Optimization of Degree of Conformance in Multiresponse–Multistage Systems with a Simulation‐based Metaheuristic

Abstract

In today's manufacturing and service systems, entities are progressed across the several stages of operations wherein one or more quality characteristic may be formed. The quality of final system outputs depends on the quality of intermediate characteristics as well as design parameters in each stage. This paper presents a new mathematical program to simultaneously optimize multiple quality characteristics in multiple stage systems. Multivariate form response surface methodology is applied with iterative seemingly unrelated regression as the estimation method to extract the relationships between the outputs and inputs in each stage. Because the intermediate response variables may act as covariates in the next stages, the probabilistic patterns of the response surfaces are considered by association with the quality of the previous stages. The objective function in the proposed model is the acceptance probability of the outputs based on predefined specification limits. A combination of Monte Carlo simulation and the genetic algorithm is also proposed to solve the final stochastic optimization model. At the end, the applicability of the proposed approach is illustrated by a numerical example. IntroductionR esponse surface methodology (RSM) is a widely used approach in offline quality control and is one of the well-grounded techniques associated with the design of experiments (DOE). It statistically estimates the underlying relationships between quality characteristics, also called response variables, and controllable factors, and then, it mathematically tries to find the optimal setting of the factors that leads to the most desirable quality. Recently, RSM has expanded its capabilities as a data mining tool to approximate the function between inputs and outputs in complex systems.Applications of this method include manufacturing processes such as assembly, machining, and welding as well as service operations such as public transportation, banking systems, and any complex service systems simulated as a black box model.The classic RSM considers only one quality characteristic as a dependent variable. But as systems become more complicated, RSM is also extended in several aspects. In this regard, multiple response variables with different priorities, importance degrees, and scales of measurement 1-3 have been recently focused to achieve compromise solutions. Variance of response surfaces as a criterion for robustness has been studied to reduce total loss of quality. 4 Taking existing correlations among response variables into the account 5 would help to reach more accurate estimation as well as more precise calculations of statistical properties of the responses. There are many systems in which covariates affect the response measurements as commitment variables, so including these noise variables would help to reach more accurate and well-fitted models. 6 Degree of conformance is a measure that helps to judge a system by its rejection rate as an economic index. This measure can be calculated by using stochastic pattern...

Optimization of degree of conformance for multi‐response systems considering model imprecision: A data‐driven metaheuristic approach

“…Several works have also been done to apply GA for multi-response optimization problems. 26,[39][40][41] This paper relaxed the constraints and added them to the objective function considering a penalty factor. The parameter settings and other characteristics of the GA are provided in Appendix.…”

Multiresponse optimization of a multistage manufacturing process using a patient rule induction method

“…Finally, an optimal setting of input variables is obtained by analyzing the empirical models. Later, stochastic aspects of the empirical models were considered in Hejazi et al 24–26 …”

“…Finally, an optimal setting of input variables is obtained by analyzing the empirical models. Later, stochastic aspects of the empirical models were considered in Hejazi et al [24][25][26] On the other hand, the desirability function-based MRSO approach explained in Section 2.1 has also been proposed for optimizing the multistage process. Mukherjee and Ray 27 applied a desirability function-based MRSO approach to a two-stage grinding manufacturing process where multiple responses exist.…”

A robust multi response surface approach for optimization of multistage processes

“…(2012), Ardakani and Wulff (2013), Hejazi and al. (2014), Hejazi and al. (2015) and Bera and Mukherjee (2016).…”

“…Considering correlation could be meaningfully effective in MRO problems. Some studies on MRO besides RSM approaches have been reviewed in the works of Shah et al (2004), Khuri and Mukhopadhyay (2010), He et al (2010), Edwards and Fuerte (2011), Costa et al (2012), Ardakani and Wulff (2013), Hejazi et al (2014, 2015) and Bera and Mukherjee (2016). Recently, the correlated responses in MRO problems have been studied by Datta et al (2009), Bashiri and Hejazi (2012) and Salmasnia et al (2013).…”