# Accession Number:

## ADA073897

# Title:

## Approximate Confidence Intervals for an Exponential Parameter from a Sequential Life Test.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## MISSOURI UNIV-COLUMBIA DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1979-08-01

# Pagination or Media Count:

## 37.0

# Abstract:

A sequential life test for the exponential location parameter was given by Epstein and Sobel 1955. This sequential test may be modified by truncating the test at r sub 0 failures andor at total test time t. There may be a need or a desire to also estimate the parameter after the test decision, using the test data. Bryant and Schmee 1979 have given confidence intervals for the mean lifetime, theta, from a truncated sequential test scheme, using methods which depend heavily on numerical techniques using a computer. A more flexible approach is considered using a martingale inequality which was also given by Wald 1947 in another context. Interval estimates are found which are functions of a positive constant d which must be chosen less than an upper bound which is itself a function of the number of failures observed. It is suggested that d be chosen as a function of the sample path i.e., after the test is complete. The validity of the confidence coefficient comes into question if this posterior selection of d is employed. Simulation studies indicate that the resulting intervals are usually conservative.

# Descriptors:

# Subject Categories:

- Statistics and Probability