss the fuzzy E-Bayesian estimation of reliability for PVC window production system. This approach is used to create the fuzzy E-Bayesian estimations of system reliability by introducing and applying a theorem called “Resolution Identity” for fuzzy sets. To be more specific, the model parameters are assumed to be fuzzy random variables. For this purpose, the original problem is transformed into a nonlinear programming problem which is divided into four sub-problems to simplify the computations. Finally, the results obtained for the sub-problems can be used to determine the membership functions of the fuzzy E-Bayesian estimation of system reliability. To clarify the proposed model, a practical example for PVC window production system is conducted.

Fuzzy x- and s Control Charts: A Data-Adaptability and Human-Acceptance Approach

For sequentially monitoring and controlling average and variability of an online manufacturing process, x¯ and s control charts are widely utilized tools, whose constructions require the data to be real (precise) numbers. However, many quality characteristics in practice, such as surface roughness of optical lenses, have been long recorded as fuzzy data, in which the traditional x¯ and s charts have manifested some inaccessibility. Therefore, for well accommodating this fuzzy-data domain, this paper integrates fuzzy set theories to establish the fuzzy charts under a general variable-sample-size condition. First, the resolution-identity principle is exerted to erect the sample-statistics’ and control-limits’ fuzzy numbers (SSFNs and CLFNs), where the sample fuzzy data are unified and aggregated through statistical and nonlinear-programming manipulations. Then, the fuzzy-number ranking approach based on left and right integral index is brought to differentiate magnitude of fuzzy numbers and compare SSFNs and CLFNs pairwise. Thirdly, the fuzzy-logic alike reasoning is enacted to categorize process conditions with intermittent classifications between in control and out of control. Finally, a realistic example to control surface roughness on the turning process in producing optical lenses is illustrated to demonstrate their data-adaptability and human-acceptance of those integrated methodologies under fuzzy-data environments.

Fuzzy E-Bayesian and Hierarchical Bayesian Estimations on the Kumaraswamy Distribution Using Censoring Data

The main purpose of this paper is to provide a methodology for discussing the fuzzy. This approach will be used to create the fuzzy E-Bayesian and Hierarchical Bayesian estimations of Kumaraswamy Distribution under censoring data by introducing and applying a theorem called “Resolution Identity” for fuzzy sets. In other words, model parameters are assumed to be fuzzy random variables. The authors also use computational methods Wu (2003). For this purpose, the original problem is transformed into a nonlinear programming problem which is then divided up into four sub-problems to simplify computations. Finally, the results obtained for the sub-problems can be used to determine the membership functions of the fuzzy E-Bayesian and Hierarchical Bayesian estimations.

Demerit-Fuzzy Rating Mechanism and Monitoring Chart

The relative magnitude of weights for defects has a substantial impact on the performance of attribute control charts. Apparently, the current demerit-chart approach is superior than the c-chart scheme, because it imposes different precise-weights on distinct types of nonconformities, enabling more severe defects to disclose the problems existing in the manufacturing or service processes. However, this crisp-weighting defect assignment, assuming defects are of equal degree of severity when classified into the same defect class, may be so subjective that it leads to the chart somewhat restricted in widespread applications. Since in many cases the severity of each defect is evaluated from practitioners' visual inspection on the key quality characteristics of products or services, when each defect is classified into one of several mutually-exclusive linguistic classes, a fuzzy-weighting defect assignment that represents a degree of seriousness of defects should be allotted in accordance. Therefore, in this paper a demerit-fuzzy rating mechanism and monitoring chart is proposed. We first incorporate a fuzzy-linguistic weight in response to the severe degree of defects. Then, we apply the resolution identity property in construction of fuzzy control limits, and further develop a new fuzzy ranking method in differentiation of the underlying process condition. Finally, the proposed fuzzy-demerit chart is elucidated by an application of TFT-LCD manufacturing processes for monitoring their LCD Mura-nonconformities conditions.