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

Abstract

Reliability monitoring and performance measuring of a failure process are important issues for complex products or repairable systems. Since traditional methods of reliability monitoring and measuring for a highly reliable process have become unsatisfactory and inapplicable, a new two-stage controlling procedure for the exponential failure process with high reliability is proposed in this paper. A 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 the t-chart fall within the control limits. An in-control process can produce bad or out of specification products. To account for the specification limit specified by the customer for measuring performance of the exponential failure process, a lifetime capability index L _tp is proposed. By taking past in-control sample data of the t-chart from the first controlling stage with no additional sampling efforts, we develop a second controlling stage where the sampling error of estimated L _tp is considered. We obtain the lower confidence bound (LCB) of estimated L _tp to assess and make a decision on how well the lifetime performance of the exponential failure process meets the specification. The advantage of this second-stage controlling procedure can motivate the manufacturer to develop the reliability requirement for the process, establish an adequate reliability programme, and perform appropriate analyses and tasks to ensure the process will meet its requirements.

Keywords:

• t-chart
• reliability monitoring
• performance measuring
• lower confidence bound