

MILHDBK338B: Electronic Reliability Design Handbook 
 

5.6.1 Basic Concepts
5.6.1 Basic Concepts
A good way to look at basic maintainability concepts is in terms
of functions which are analogous to those in reliability. They may be derived
in a way identical to that done for reliability in the previous section by
merely substituting t (timetorestore) for t (timetofailure), m (repair rate) for
l (failure rate),
and M(t) (probability of successfully completing a repair action in time t, or
P(T £ t)) for
F(t) (probability of failing by age t, or P(T £
t)). In other words, the following
correspondences prevail in maintainability and reliability engineering
functions.
(1) 

The timetofailure probability density function (pdf)
in reliability corresponds to the timetomaintain pdf in
maintainability.

(2) 

The failure rate function in reliability corresponds to
the repair rate function in maintainability. Repair rate is the rate
with which a repair action is performed and is expressed in terms of
the number of repair actions performed and successfully completed per
hour.

(3) 

The probability of system failure, or system
unreliability, corresponds to the probability of successful system
maintenance, or system maintainability. These and other analogous
functions are summarized in Table
5.61. 
Thus, as illustrated in Figure
5.61, maintainability can be expressed either as a measure of the time (T)
required to repair a given percentage (P%) of all system failures, or as a
probability (P) of restoring the system to operational status within a period
of time (T) following a failure.
Some of the commonly used
maintainability engineering terms are portrayed graphically in Figure 5.62 as a maintainability “function” derived as
illustrated for the case where the pdf has a lognormal distribution. Points
(1), (2), and (3) shown in the figure identify the mean, median, and maximum
corrective timetorepair, respectively.
TABLE 5.61: COMPARISON OF
BASIC RELIABILITY AND MAINTAINABILITY FUNCTIONS
"1">
FIGURE 5.61: BASIC METHODS OF MAINTAINABILITY
MEASUREMENT
FIGURE 5.62: EXAMPLE
MAINTAINABILITY FUNCTION DERIVED FROM TIMETOREPAIR DISTRIBUTION
Points (1), (2), and (3) are
defined as follows:
(1) 

Mean Time to Repair, _{ct}: The mean time
required to complete a maintenance action, i.e., total
maintenance downtime divided by total maintenance actions for
a given period of time, given as




(5.75) 


where: 
l_{i} 
= 
failure rate for the
i^{th} repairable
element of the item for which maintainability is to be
determined, adjusted for duty cycle, catastrophic failures,
tolerance and interaction failures, etc., which will result in
deterioration of item performance to the point that a
maintenance action will be initiated.

_{} 
_{cti} 
= 
average corrective time required to repair the ith repairable element in the event of its
failure.
 
(2) 

Median Time to Repair, _{ct}: The downtime
within which 50% of all maintenance actions can be
completed.

(3) 

Maximum Time to Repair: The maximum time required to
complete a specified, e.g., 95%, percentage of all maintenance
actions. 
These terms will be described in
more detail in the following sections, in terms of the form that they take,
given the statistical distribution of
timetorepair.




 
 