Computer-aided variables sampling inspection plans for compositional proportions and measurement error adjustment

• A computer-aided methodology is developed for lot grading.
• Estimation of shape parameters is discussed for compositional data.
• Prior knowledge of underlying distribution determines discriminating power of plans.
• Weighted kernel density deconvolution method adjusts the measurement error effect.

Many quality characteristics encountered in the food industry are compositional proportions, e.g. protein percentage in milk powder. The distributions of these quality characteristics are intrinsically not normal as well as cannot be well-approximated by it. Moreover the shape of underlying distribution of the quality characteristic in each lot is likely to change in a short-run production process due to process adjustment actions and heterogeneity in raw materials. As a result, the standard variables sampling plans based on the normal distribution are not appropriate. The impact of measurement error, which is often strongly present in analytical testing, has not yet been well-addressed in the non-normal variables sampling inspection procedures. This paper proposes a computer-aided procedure for the identification of the underlying distribution, adjustment for the measurement error, and then the design of the sampling inspection plan. The weighted kernel deconvolution approach is employed for measurement error adjustment and a new procedure for designing a variables plan allowing for uncertainty in the shape parameters of the underlying distribution is developed.