Jionghua Jin

State Space Modeling of Sheet Metal Assembly for Dimensional Control

In this paper, a state space modeling approach is developed for the dimensional control of sheet metal assembly processes. In this study, a 3-2-1 scheme is assumed for the sheet metal assembly. Several key concepts, such as tooling locating error, part accumulative error, and re-orientation error, are defined. The inherent relationships among these error components are developed. Those relationships finally lead to a state space model which describes the variation propagation throughout the assembly process. An observation equation is also developed to represent the relationship between the observation vector (the in-line OCMM measurement information) and the state vector (the part accumulative error). Potential usage of the developed model is discussed in the paper.

Feature-preserving data compression of stamping tonnage information using wavelets

Tonnage information is referred to as stamping force measurement in a complete forming cycle. Tonnage data contains rich information and features of stamping process failures. Due to its nonstationary nature and lack of physical engineering models, tonnage information cannot be effectively compressed using conventional data-compression techniques. This article presents a statistical method for “feature-preserving” data compression of tonnage information using wavelets. The technique provides more effcient data-compression results while maintaining key information and features for process monitoring and diagnosis. Detailed criteria, algorithms, and procedures are presented. A real case study is provided to illustrate the developed concepts and algorithms.

Optimal sensor distribution for variation diagnosis in multistation assembly processes

This paper presents a methodology for optimal allocation of sensors in a multistation assembly process for the purpose of diagnosing in a timely manner variation sources that are responsible for product quality defects. A sensor system distributed in such a way can help manufacturers improve product quality while, at the same time, reducing process downtime. Traditional approaches in sensor optimization fall into two categories: multistation sensor allocation for the purpose of product inspection (rather than diagnosis); and allocation of sensors for the purpose of variation diagnosis but at a single measurement station. In our approach, sensing information from different measurement stations is integrated into a state-space model and the effectiveness of a distributed sensor system is quantified by a diagnosability index. This index is further studied in terms of variation transmissibility between stations as well as variation detectability at individual stations. Based on an understanding of the mechanism of variation propagation, we develop a backward-propagation strategy to determine the locations of measurement stations and the minimum number of sensors needed to achieve full diagnosability. An assembly example illustrates the methodology.

Process-oriented tolerancing for multi-station assembly systems

In multi-station manufacturing systems, the quality of final products is significantly affected by both product design as well as process variables. Historically, however, tolerance research has primarily focused on allocating tolerances based on the product design characteristics of each component. Currently, there are no analytical approaches to optimally allocate tolerances to integrate product and process variables in multi-station manufacturing processes at minimum costs. The concept of process-oriented tolerancing expands the current tolerancing practices, which bound errors related to product variables, to explicitly include process variables. The resulting methodology extends the concept of “part interchangeability” into “process interchangeability,” which is critical due to increasing requirements related to the selection of suppliers and benchmarking. The proposed methodology is based on the development and integration of three models: (i) the tolerance-variation relation; (ii) variation propagation; and (iii) process degradation. The tolerance-variation model is based on a pin-hole fixture mechanism in multi-station assembly processes. The variation propagation model utilizes a state space representation but uses a station index instead of a time index. Dynamic process effects such as tool wear are also incorporated into the framework of process-oriented tolerancing, which provides the capability to design tolerances for the whole life-cycle of a production system. The tolerances of process variables are optimally allocated through solving a nonlinear constrained optimization problem. An industry case study is used to illustrate the proposed approach.

Diagnostic Feature Extraction From Stamping Tonnage Signals Based on Design of Experiments

Diagnostic feature extraction with consideration of interactions between variables is very important, but has been neglected in most diagnostic research. In this paper, a new feature extraction methodology is developed to consider variable interactions by using a fractional factorial design of experiments (DOE). In this methodology, features are extracted by using principal component analysis (PCA) to represent variation patterns of tonnage signals. Regression analyses are performed to model the relationship between features and process variables. Hierarchical classifiers and the cross-validation method are used for root-cause determination and diagnostic performance evaluation. A real-world example is used to illustrate the new methodology.

Causation-Based T2 Decomposition for Multivariate Process Monitoring and Diagnosis

Multivariate process monitoring and diagnosis is an important and challenging issue. The widely adopted Hotelling T2 control chart can effectively detect a change in a system but is not capable of diagnosing the root causes of the change. The MTY approach makes efforts to improve the diagnosability by decomposing the T2 statistic. However, this approach is computationally intensive and has a limited capability in root-cause diagnosis for a large dimension of variables. This paper proposes a causation-based T2 decomposition method that integrates the causal relationships revealed by a Bayesian network with the traditional MTY approach. Theoretical analysis and simulation studies demonstrate that the proposed method substantially reduces the computational complexity and enhances the diagnosability, compared with the MTY approach.

Quality-reliability chain modeling for system-reliability analysis of complex manufacturing processes

System reliability of a manufacturing process should address effects of both the manufacturing system (MS) component reliability, and the product quality. In a multi-station manufacturing process (MMP), the degradation of MS components at an upstream station can cause the deterioration of the downstream product quality. At the same time, the system component reliability can be affected by the deterioration of the incoming product quality of upstream stations. This kind of quality & reliability interaction characteristics can be observed in many manufacturing processes such as machining, assembly, and stamping. However, there is no available model to describe this complex relationship between product quality, and MS component reliability. This paper, considering the unique complex characteristics of MMP, proposes a new concept of quality & reliability chain (QR-Chain) effect to describe the complex propagation relationship of the interaction between MS component reliability, and product quality across all stations. Based on this, a general QR-chain model for MMP is proposed to integrate the product quality with the MS component reliability information for system reliability analysis. For evaluation of system reliability, both the exact analytic solution, and a simpler upper bound solution are provided. The upper bound is proved to be equal to the exact solution if the product quality does not have self-improvement, which is generally true in many MMP. Therefore, the developed QR-chain model, and its upper bound solution can be applied to many MMP.

State Space Modeling for 3-D Variation Propagation in Rigid-Body Multistage Assembly Processes

Dimensional variation propagation modeling is a critical enabling technique for product quality variation reduction in a multistage assembly process (MAP). However, the complex inter-stage correlations make the modeling extremely difficult. This paper aims to improve the existing techniques by developing a generic state space approach to modeling 3-D variation propagation induced by various types of variation sources in general MAPs. A concept of differential motion vector (DMV) is adopted to represent deviations with respect to four types of coordinate systems and to formulate the variation propagation as a series of homogeneous transformation among different coordinate systems. Based on this representation and formulation strategy, a novel generic mechanism is proposed to model the effect of variations induced by part fabrication processes and a MAP. A case study on 3-D variation propagation in a panel fitting process is presented to demonstrate the modeling and analysis capability of the proposed methodology.

Characterization of non-linear profiles variations using mixed-effect models and wavelets

There is an increasing research interest in the modeling and analysis of complex non-linear profiles using the wavelet transform. However, most existing modeling and analysis methods assume that the total inherent profile variations are mainly due to the noise within each profile. In many practical situations, however, the profile-to-profile variation is often too large to be neglected. In this article, a new method is proposed to model non-linear profile data variations using wavelets. For this purpose, a wavelet-based mixed-effect model is developed to consider both within- and between-profile variations. The utilization of wavelets not only simplifies the computational complexity of the mixed-effect model estimation but also facilitates the identification of the sources of the between-profile variations. In addition, a change-point model involving the likelihood ratio test is applied to ensure that the collected profiles used in the model estimation follow an identical distribution. Finally, the performance of the proposed model is evaluated using both Monte Carlo simulations and a case study.

Integration of Process-Oriented Tolerancing and Maintenance Planning in Design of Multistation Manufacturing Processes

Manufacturing systems are inherently imperfect both statically and dynamically. Tolerance and maintenance design are two major tools to address the static and dynamic imperfection of manufacturing processes (i.e., inherent process imperfection and tooling deterioration, respectively). Yet, traditionally, tolerance and maintenance designs have been studied separately to address these two critical areas of manufacturing systems. This paper presents an integrated framework of tolerance and maintenance design for multistation manufacturing processes. Two nonlinear optimization problems are formulated to minimize the overall average production cost in the long run, which includes the tolerance cost of tooling fabrication, maintenance cost, and the overall loss of quality (as a part of the objective function or as a constraint function). The proposed methodology is illustrated, analyzed, and further discussed in the context of a multistation automotive body assembly process. Extensive numerical analyses are conducted to demonstrate the efficiency of the developed methodology. Given various cost components and time horizons, the integrated design scheme is compared with traditional design schemes in terms of cost efficiency, offering new insights into the interrelation between manufacturing process maintenance and tolerancing in the context of the product life cycle. Note to Practitioners-With intensified competition as a result of economic globalization, quality and cost have become crucial factors to the success of any manufacturing industry. Decisions in the process design phase, such as process tolerance assignment and maintenance planning, play a substantial role for overall manufacturing quality and costs. Tolerance of process variables determines the inherent variation level of a manufacturing process. Preventive maintenance oversees and controls process degradation and its resulting deterioration on product quality. Significant tooling and operational costs result from both tolerancing and maintenance activities. Traditionally, tolerancing and maintenance decision-making have been studied separately. Tolerancing was mainly conducted during the design stage; while maintenance policy was often determined after a manufacturing system was designed and installed. However, tolerancing of process variables and maintenance decision-making policy are interconnected in modern manufacturing systems. Intuitively, tight initial tolerances specified on process variables are able to reduce the frequency of conducting maintenance during production, since the process can accommodate more deterioration to reduce maintenance cost; but they take a toll on tolerance cost. On the other hand, loose initial tolerances specified on process variables can lower design cost but increase the frequency of maintenance during production. Hence, there is a critical need to strike a balance between the tolerance cost of tooling fabrication and the maintenance cost of tooling replacement. This paper presents a new framework to integrate tolerance design and maintenance planning for multistation manufacturing processes. Optimization problems are formulated to minimize the overall production costs including tooling costs, maintenance costs, and quality loss. The proposed framework is illustrated in the context of automotive body assembly processes. When compared to other separated designs, this integrated design methodology leads to more desirable system performance with a significant reduction in production cost