Choosing a reliability inspection plan for interval censored data

ABSTRACT

Reliability test plans are important for producing precise and accurate assessment of reliability characteristics. This article explores different strategies for choosing between possible inspection plans for interval-censored data given a fixed testing timeframe and budget. A new general cost structure is proposed for guiding precise quantification of total cost in inspection test plan. Multiple summaries of reliability are considered and compared as the criteria for choosing the best plans using an easily adaptable method. Different cost structures and representative true underlying reliability curves demonstrate how to assess different strategies given the logistical constraints and nature of the problem. Results show several general patterns exist across a wide variety of scenarios. Given the fixed total cost, plans that inspect more units with less frequency based on equally spaced time points are favored due to the ease of implementation and consistent good performance across a large number of case study scenarios. Plans with inspection times chosen based on equally spaced probabilities offer improved reliability estimates for the shape of the distribution, mean lifetime, and failure time for a small fraction of population only for applications with high infant mortality rates. This article uses a Monte Carlo simulation-based approach in addition to the commonly used approach based on the asymptotic variance and offers comparison and recommendation for different applications with different objectives. In addition, the article outlines a variety of different reliability metrics to use as criteria for optimization, presents a general method for evaluating different alternatives, as well as provides case study results for different common scenarios.

KEYWORDS:

• cost ratio
• cost structure
• equally probability-spaced plan
• equally time-spaced plan
• inspection frequency
• mean time to failure
• percentile life
• Weibull distributions

Additional information

Notes on contributors

Lu Lu

Lu Lu is an Assistant Professor of Statistics in the Department of Mathematics and Statistics at the University of South Florida in Tampa. She was a postdoctoral research associated in the Statistics Sciences Group at Los Alamos National Laboratory. She earned a doctorate in statistics from Iowa State University in Ames, IA. Her research interests include reliability analysis, design of experiments, response surface methodology, survey sampling, and multiple objective/response optimization.

Christine M. Anderson-Cook is a Research Scientist at Los Alamos National Laboratory in the Statistical Sciences Group. Her research areas include design of experiments, response surface methodology, reliability, multiple criteria optimization, and statistical engineering. She is a Fellow of the American Statistical Association and the American Society for Quality.