Keywords: attribute double sampling plan, genetic algorithms, lot-by-lot acceptance sampling.

An acceptance-sampling (AS) plan is a statement of the sample size to be used and the associated acceptance or rejection criteria for sentencing an individual lot. There are different ways for classifying AS plans. One major classification is by attributes and variables. 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 a variables sampling plan (VSP) requires basic statistical knowledge such as the calculation of the standard deviation and the decision parameter as well as checking the quality index table. In contrast to a VSP, the attributes sampling plan (ASP) is easy to use and does not involve statistical calculation for processing data. Construction inspectors usually do not have the statistical knowledge necessary for data processing in a VSP [1]. Hence, an ASP plays an important role in the design quality assurance specification in construction.

An 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 based on one sample. However, in a double sampling plan, a second sample may be required before a lot can be be accepted or rejected. This depends on whether the first sample conforms or does not conform 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, attribute double sampling plan (ADSP) usually (not always) uses a smaller sample size and is commonly used in designing quality assurance specification [1,2].

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 that is defective. These points include the AQL- and RQL-. The AQL (acceptable quality level) represents the poorest level of quality for the producer's process where the consumer would consider accepting the product. The RQL (rejectable quality level) would lead the consumer to reject the product. The chance of rejecting the AQL product is the producer's risk and the probability that a RQL product would be accepted is the consumer's risk. After the AQL- and the RQL- points being decided, a proper combination of acceptance parameters including (1) the required sample size in the first sampling, (2) the sample size in the second sampling, (3) the first accepted number, (4) the first rejected number, and (5) the second accepted number, can then be selected to match these two points on the OC curve. The binominal distribution is applied toward developing the sampling equations for acceptance parameters. 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 used to seek the solutions [3].

The smaller the total sample sizes, the less cost and time is required for the quality inspection process. This is true both from the producer's and the consumer's point of view. However, the trial-and-error method does not guarantee that the minimum sample sizes can be reached. Moreover, infeasible solutions can be obtained if the fitting of the OC curve is strictly limited by both the AQL- and RQL- points. The genetic algorithm is applied in this paper for optimizing the design process such that the ADSP is used for construction quality control. Minimizing the deviations for fitting the AQL- and the RQL- points and the total sample sizes are concerned in the optimization process. A computer program, for facilitating the ADSP design process is developed and will be presented in this paper.

1

L.-M. Chang and M. Hsie, "Developing acceptance-sampling methods for quality construction", Journal of Construction Engineering and Management, 121(2), 246-253, 1995. doi:10.1061/(ASCE)0733-9364(1995)121:2(246)

2

M. Hsie and L.-M. Chang, "Attribute-double-sampling method for infrastructure quality assurance", Journal of Infrastructure Systems, 1(2), 126-133, 1995. doi:10.1061/(ASCE)1076-0342(1995)1:2(126)

3

D.C. Montgomery, "Introduction to statistical quality control", John Wiley & Sons, Inc., New York, N. Y., 1997.

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