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Acceptance sampling is the statistical method used to accept or reject product based on a random sample of the products. When done correctly, accepting sampling is effective for quality control. The acceptance number (c) and the sample size (n) are the basic objectives of any sampling plan. This study aims to construct two goal programing models for the determination of (n) and (c) with regard to four conflicting criteria. It applies non-linear integer goal programing techniques. The first model is assumed, a known and constant lot fraction defective, whereas the other model expected that it is a random variable having a Gamma prior distribution. The resulting two models were non-linear integer goal programing models. Consequently, these models could be worked out using any non-linear integer goal programing package.

The factors associated with small industrial business have a significant impact on their performance and they need to be determined considering their contribution to the business performance. This study aims to recognize a set of variables that have the paramount impact on the performance of small industrial business. It also constructs a statistical model that is used to estimate the probability of faltering for any small industrial enterprise, and to determine its expected survival time. It applies cluster analysis to classify depending on variables, i.e., faltering and non faltering using Cox's regression model. Incredibly, the obtained results show that (i) the most influential variables affecting the success or failure of a small industrial business are: establishment expenses, workers wages, and cost of marketing products, (ii) the maximum degree of risk to small industrial business was during the fifth, sixth and seventh years, and the average lifetime of a small industrial enterprise ranged from 8 to 9 years. The results indicate that stakeholders must consider the faltering variables when making business decisions and looking into the policies implementation after the ninth year of the variables adoption.