Robust economic-statistical design of X-bar control chart

Abstract

Control charts are developed to monitor the service and production processes. The fact that many processes have uncertain parameters is a barrier to obtain the best design of the control charts. In this paper, economic statistical design (ESD) of the X-bar control chart utilising robust optimisation approach that considers interval estimates of uncertain parameters is investigated. A heuristic algorithm is developed to obtain the robust scheme of the control chart. Robust design for an industrial problem is compared with traditional ESD, and heuristic design. Numerical analyses and simulation study show that the proposed X-bar control chart offers a better approach and more reliable solutions for practitioners.

A robust optimization model for software development costs considering time value of money

“…This method aims to reduce the loss of deviation of input parameters from their nominal value and optimize the worst-case scenario for parameters using a MiniMax objective function. 23 The main reasons for using this approach in many applications are the ease of modeling uncertainty for the parameters and the simplicity of the approach in terms of computational volume and complexity. 24 To further adapt the problem assumptions to the real condition of the software industry, this research develops a robust optimization SRGM to find the best time for releasing the software and stopping the test process so that the software development costs are optimized.…”

“…Furthermore, this paper suggests a robust counterpart model by considering the interval estimates for the uncertain parameters instead of point estimates. The aim of this method (which is based on Safaei et al 23 ) is to optimize the development costs by generating a set of scenarios that may occur within the uncertain parameter intervals. It should be pointed out that in the literature, point estimates have been used for input parameters.…”

“…Model III is the main model of the current paper that considers the uncertainty for the parameters in Model II to increase the usability of the mathematical model in real situations. First, this model determines interval estimates for the uncertain parameters and then constructs a robust mathematical model according to the procedure in Safaei et al 23 and Salmasnia et al 18 This approach generates various scenarios based on the interval estimates of the uncertain parameters in which the set S 0 denotes potential scenarios of the robust mathematical model such that each scenario s 0 S 0 is obtained by a vector of the uncertain input parameters (V) as follows.…”

Economic-Statistical Design of Integrated Model of VSI Control Chart and Maintenance Incorporating Multiple Dependent State Sampling

“…In order to make the developed model more suitable for a real production environment, some constraints of the sample size, the sampling interval and the false alarm rate are added. To constitute the best protection against the high false alarm rate, the ATS of the in-control state is set to equal to 370.4 by referring to the experience of [33] and [34]. Likewise, it also has h min = 0.01, h max = 5, and n max = 20.…”

A robust S2 control chart with Tukey's and MAD outlier detectors

“…During the estimation of parameter(s) from Phase‐I, the process is assumed to be working under IC situation with no outliers, ie, . The problem of having outliers in Phase‐I samples has been discussed in detail by Rocke, Tatum, Schoonhoven et al, Safaei et al, and the references therein. This section discusses the effect of having outliers in Phase‐I samples and what can be done to minimize that effect.…”