Reliability HotWire

Issue 26, April 2003

Reliability Basics
Relationship Between Availability and Reliability

Availability is defined as the probability that the system is operating properly when it is requested for use. In other words, availability is the probability that a system is not failed or undergoing a repair action when it needs to be used. At first glance, it might seem that if a system has a high availability then it should also have a high reliability. However, this is not necessarily the case. This article will explore the relationship between availability and reliability and will also present some of the specified classifications of availability.

Availability and Reliability

Reliability represents the probability of components, parts and systems to perform their required functions for a desired period of time without failure in specified environments with a desired confidence. Reliability, in itself, does not account for any repair actions that may take place. Reliability accounts for the time that it will take the component, part or system to fail while it is operating. It does not reflect how long it will take to get the unit under repair back into working condition.

As stated earlier, availability represents the probability that the system is capable of conducting its required function when it is called upon given that it is not failed or undergoing a repair action. Therefore, not only is availability a function of reliability, but it is also a function of maintainability. Table 1 below displays the relationship between reliability, maintainability and availability. Please note that in this table, an increase in maintainability implies a decrease in the time it takes to perform maintenance actions.

Table 1: Relationship between reliability, maintainability and availability.

As you can see from the table, if the reliability is held constant, even at a high value, this does not directly imply a high availability. As the time to repair increases, the availability decreases. Even a system with a low reliability could have a high availability if the time to repair is short.

Availability Classifications

The definition of availability is somewhat flexible, depending on what types of downtimes are considered in the analysis. As a result, there are a number of different classifications of availability. In BlockSim 6, the following availabilities can be obtained directly from simulation or can be indirectly calculated with values returned from analysis:

• Point (instantaneous) availability
• Average up-time availability (mean availability)
• Steady state availability
• Operational availability

Point Availability

Point, or instantaneous, availability is the probability that a system (or component) will be operational at any random time, t. This is very similar to the reliability function in that it gives a probability that a system will function at the given time, t. Unlike reliability, the instantaneous availability measure incorporates maintainability information. At any given time t, the system will be operational if the following conditions are met:

1. It functioned properly during time t with probability R(t), or,
2. It functioned properly since the last repair at time u, 0 < u < t, with probability:

With m(u) being the renewal density function of the system.

The point availability is the summation of these two probabilities, or:

Mean Availability

The mean availability is the proportion of time during a mission or time-period that the system is available for use. It represents the mean value of the instantaneous availability function over the period (0, T):

Steady State Availability

The steady state availability of the system is the limit of the instantaneous availability function as time approaches infinity. The instantaneous availability function approaches the steady state value very closely at time approximate to four times the MTBF:

Operational Availability

Operational availability is a measure of availability that includes all experienced sources of downtime, such as administrative downtime, logistic downtime, etc. The equation for operational availability is:

 (1)

where the operating cycle is the overall time period of operation being investigated and uptime is the total time the system was functioning during the operating cycle.

When there is no logistic downtime or preventive maintenance specified, Eqn. (1) returns the mean availability of the system. The system's availability measure returned in BlockSim approaches the operational availability as more sources of downtime are specified, such as crew logistic downtime, spares logistic downtime, restock logistic downtime, etc. In all other cases, the availability measure is the mean availability. A separate availability measure, the point availability, is also returned by BlockSim.

Note that the operational availability is the availability that the customer actually experiences. It is essentially the a posteriori availability based on actual events that happened to the system. The previous availability definitions are a priori estimations based on models of the system failure and downtime distributions. In many cases, operational availability cannot be controlled by the manufacturer due to variation in location, resources and other factors that are the sole province of the end user of the product.

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