Model for treatment of incomplete records in preventive maintenance

In today´s semiconductor industry, the wafer throughput of some manufacturing equipment goes beyond hundreds of wafers per hour. Therefore, unavailability of a tool can delay millions of dollars of products per hour. The related cost of unavailability can be similarly huge if the safety of hazardous process gases, electromagnetic fields, and health risks are considered. Preventive maintenance is effectively used to address some of these costs and safety concerns, but sacrifices production hours to prevent failure events. Preventive maintenance scheduling relies on reliability models of critical components and subsystems. These reliability models, in turn, are developed using historical failure data for the component of interest. Complete reliability data is rarely available in the form required by most classical approaches. This is especially the case for sensitive information such as hours of operation, processed wafers, and utilization rate that happen to be the most important pieces of information for reliability analysis. Additionally the real operating time and wafer throughput is highly dependent upon the recipes run by manufacturers that may be confidential due to the competitiveness of this industry. Therefore the field data is routinely flawed by missing and incomplete data. Ignoring the incomplete records is usually not a compelling option because it results in smaller sample size which consequently reduces the statistical power of the inferred reliability measures. The significance of missing and incomplete records depends on the quality and quantity of the information they carry. For example, consider the calendar days in service and real operation time of a component. The reliability model of the component obviously concerns the latter, because the real operation time is when the underlying failure mechanism is in action (e.g. damage accumulation). When the real failure data is often sensitive and hard to obtain, the days in service information may be- readily available. One objective of this research is therefore to develop a data analysis platform in which such lateral information available on the failure data can be considered when rational decisions regarding missing records are made. Such inferences usually carry a great deal of uncertainty with them, as is the case for applications of days in service for estimation of real operational hours. The secondary objective of this research is then to employ Bayesian inference framework such that the associated uncertainties can be appropriately accounted for during the data analysis process. In the first stage of this work a correlation model is proposed for the real-time-to-failure and calendar days in service. This model utilizes the multiplicative error concept with unconventional distributions to address the mathematical constraints present in the problem. In the next step, Bayesian inference is effectively utilized to characterize the uncertainty of the proposed model. This model is later used to estimate the approximate time-to-failure from available calendar days in service for missing records. Using the point estimates from the model, one may overlook the model uncertainty concealed in the correlation. Such analytical inaccuracies will artificially boost the statistical significance of the results which may lead to overconfidence in estimation. The challenge therefore will be how to include the uncertainty of correlation model into the analysis. The proposed approach, once again, utilizes Bayesian likelihood averaging method to effectively include the model uncertainty into the subsequent reliability analysis. The case study consists of preventive maintenance scheduling for a component with flawed and incomplete dataset. In order to highlight the advantages, the results are compared with the case for which the missing records are completely ignored. The applications of proposed model for treatment of missing data shows limited impact on the best estimates o