Methodology To Develop A Minimum Cost Acceptance Sampling Plan For Highway Construction

Quality Assurance has always been a part of manufacturing processes. Since World War II, Acceptance Sampling has been introduced and implemented for quality control and improvement. Since statistical methods are applied for quality assurance, especially in acceptance sampling, various methods are becoming popular among the highway agencies over the period of time. As a result, several specifications have been designed to date based upon different statistical theories, each with its own advantages and shortcomings. Acceptance is a form of quality assurance which is employed as an audit tool for decision making to accept or reject the product based on its quality. A Sampling Plan has to be designed so as to define the number of samples to be tested from a given quantity of product, referred to as a Lot. Sampling tends to induce certain risks in the process of acceptance due to the fact that 100% inspection is not being carried out. These risks are generally called the Buyer\u27s Risk and Seller\u27s Risk, which are in fact the probabilities of erroneously accepting/rejecting a bad/good lot respectively due to insufficient inspection. Statistical theories provide us the means to either reduce or fix these unavoidable risks by selecting an appropriate sample size, i.e., number of samples. A sample size has to be selected in a manner that is it practical in the sense of damage to the lot while testing and also the cost of testing which increases with sample size. With the tremendous amount of highway construction each year (e.g., 82 billion dollars of highway and street construction took place in 2008 (Construction Spending, 2008)), sample size and, in turn, the risks associated play important roles in affecting economy, even with a slightest change in terms of the cost of erroneous decisions. Typically, a sample size of 3 to 7 per lot is used by highway agencies. Considering the aforementioned economical impact, the need arises for the Practical Sample Size (PSS) which is a sample size corresponding to minimum total cost of acceptance (i.e., cost of testing and costs incurred due to erroneous decisions). Many theories are designed to find minimum sample size but very little work has been done to find PSS with economic considerations for sampling plans for variables. This research has been carried out to determine whether current sample size standards are practical (i.e., cost effective). A methodology was developed to find PSS (i.e., to generate practical sampling plan) by using the variable sampling method for unknown mean and standard deviation for single and multiple acceptance quality characteristics (AQCs); considering decision and sampling costs and historical distribution of lot quality, compared with the existing sample sizes, and recommendations were made. This study shows that the sample sizes calculated with the traditional method of constant risk levels are not always practical. The major advantage of proposed plan is that it does not leave an agency with the decision of evaluating the risks involved in the sampling plan, but instead, provides it with a concrete reason to accept the sampling plan based on decision costs