An attribute control chart for the inverse Weibull distribution under truncated life tests

Abstract

Statistical Process Control (SPC) is applied to monitor production processes in order to discover any problems or issues that may arise during the production process and to help in finding solutions for these issues. In this paper, we consider a situation in which the product's quality, as measured by its lifetime, is monitored. Since the monitoring requires life tests to be performed and this may take relatively long time, the test time is truncated at some pre-specified time t0, chosen to be related to the product's target mean life. This results in a truncated life test. The number of failures during the life test is used as an indicator of the quality of the product. We consider the situation in which the lifetimes follow the Inverse Weibull distribution. A control chart is proposed for this specific situation, thus extending the applicability of control charts methodology to situations involving truncated life tests. Simulation techniques has been employed to obtain the quantities needed for constructing the control chart with the aim that the average run length (ARL) is close to its target value. The control chart is evaluated by obtaining the ARL values when the process is out-of-control for various values of the shift coefficient. We obtained the coefficients of the control limit and the truncation coefficient for different sample sizes and average run length target values. An example on the application of the proposed control chart is provided.