DEVELOPING VSI (EWMA 3) CONTROL CHART FOR MONITORING SIMPLE LINEAR PROFILES

Control charts are used to monitor the variation of productions and processes. They can detect an outof- control signal when an assignable cause is occurred. Recently, many researchers have investigated dierent types of proles. Simple linear prole is one of the most important types of proles, which has many applications in industry, especially in calibration. The simple linear prole is characterized by a relationship between a response variable and one explanatory variable. Monitoring simple linear proles in both phases I and II is well studied in the literature. In phase I, the parameters are unknown and are estimated by historical dataset while the process parameters are known in phase II and the main aim is detecting assignable causes as quickly as possible. One of the most popular methods in phase II monitoring of the simple linear prole is EWMA 3 scheme. In the EWMA 3 scheme, three EWMA control charts are used to monitor the regression parameters of the simple linear prole, including intercept, slope and standard deviation- separately. In this paper, we specically concentrate on phase II monitoring of the simple linear proles through EWMA 3 scheme. Since the third statistic in the EWMA 3 scheme does not follow any specic distribution, we rst propose an EWMA control chart for monitoring the standard deviation instead of the third control chart used in the EWMA 3 scheme. Then, a variable sampling interval (VSI) method is proposed to improve the performance of the modied EWMA 3 control chart. In the VSI procedure, the sampling interval for the next sample depends on the current sample situation on the control chart and it varies over time. The performance of the proposed VSI EWMA 3 control chart is evaluated in terms of the adjusted average time to signal (AATS) obtained by a Markov chain approach. A numerical example is provided to demonstrate the eectiveness of the proposed adaptive control chart. The results show that the VSI EWMA 3 control chart is more eective than the FSI EWMA 3 control chart.