# Reliability calculation for repairable system

#### tahirawan11

##### Involved In Discussions
Hi,

I have two machines which are running under life time test. Every time a component of the machine fails, the component is replaced with a new component and the lifetime test is resumed until the full lifetime of the machine is achieved. I would like to know how to calculate the reliability of the machine at the end of lifetime test?

#### Miner

##### Forum Moderator
Try using the Mean Cumulative Function (MCF).

#### Steve Prevette

##### Deming Disciple
Super Moderator
Do I assume your test is - What is the lifetime of the machine given I can replace individual components and get it running again?

If so, and you are trying to state to a customer what the lifetime of the machine is, I would also include the "availability" of the machine - that is - a comparison of the total amount of time the machine was down for replacement of a component, divided by the total amount of time the machine "should have" been running if there were no component failures.

I would think it disingenuous to state the machine had a certain life, but required replacement of parts to get there.

#### tahirawan11

##### Involved In Discussions
Hi Steve,

We have a requirement to demonstrate a Reliability of R90C60 but due to resources limitations we can test only 2 - 6 machines (the lifetime runs in hundreds of hours and it is expensive to re start the test after a component failure). In this scenarios what kinds of life time test you will suggest and what to report to customers?

This also brings a question in my mind that we sometime struggle to answer when discussing with marketing. How to define the 'Lifetime' of a product because you can always repair or replace a component and increase the lifetime of the product. For e.g in a car you can replace the complete engine or rework the chassis and the lifetime of the car will increase accordingly.

#### Miner

##### Forum Moderator
This sounds like you are more interested in defining the durability or useful life of the machine. This is a balance between the increasing expense of repairing the unit versus the value remaining in the equipment. In your car example, the failures (quantity, expense of, and frequency) increases as the car ages. In addition the value of the car decreases. At some point the car is no longer worth the expense of a repair. Say the car is 20 years old with 300,000 miles and needs a new water pump. Yes, you could repair it and keep it going, but is it worth the expense?

#### Steve Prevette

##### Deming Disciple
Super Moderator
Hi Steve,

We have a requirement to demonstrate a Reliability of R90C60 but due to resources limitations we can test only 2 - 6 machines (the lifetime runs in hundreds of hours and it is expensive to re start the test after a component failure). In this scenarios what kinds of life time test you will suggest and what to report to customers?

This also brings a question in my mind that we sometime struggle to answer when discussing with marketing. How to define the 'Lifetime' of a product because you can always repair or replace a component and increase the lifetime of the product. For e.g in a car you can replace the complete engine or rework the chassis and the lifetime of the car will increase accordingly.

In my experience, "lifetime testing" usually means how long with the system keep running until something causes it to fail, to stop doing its function. Now perhaps you could have a "minor failure" that would not affect the operability of the system, and I would keep the machine / system running. But I would say that once the system stops functioning, and you have to do something to repair it (or replace a component) then that was "end of life failure".

Again, depends on what the customer is asking for in the specification. For example, in the "real world" you do preventive/predictive maintenance on you automobile. By the fact you change the oil every so often, you extend the life of the automobile. In the "real world" I am also looking at, through Corrective Maintenance and Preventive Maintenance programs, what is the expected life cycle dollar cost to maintain the machine, and what can I expect for an availability rate (Mean Time Between Failure and Mean Time to Restore).

Without knowing the details of what you are testing, and more important, WHY are you testing it, hard to give firm advice.

#### Miner

##### Forum Moderator
The following are definitions of some terms. Review them and determine which best describes your goal.

RELIABILITY: The probability of an item operating for a given amount of time without failure. More generally, reliability is the capability of parts, components, equipment, products and systems to perform their required functions for desired periods of time without failure, in specified environments and with a desired confidence.

DURABILITY: The probability that an item will have a relatively long, continuous useful life, without requiring an inordinate degree of maintenance.

Is your goal to quantify the failure free operation or overall useful life given occasional repairs?

#### tahirawan11

##### Involved In Discussions
The following are definitions of some terms. Review them and determine which best describes your goal.

RELIABILITY: The probability of an item operating for a given amount of time without failure. More generally, reliability is the capability of parts, components, equipment, products and systems to perform their required functions for desired periods of time without failure, in specified environments and with a desired confidence.

DURABILITY: The probability that an item will have a relatively long, continuous useful life, without requiring an inordinate degree of maintenance.

Is your goal to quantify the failure free operation or overall useful life given occasional repairs?
The test subject is a Floor Scrubber (Floor care machine) and the 'desired period of time' is 1000 hours of operation without failure (except for serviceable components). Therefore if a component fails before 1000 hours we need to improve the design of the component and continue the test but we do not want to restart the test from beginning every time a component fails as it is expensive and time consuming and once machine reaches 1000 hours of testing i need to calculate the reliability @ 1000 hours