# The importance, purpose, and results of maintainability efforts

The main reasons for the emphasis on maintainability are the alarmingly high operating and support costs of many systems and equipment, in part due to failures and necessary subsequent repairs. Some examples of these costs are the expense of maintenance personnel and their training, maintenance-related instructions and data, repair parts, test and support equipment, training-related equipment, and maintenance facilities.

The main objectives for applying maintainability engineering principles to engineering systems and equipment are as follows [8]:

- • Reducing projected maintenance-related costs and time through design modifications directed at simplifications of maintenance.
- • Using maintainability data for estimating item/system availability or unavailability.
- • Determining labor hours and other related resources needed for performing the projected maintenance.

Past experiences indicate that when maintainability engineering principles are applied effectively to any system/product, the following results can be expected [9]:

- • Reduced downtime for the system/product and consequently an increase in its operational readiness or availability.
- • Maximizing operational readiness by eliminating failures that are due to wear-out or age.
- • Efficient restoration of the system's/product's operating condition when random failures are the cause of downtime.

# Maintainability versus reliability

Maintainability is a built-in design and installation characteristic that provides the resulting system/equipment/product with an inherent ability to be maintained, resulting in factors such as better mission availability and lower maintenance-related cost, required tools and equipment, required skill levels, and required man-hours.

In contrast, reliability is a design characteristic that results in durability of the equipment/system, as it conducts its assigned function according to a stated condition and time period. It is accomplished through actions such as choosing optimum engineering principles, testing, controlling-related processes, and satisfactory component/part sizing.

Eight of the important specific general principles of maintainability and reliability are presented below, separately for comparison purposes [10].

- •
**Specific general principles: Maintainability** - •
**I:**Reduce life cycle maintenance-related costs. - •
**II:**Reduce the amount, frequency, and complexity of maintenance-related tasks. - •
**III:**Lower mean time to repair (MTTR). - •
**IV:**Determine the extent of preventive maintenance to be conducted. - •
**V:**Provide for maximum interchangeability. - •
**VI:**Reduce the amount of supply needed. - •
**VII:**Reduce or eliminate altogether the need for maintenance. - •
**VIII:**Consider advantages of modular replacement versus repair or throwaway design. - •
**Specific general principles: Reliability** - •
**I:**Maximize the use of standard parts/components. - •
**II:**Use fewer parts/components for conducting multiple functions. - •
**III:**Design for simplicity as much as possible.

- •
**IV:**Provide adequate safety factors between strength and peak stress values. - •
**V:**Provide fail-safe designs as much as possible. - •
**VI:**Provide redundancy when needed. - •
**VII:**Minimize stress on parts and components as much as possible. - •
**VIII:**Make use of parts and components with proven reliability.

# Maintainability functions

Just like in other areas of engineering, probability distributions play an important role in maintainability engineering. They are used for representing repair times of systems, equipment, and parts. In this case, after the identification of the repair time distribution, the corresponding maintainability function may be obtained. This function is concerned with predicting the probability that a repair, beginning at time t = 0, will be accomplished in a time t.

Mathematically, the maintainability function is expressed by [8,9]

*t*

*MF(t) = jf _{r}(t)dt*

- (3.44)
- 0

where

t is time.

*f,* (t) is the probability density function of the repair time.

MF(t) is the maintainability function.

Maintainability functions for exponential, Rayleigh, and Weibull probability distributions are obtained below [8-12].

## Exponential distribution: Maintainability function

This distribution is simple and straightforward to handle and is quite useful for representing repair times. Its probability density function in regard to repair times is expressed by

= (3.45)

where

t is the variable repair time.

u is the constant repair rate or reciprocal of the MTTR.

*f _{re} (t)* is the repair time probability density function of the exponential distribution.

By substituting Equation (3.45) into Equation (3.44), we obtain

*MF _{e}(t) =*

- (3.46)
- 0

= l-e-^{g}'

where

*MR.* (t) is the maintainability function for exponential distribution.

Since p = 1/*MTTR,* Equation (3.46) becomes

A4F,.(f) = l-/^{Mrr}^'

(3.47)

**Example 3.10**

Assume that the repair times of an engineering system are exponentially distributed with a mean value of 8 hours. Calculate the probability of completing a repair within 9 hours.

By substituting the given data values into Equation (3.47), we obtain

A4F_{e}(9) = l-e’^^{9)}

= 0.6753

Thus, the probability of completing the repair within 9 hours is 0.6753.

## Rayleigh distribution: Maintainability function

This distribution is often used in reliability-related studies, and it can also be used for representing corrective maintenance times (i.e., repair times). Its probability density function in regard to repair times is expressed by

(3.48)

where

t is the variable repair time.

0 is the distribution scale parameter.

*f _{rr}* (f) is the repair time probability density function.

By inserting Equation (3.48) into Equation (3.44), we obtain

*' (t ^{2}*

_{(W)}

where

*MF _{r}* (t) is the maintainability function for Rayleigh distribution.

## Weibull distribution: Maintainability function

Sometimes this distribution is used for representing repair times, particularly for electronic equipment. Its probability density function in regard to repair times is defined by

*Mt) = ^t ^{a}-'e^* (3.50)

where

t is the variable repair time.

a is the distribution shape parameter.

0 is the distribution scale parameter.

*f _{m}* is the repair time probability density function.

By substituting Equation (3.50) into Equation (3.44), we obtain

where

*MF„,* (f) is the maintainability function for Weibull distribution.

It is to be noted that at a = 1 and *a =* 2, Equation (3.51) reduces to Equations (3.46) and (3.49), respectively. Thus, exponential and Rayleigh distributions are the special case distributions of the Weibull distribution.