A BOOTSTRAP APPROACH FOR CONSTRUCTING CONTROL CHARTS FOR BETA-BINOMIAL PROCESSES WITH APPLICATIONS IN MANUFACTURING QUALITY

Abstract

Statistical process control (SPC) for attribute data traditionally relies on p-charts or c-charts based on Binomial or Poisson distributions, which are often inadequate for processes exhibiting over-dispersion. This paper proposes a novel bootstrapbased framework for constructing Shewhart-type control charts specifically designed for processes following a Beta-Binomial distribution (BBD). The methodology utilizes parametric bootstrap sampling to estimate empirical sampling distributions of relevant statistics, enabling accurate control limit derivation without relying on restrictive normality assumptions. Comprehensive Monte Carlo simulations demonstrate that the proposed bootstrap  and  charts effectively maintain desired in-control average run lengths (ARL) while exhibiting high sensitivity in detecting various parameter shifts. The practical utility of this approach is further validated through a real-world case study involving defective transformer counts in manufacturing, where the Beta-Binomial model provided superior fit compared to standard distributions and established reliable control limits for quality monitoring.