Control Charts for Zero-Inflated Binomial Models

Abstract

In this paper, we study the performance of control charts when zero-inflated counts are observed in a binomial distribution. The control charts are based on different binomial confidence interval methods, namely, np_ZIB-chart by ZIB model, np_J-chart by Jeffreys prior interval, np_w-chart by Wilson interval, np_AC-chart by Agresti-Coull interval, np_BS-chart by Blyth-Still interval and compared with the traditional Shewhart control chart, np-chart. The proportions of observed zero (φ) are studied in 0.3(0.1)0.9 and variances (σ²) are studied in 2(1)5 with a different magnitude of the shift in the nonconforming proportion (θ).The Average Run Length (ARL) and the Average Coverage Probability (ACP) are used as performance indicators. The control charts signal an out-of-control process when K consecutive points exceed an upper control limit, K = 1, 2, 3, 4, 5. The result shows that when the process is in-control, the np_w-chart is more preferable if K is low (K = 1 and 2) and φ is high (0.9) for all levels of σ². The np-chart performs better than the other control charts if K is high (K = 3, 4 and 5) and φ is also high (0.8-0.9) in all levels of σ². For the out-of-control process, when K = 2, 3 and 4, the npj-chart has a higher efficiency than the other control charts if σ² and φ are relatively low (σ² = 2 and φ = 0.3) in all levels of θ. Moreover, the np-chart is more fitting when K = 2, 3, 4 and 5 and φ is considerably high (0.9) in all levels of σ² and θ.