New Shewhart and EWMA Type Control Charts using Exponential Type Estimator with Two Auxiliary Variables under Two Phase Sampling

Abstract

In this paper, two new control charts have been proposed, one is shewhart-type and other one is EWMA-type control chart. The proposed control charts are based on the exponential type estimator for mean proposed by Noor-ul-Amin and Hanif (2012). We name them as DS-Shewhart control chart and DS-EWMA control chart. The results shows that the DS-Shewhart control chart shows more efficient results to traditional/simple Shewhart  and EWMA control charts whereas, the DS-EWMA control chart shows more efficient results to traditional Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts because they uses the information from two phase sampling with two auxiliary variables. The proposed control charts can be used for efficient monitoring of the production process in manufacturing industries. The control limits of the proposed chart are based on estimator, its mean square errors and bias. A simulated example has been used to compare the proposed and traditional/simple EWMA and CUSUM control charts performance based on the average run length-out of control (ARL₁). It is observed that the proposed chart performs better than existing EWMA and CUSUM control charts. At the end of the paper a real life implementation of the proposed control charts is also provided.