Robert D. Plante

Run-Length Distributions of Special-Cause Control Charts for Correlated Processes

We derive run-length distributions of the special-cause control chart proposed by Alwan and Roberts for correlated observations, given that the assignable cause to be detected is a shift in the process mean. Both recursive and closed-form solutions are derived for the run-length distribution, average run length (ARL), and standard deviation of the run length (SRL) for any AR(p) process, and approximate solutions are derived for the more general ARMA(p,q) processes. The expressions derived do not depend on the type of shift in the process mean. Numerical results are illustrated for the ARL and SRL of the ARMA(l,l) model, given that the shift in the mean is a step shift. These results show that the ARL and SRL of the specialcause control chart are relatively smaller when the process is negatively rather than positively autocorrelated. Regardless of the sign of the autocorrelation, the shape of the probability mass function of the run length reveals that the probability of detecting shifts very early is subs...

Aggregation and Disaggregation Techniques and Methodology in Optimization

A fundamental issue in the use of optimization models is the tradeoff between the level of detail and the ease of using and solving the model. Aggregation and disaggregation techniques have proven to be valuable tools for manipulating data and determining the appropriate policies to employ for this tradeoff. Furthermore, aggregation and disaggregation techniques offer promise for solving large-scale optimization models, supply a set of promising methodologies for studying the underlying structure of both univariate and multivariate data sets, and provide a set of tools for manipulating data for different levels of decision makers. In this paper, we develop a general framework for aggregation and disaggregation methodology, survey previous work regarding aggregation and disaggregation techniques for optimization problems, illuminate the appropriate role of aggregation and disaggregation methodology for optimization applications, and propose future research directions.

Process and Product Improvement in Manufacturing Systems with Correlated Stages

Manufacturing systems typically contain processing and assembly stages whose output quality is significantly affected by the output quality of preceding stages in the system. This study offers and empirically validates a procedure for 1 measuring the effect of each stages performance on the output quality of subsequent stages including the quality of the signal product, and 2 identifying stages in a manufacturing system where management should concentrate investments in process quality improvement. Our proposed procedure builds on the precedence ordering of the stages in the system and uses the information provided by correlations between the product quality measurements across stages. The starting point of our procedure is a computer executable network representation of the statistical relationships between the product quality measurements; execution automatically converts the network to a simultaneous-equations model and estimates the model parameters by the method of least squares. The parameter estimates are used to measure and rank the impact of each stages performance on variability in intermediate stage and final product quality. We extend our work by presenting an economic model, which uses these results, to guide management in deciding on the amount of investment in process quality improvement for each stage. We report some of the findings from an extensive empirical validation of our procedure using circuit board production line data from a major electronics manufacturer. The empirical evidence presented here highlights the importance of accounting for quality linkages across stages in a identifying the sources of variation in product quality and b allocating investments in process quality improvement.

Incentive maintenance outsourcing contracts for channel coordination and improvement

Consider a manufacturer who has a process with an increasing failure rate over time. In order to improve the process performance, the following two types of maintenance activity are outsourced to an external contractor: (i) preventive maintenance is performed periodically to improve the reliability of the process when the process is functional; and (ii) corrective maintenance is used to restore the process to a specified condition when it fails. We consider the use of incentive contracts to induce the contractor to select the maintenance policy that optimizes the total profit of the manufacturer and contractor. It is demonstrated that an incentive contract based on a combination of a target uptime level and a bonus always leads to the desired win-win coordination, and provides flexibility in allocating the extra profit generated from coordination and, importantly, an incentive to the contractor to improve the efficiency of the maintenance operations. The incentive contract can also be used to select the most economically efficient contractor from multiple contractors with different maintenance capabilities.

Statistical Process Control via the Subgroup Bootstrap

The most commonly used techniques in statistical process control are parametric, and so they require assumptions regarding the statistical properties of the underlying process. For example, Shewhart control charts assume that the observations are indepe..

Process capability: a criterion for optimizing multiple response product and process design

Abstract In this research, we consider the maximization of process capability as the criterion in product/process design that is used for selecting preferred design factor levels and propose several approaches for single and multiple response performance measure designs. All of these approaches assume that the relationship between a process performance measure and a set of design factors is represented via an estimate of a response surface function. In particular, we develop; (i) criteria for selecting an optimal design, which we call MCpk and MCpm; (h) mathematical programming formulations for maximizing MCpk and MCpm, including formulations for maximizing the desirability index (Harrington, 1965) and for maximizing the standardized performance criteria (Barton and Tsui, 1991) as special cases of the formulation for maximizing MCpk, (iii) formulations for considering cost when maximizing MCpk and MCpm, (iv) a means for assessing propagation of error; (v) a robust design method for assessing design factor effects on residual variance; (vi) a means for assessing the optimality of a proposed solution: and (vii) an original application in the screening of printed circuit board panels.

A self-starting procedure for monitoring process quality in multistage manufacturing systems

Manufacturing systems typically contain processing and assembly stages whose output quality is significantly affected by the output quality of preceding stages. The deficiencies of using standard statistical process-monitoring procedures in such systems have been highlighted in the literature. This article proposes a procedure to monitor process and product quality in multistage systems. By accounting for the quality of the input to each stage, the procedure not only detects the presence of out-of-control conditions but also helps to identify the stages responsible for such departures. We extend previous research to the common case where the process parameters are unknown. An extensive performance study shows that the procedure is effective in detecting out-of-control conditions and that it convincingly outperforms existing methods. We illustrate the use of the procedure using production line data from a major electronics manufacturer. †Deceased

Multicriteria models for the allocation of design parameter targets

The allocation of process mean locations for design parameters is important in establishing the mean of a performance characteristic within performance limits. This is an especially difficult problem when there is a multivariate set of performance measures that are all functions of a common set of design parameters. We propose multicriteria models for the allocation of design parameters that either (1) attempt to minimize the deviation of performance measures from prespecified nominal values, or (2) attempt to place performance measure means well within tolerance ranges. Empirical comparisons with established procedures, via case studies and examples, are used to illustrate both the effectiveness of the proposed procedures as well as the degree of flexibility that these procedures possess for modeling a wide range of product/process design decision environments.

Run Length Distributions of Residual Control Charts for Autocorrelated Processes

A FORTRAN program is given to calculate the run length distribution (RLD), the average run length (ARL), and the standard deviation of the run length (SDRL) for residual control charts used to monitor autocorrelated process output. RLD, ARL, and SDRL values are calculated for processes that can be modeled by pure autoregressive models of order p (AR(p)), pure moving-average models of order 1 (MA(1)), and mixed autoregressive moving-average models of orders p and 1 (ARMA(p,1)), given that the assignable cause to be detected is a step shift in the process mean.

Maintenance outsourcing of a multi-process manufacturing system with multiple contractors

Consider a manufacturer with a manufacturing system that consists of multiple processes. The manufacturers revenue is determined by the minimum of the uptimes among the processes. The maintenance functions of the processes are outsourced to independent contractors so that each contractor is responsible only for one process. A performance-based incentive contract is offered to each contractor, consisting of an uptime target level and a bonus rate for exceeding the uptime target. Under the incentive contract, a contractor receives a bonus only when the achieved uptime exceeds the target level specified in the contract. We develop a model for jointly determining the uptime target levels and bonus rates for the contractors which maximize system profit. We also demonstrate the financial benefits of coordination and added flexibility in allocating the additional profit to the contractors. In addition we show the impact of the variation in individual process maintenance times and costs on channel coordination and profits.