On the Effect of Estimation Error for the Risk-Adjusted Charts

Abstract

Control charts are a popular statistical process control (SPC) technique for monitoring to detect the unusual variations in different processes. Contrary to the classical charts, control charts have also been modified to include covariates using regression approaches. is study assesses the performance of risk-adjusted control charts under the complexity of estimation error by considering logistic and negative binomial regression models. To be more precise, risk-adjusted Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charts are used to evaluate the impact of the estimation error. To compute the average run length (ARL), Markov Chain Monte Carlo simulations are conducted. Furthermore, a bootstrap method is also used to compute the ARL assuming different Phase-I data sets to minimize the effect of estimation error on risk-adjusted control charts. e results for cardiac surgery and respiratory disease data sets show that the modified control charts improve the performance in detecting small shifts.

Monitoring multistage multivariate therapeutic processes using risk‐adjusted model‐based group multivariate EWMA control chart

“…They were followed by researchers such as Steiner et al, [41][42][43] Alemi and Olivier, 44 Cook et al, 45 Sego et al, 46,47 Cockings et al, 48 Grigg and Spiegelhalter, 49 Steiner and Jones, 50 Cook et al, 51 Chen et al, 52 Szarka and Woodall, 53 Paynabar and Jin, 54 Shojaei and Niaki, 55 Tian et al, 56 Mohammadian et al, 57 Zhang et al, 58 Zhang and Woodall, [59][60][61] and Sparks 62 who developed the risk-adjusted control charts. In recent years, Sachlas et al, 63 Begun et al, 64 Roy et al, 65 Ali et al, 66 Ding et al, 67 Rafiei and Asadzadeh, 68 Keshavarz et al, 69 Keshavarz and Asadzadeh, 70 and Kazemi et al 71 proposed some novel approaches for medical risk-adjustment monitoring. Also, Grigg and Farewell, 72 Woodall, 73 Cook et al, 74 and Woodall et al 75 reviewed the use of risk-adjusted control charts in health services.…”

Robust proportional hazard‐based monitoring schemes for reliability data

“…Olteanu 12 proposed likelihood ratio-based CUSUM control charts for right-censored data assuming Weibull distribution. Accelerated failure time (AFT) regression chart is also proposed by Asadzadeh et al 5 Zhang et al 13 presented a risk-adjusted 14 Shewhart scheme to monitor phase-1 data. Asadayyoobi and Niaki 15 discussed a general phase-1 AFT risk-adjusted chart to monitor continuous surgical outcomes using changepoint methodology.…”

Adaptive risk adjusted exponentially weighted moving average control chart based on accelerated failure time regression

“…Sogandi et al 9 proposed a risk adjusted Bernoulli chart for the process of multistage healthcare by using the state-space model with dynamic probability control limits and obtained satisfactory results under different shifts. Ali et al 10 studied to evaluate the effect of risk adjusted EWMA and CUSUM control chart conducted by the estimation error. Ding et al 11 persist in the use of the most accurate method for surgical outcomes.…”