A Sequential Experimental Design for Estimating a Scale Parameter From Quantal Life Testing Data

Abstract

A quanta1 life testing experiment in which failures can be detected only at inspection is discussed. If each unit is inspected only once, the data acquired are censored; the inspection time is a lower limit on failure time if the unit has not yet failed or an upper limit if it has failed. The resulting data can be used to estimate the distribution of times to failure. A sequential experimental plan for use when the distribution of times to failure is known apart from a scale parameter is introduced. Advantages of this design over other sequential plans include a computationally simple asymptotic analysis and the ability to know ahead of time the number of units to be inspected at each stage. Under certain conditions, the design is shown to be asymptotically efficient, and finite sample efficiencies are presented for the exponential distribution.

KEY WORDS:

• Asymptotic efficiency
• Destructive test
• Expected information
• Reliability
• Sequential design
• Serial sacrifice experiment