Nurul Hila Zainuddin, Muhamad Safiih Lola, Nur Shazrahanim Kamar

The Performance of BB-MCEWMA Model: Case Study on Normal & Non-Normal Data

The dependent and non-random information data is given a special concern in Statistical Process Control (SPC). This kind of data is best defined as autocorrelation data and it’s commonly found in financial and chemical process fields. The uniqueness of autocorrelation data comes from its nature where the current data can be described to be dependable with previous data. In SPC, an extensively research on monitoring the autocorrelation data done by applying the Autoregressive (AR) base chart compared to the alternative chart such as Moving Centerline Exponentially Weighted Moving Average (MCEWMA). In this study, the alternative chart is considered to use due to its advantage on detecting small shift that occur in process mean. However, monitoring the autocorrelation seems to have an indirect issue where it is often influenced by inaccurate estimation, especially in the base model. The inaccurate estimation will eventually causing some major problems where the model tend to give low performance of effectiveness. Thus, in this study, an approach is given to the base model of MCEWMA chart as a solution for the inaccuracy estimation issue. The approach is double bootstrap, where it is basically used the error of model for sampling with replacement method. The main objective of this approach is to reduce the error value in model as a solution to reduce the inaccuracy of estimation. Continuity with this, a new modelling of Double Bootstrap MCEWMA (BB-MCEWMA) chart is introduced in this study. The focus on this study is limit to the base model only. The performance of hybrid model will tested in Monte Carlo simulation study using normal and non-normal distribution. As for comparison, the MCEWMA and Single Bootstrap MCEWMA (B-MCEWMA) also are used in this simulation study. Basically, the performances of models are tested in terms of effectiveness of point estimator and interval estimator. An interesting finding in both distributions is that new model; BB-MCEWMA gives smallest value of bias and error (MSE and RMSE) and shortest length of intervals (Normal, Student’s-t and BCa) compare to non-hybrid and single approach bootstrap model. Thus, it is proven statistically that BB-MCEWMA increase the accuracy of model estimation whether in normal or non normal data distribution.

Keywords:

double bootstrap mcewma monte carlo simulation, point estimator, interval estimator,

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