A GA mechanism for optimizing the design of attribute double sampling plan Tao-ming Cheng ⁎ , Yen-liang Chen Department of Construction Engineering, Chaoyang University of Technology, Taiwan, ROC Accepted 25 July 2006 Abstract An attribute double sampling plan (ADSP) can be performed when the acceptance parameters are known. These include first sample size, second sample size, first acceptance number, first rejectable number, and second acceptance number. The acceptance parameters must match the predefined probability 1-α of accepting a lot if the lot proportion defective is at the acceptable quality level (AQL) and β of accepting a lot if the lot proportion defective is at the rejectable quality level (RQL). In addition, the parameters must be all nonnegative integers and thus the system can not be solved as a closed-form solution. As a result, the trial-and-error method is usually used to seek the solutions. This paper presents a genetic algorithms-based mechanism for facilitating the ADSP design process. Objectives of minimizing both the deviations of fitting AQL-α and RQL-β and the total sample sizes are traded off in the optimization process. Case studies show that the new mechanism can effectively locate the acceptance parameters and therefore facilitate the task of ADSP design. In addition, a computer program is developed for facilitating the task of performing the design of an ADSP. © 2006 Elsevier B.V. All rights reserved. Keywords: Attribute double sampling plan; Genetic algorithms; Quality control; Statistical sampling; Pareto optimization 1. Introduction An acceptance-sampling (AS) plan is a statement of the sample size to be used and the associated acceptance for judging an individual lot. There are different ways for classifying AS plans. One major classification is by variables and attributes. Variables are quality characteristics that are measured on a numerical scale and attributes are quality characteristics that are expressed on “go” and “no-go” basis. Performing variables sampling plan (VSP) requires basic statistical knowledge such as the calculation of standard deviation and the decision parameter as well as checking the quality index table. Contrast to VSP, attributes sampling plan (ASP) is easy to be used and does not involve statistical calculation for processing data. Construction inspectors usually do not have statistical back- ground necessary for data processing in VSP [1]. Hence, an ASP plays an important role in designing quality assurance specifications in construction. ASP can be categorized as single or double sampling depending on the number of samples taken. In a single sampling plan, the decision to accept or reject a lot is made based on one sample. However, in a double sampling plan, a second sample may be required before a lot can be judged. A lot would be accepted or rejected depending on whether the first sample conforms to the specified requirements. Otherwise, the second sample has to be taken before a decision is made. Since the sampling phase is divided into two stages, as a result, performing an attribute double sampling plan (ADSP) usually (not always) uses a smaller sample size and is commonly used in designing quality assurance specifications [2–4]. To properly design an ADSP, the users first have to focus on certain points on the operation characteristics (OC) curve which plots the probability of accepting the lot versus the lot fraction defective. These points include the AQL-α and RQL-β (as shown in Fig. 1). AQL (acceptable quality level) represents the poorest level of quality for the producer's process that the consumer would consider to accept the product. RQL (rejectable quality level) would lead the consumer to reject the product. The probability of rejecting a lot at the acceptable quality level (AQL) is α and that of accepting a lot at the Automation in Construction 16 (2007) 345 – 353 www.elsevier.com/locate/autcon ⁎ Corresponding author. 168 Gifeng E. Rd., Wufeng, Taichung County 413, Taiwan, ROC. Tel.: +886 4 23323000x4238; fax: +886 4 23742325. E-mail address: tmcheng@mail.cyut.edu.tw (T. Cheng). 0926-5805/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2006.07.003