The Statistics Involved in Availability Calculations
Abstract
The availability A is defined in terms of MTBF (Mean Time Between Failures) and MTTR (Mean Time To Repair). The best statement which can be made about either of these, based on limited measurements, is the confidence with which we can depend upon stating correctly a range of values which will include the true value of the quantity in question. To convert such statements into equivalent information about A is difficult and far from straightforward arithmetically. On the other hand, a qualitative judgment concerning A can be obtained from quantitative information concerning ranges for MTBF and MTTR. A very good procedure is available for obtaining confidence intervals with associated confidence coefficients for MTBF. The MTTR depends upon the ERT (Equipment Repair Time) and sigma(r), which is the standard deviation of the measured repair time. A good procedure for establishing confidence intervals and associated confidence coefficients for ERT exists. Unfortunately, calculation of MTTR from ERT depends on a knowledge of the true (population) sigma(r). This true value cannot be known from a restricted set of measurements. Even using an estimate leads to difficulties in arithmetic computation similar to those mentioned in connection with finding A from MTBF and MTTR. However it can be assumed that sigma(r) generally lies between 0.4 and 0.7. Therefore one can obtain a qualitative feel for the range of MTTR from quantitative confidence interval information about ERT and from the historically estimated range for sigma(r) from equipments in general.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 19, 1964
- Accession Number
- ADA032024
Entities
People
- W. A. Youngblood
Organizations
- Tracor