Mathematical Nonlinear Goal Programming in Quality Control

Main Article Content

Safia M. Ezzat


This paper concerned with applying suggested mathematical programming and nonlinear goal programming models to determine the producer's risk (α), consumer's risk (β) and acceptance level (c) simultaneously. The suggested nonlinear goal programming model allowed α and β values to be free and determined their values more accurately which make balance between the power of a statistical test (1-β) and level of significance α. Real quality control data are used to evaluate the performance of the suggested models . This enables decision makers in quality control to develop more accurate and free acceptance sampling plans.

Hypotheses tests, mathematical programming, nonlinear goal programming model, quality control, acceptance sampling

Article Details

How to Cite
Ezzat, S. (2019). Mathematical Nonlinear Goal Programming in Quality Control. Journal of Engineering Research and Reports, 5(1), 1-8.
Method Article


Grant EL, Leavenworth RS. Statistical quality control. 7th Edition, McGraw-Hill, New York; 1996.

Montgomery DC. Introduction to statistical quality control. 7th Edition, John Wiley & Sons, Inc.; 2012.

Chandra MJ. Statistical quality control. CRC Press LLC; 2001.

Duarte BPM, Saraiva PM. An optimization‐based framework for designing acceptance sampling plans by variables for non‐conforming proportions. International Journal of Quality & Reliability Management. 2010;27(7):794-814.

Elrefaey AMM, Hamid R, Ismail EA, Ezzat SM. Mathematical programming for statistical inference. Asian Journal of Probability and Statistics. 2018;1(1):1-8. Article no.AJPAS.41012.

Juran JM, Godfrey AB. Juran's quality control handbook. 5th Edition, McGraw-Hill, New York; 1999.

Dumicic K, Vlasta Bahovec V, Zivadinovic NK. Analysing the shape of an OC curve for an acceptance sampling plan: A quality management tool. WSEAS Transactions on Business and Economics. 2006;3(3): 169-177.

Schilling EG, Neubauer DV. Acceptance sampling in quality control. 4th Edition, Taylor & Francis Group, LLC. New York; 2017.

Mitra A. Fundamentals of quality control and improvement. 4th Edition, John Wiley and Sons, Inc.; 2016.

Ignizio JP. Goal programming and extensions. D.C. Health, Lexington, Massachusetts, U.S.A.; 1976.

Steuer RE. Multiple criteria optimization: Theory, computation and application. John Wiley, New York; 1986.

Rustem B. Algorithms for nonlinear programming and multiple - objective decision. John Wiley and Sons, Inc., New York; 1998.