A two-stage controlling procedure for the exponential failure process with high reliability

Reliability monitoring and measuring of a failure process are important issues for complex products or repairable systems. In this paper, the t-chart is used as a first controlling stage to monitor an exponential failure process. A process is considered stable when special causes for unpredictable variations have been removed from the process and all of the measurements on t-chart fall within the control limits. But, being in control of a process by statistical process control is not enough since an in-control process can produce bad or out of specification products. In order to measure the performance of the exponential failure process, a lifetime capability index denoted as L-tp is proposed. L-tp has one-to-one corresponding relationships with the lifetime conforming rate. By taking past in-control sample data of t-chart from the first controlling stage without additional sampling efforts, we develop the second controlling stage that the sampling error is considered to obtain the lower confidence bound (LCB) of estimated L-tp and to make a decision oil how well the process reliability meets specifications.