System Operational Readiness and Equipment Dependability

Abstract

The concept of operational readiness of repairable systems is defined in terms of finite queueing theory as the probability that a multidevice, multimodal system will meet specified operational requirements at any given time. The primary determinants are shown to be design parameters and use parameters. Design parameters, which include reliability and maintainability (as measured by MTBF and MTR), can be lumped into a single non-dimensional design parameter, the ``dependability ratio.'' Relationship of this design parameter to single-device availability is first shown. Next, the more general cases are developed: Readiness of exactly N devices, assuming Q ≡ N repairmen (multiple or compound availability). Readiness of at least N - k devices, assuming Q ≦ N repairmen (operational readiness). Single-device availability is shown to be a special case of operational readiness in which full-time availability of a repairman is implicitly assumed. By the use of an example, certain possibilities for tradeoffs among men, machines, and operational requirements are examined, along with implications for design costs vs. procurement costs vs. personnel costs, using the nondimensional dependability ratio as a system variable. For repairable systems, the tradeoff possibilities between reliability and maintainability are indicated. Limitations of the work to date are noted, and directions for further work are indicated. An appendix contains a derivation of singledevice availability for Weibull-distributed time to failure and repair.