Using T Statistic for Shewhart and EWMA Control Charts for Monitoring Mean Process with Unknown the Process Standard Deviation
Abstract
Control charts are effective tools in statistical process control (SPC) for process monitoring and quality improvement. The and the Exponentially Weighted Moving Average () charts used to determine whether the production process is in-control or out-of-control. Assuming that the quality characteristic of interest is a normally distributed random variable with mean and standard deviation .The process is in control when, otherwise, the process has shifted .But and charts are not robust enough to prevent errors in estimating the process standard deviation or a changing standard deviation, to overcome this problem , the t and charts suggested based on the statistic is a Student’s t-distribution with (n-1) degrees of freedom when the random sample of size n drawn from the process at time i .The process standard deviation of t and charts does not need to be estimated in making up the control limits.
In this paper, we discuss the used t and charts instead of and charts in detecting process mean shifts when the process standard deviation is estimated.We used t,,andcharts for monitoring a process mean for observations selected from continuous manufacturing process.The performance of t chart compared with chart in terms of Average Run Length(ARL). And the performance of chart compared with chart in terms of Average Run Length (ARL) and the Standard Deviation Average Run Length (SDRL).
The results showed that the t and charts are better than the and charts in detecting process mean shifts when the process standard deviation is unstable. In despite of the performance chart be better than t chart according to smallest value for the Average run length for several values in the process mean shifts and the process standard deviation shifts. Also, the performance chart be better than chart according to smallest value for the Average and the Standard Deviation Run Length for several values in the process mean shifts and the process standard deviation shifts and different values for the smoothing parameter of chart.
