Optimization of Exponentially Weighted Moving Average Statisitics Using Empirical Bayesian Weighting Factor

Abstract

Quality control managers are faced with the challenge of detecting out-of-control during production which may be assignable or common causes. To monitor and get quality products there is need for the use of Statistical Process Control (SPC). The study uses empirical Bayesian (EB) models for estimating Exponentially Weighted Moving Average (EWMA) statistic weighting factor. This is applied to data collected from a tyre producing company on the weight of radial car tyre of sizes 185, rim 14 Elite. A random sample of size 30 containing five subgroups was taken. The simulation was done using Markov chain Monte Carlo (MCMC) of 10000 samples. The study further obtained the values for λ (weighting factor) in the two EB models as 0.493 ≤ λ ≤ 0.506 for beta-Bernoulli model while uniform-Bernoulli model is 0.494 ≤ λ ≤ 0.506, which are useful for EWMA quality control charts. The results show that the uniform-Bernoulli model and the beta-Bernoulli model give almost identical results, which are reliable in plotting EWMA quality control charts as the classical approach.