# 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

#### Miner

##### Forum Moderator
... (except for serviceable components).

What do you mean by serviceable components? Are these components that are anticipated to wear out and be replaced (e.g., automotive brake pads)?

#### tahirawan11

##### Involved In Discussions
What do you mean by serviceable components? Are these components that are anticipated to wear out and be replaced (e.g., automotive brake pads)?
Yes, by serviceable parts i mean parts which we do expect to wear out and should be replaced before 1000 hours of operation but other components such as motor etc should last for 1000 hours of operation without failure

Thread starter Similar threads Forum Replies Date
Sample Size Calculation (Confidence Interval and Reliability) - Medical Devices Reliability Analysis - Predictions, Testing and Standards 9
S Reliability Calculation - MTBF/MTTF for Static Mounts of Rail Industry Reliability Analysis - Predictions, Testing and Standards 2
C Reliability Calculation without Failure (Success Run) Reliability Analysis - Predictions, Testing and Standards 10
D Validate 99.5% reliability 90% confidence - Sample size calculation Reliability Analysis - Predictions, Testing and Standards 4
Unfamiliar Reliability Term Reliability Analysis - Predictions, Testing and Standards 7
Reliability or robustness Reliability Analysis - Predictions, Testing and Standards 23
Reliability issue - Frequent component failure of the product Reliability Analysis - Predictions, Testing and Standards 2
Forklift Reliability Analysis Manufacturing and Related Processes 6
Reliability Testing - Weibull Analysis Help Reliability Analysis - Predictions, Testing and Standards 4
A Accelerated Reliability Demonstration Test Reliability Analysis - Predictions, Testing and Standards 4
ISO 2859-2 LQL sampling plan linked to %confidence/%reliability Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
95% reliability for calibration frequency Calibration Frequency (Interval) 7
How to Plan and Test the Reliability of Medical Devices Reliability Analysis - Predictions, Testing and Standards 1
Reliability Block Diagrams (RBDs) helper for review. Reliability Analysis - Predictions, Testing and Standards 1
K Taguchi Experiments for Factorial Design Analysis - Reliability of Minitab Results Using Minitab Software 1
Calculating Reliability for Subsystems in Series Reliability Analysis - Predictions, Testing and Standards 15
N Reliability Testing of a Single-Use (Disposable) Medical Device Reliability Analysis - Predictions, Testing and Standards 4
Regression for MTBF (Medical Device: Repairs vs Install Base) with Reliability Data Reliability Analysis - Predictions, Testing and Standards 16
Demonstration Test Plan for Reliability of Big Equipment Reliability Analysis - Predictions, Testing and Standards 5
I want to calculate reliability at 750 hours Reliability Analysis - Predictions, Testing and Standards 8
Metrology Laser Reliability General Measurement Device and Calibration Topics 2
S Reliability Software Recommendations Reliability Analysis - Predictions, Testing and Standards 4
D Cpk relation to Reliability Capability, Accuracy and Stability - Processes, Machines, etc. 4
Formula to tie together - Confidence/Reliability Level AQL? LTPD? Reliability Analysis - Predictions, Testing and Standards 3
M Defining Reliability and Confidence Levels Reliability Analysis - Predictions, Testing and Standards 8
R Standard for Reliability/Performance Test on a Electro Mechanical Device IEC 60601 - Medical Electrical Equipment Safety Standards Series 1
"Time of Demonstration" requirement for Reliability Test Reliability Analysis - Predictions, Testing and Standards 1
C Reliability Testing Protocol on a new Peristaltic Pump Reliability Analysis - Predictions, Testing and Standards 14
Reliability Lifetime Requirement Demonstration Test Reliability Analysis - Predictions, Testing and Standards 3
A Assessing a Preventive Maintenance Strategy - Reliability or Maintenance Statistics Reliability Analysis - Predictions, Testing and Standards 2
A Repairable System Reliability Analysis: Uptime/Downtime Hours, Failure Modes Data Reliability Analysis - Predictions, Testing and Standards 2
D Reliability of an Attribute Inspection based on Historical Data Capability, Accuracy and Stability - Processes, Machines, etc. 8
R Minitab - Reliability / Survival Distribution Analysis Using Minitab Software 1
C CRE (Certified Reliability Engineer) Exam 03/02/2013 Professional Certifications and Degrees 11
D Demonstration Reliability Test Formula with allowance for 'x' Failures Reliability Analysis - Predictions, Testing and Standards 6
R Military Land Vehicle Reliability with Only 1 vehicle & Only 1 Endurance Test Reliability Analysis - Predictions, Testing and Standards 5
J Reliability Prove-out, Pass-Fail Testing Reliability Analysis - Predictions, Testing and Standards 2
J Relationship between Quality, Reliability, Price and Delivery Misc. Quality Assurance and Business Systems Related Topics 7
L Determining Cpk based on a given Sample Size, Confidence Level, & Reliability Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
Is testing 99.7% reliable? Reliability Question Reliability Analysis - Predictions, Testing and Standards 3
J Reliability Centered Maintenance - Nowlan & Heap's AD-A066579 (1978) Reliability Analysis - Predictions, Testing and Standards 1
E Question on the Reliability of the Faroarm vs. Romer Arm Calibration and Metrology Software and Hardware 10
Can anyone recommend appropriate standard for Reliability Testing of Cables Other Medical Device Related Standards 3
M ERTMS/ETCS RAM (Reliability, Availability & Maintainability) Requirements Specs. Various Other Specifications, Standards, and related Requirements 2
D Reliability Growth methodology (Duane, CrowAMSAA) - Test Planning Reliability Analysis - Predictions, Testing and Standards 5
F Reliability of a System - Estimation of R(t) having constant failure rate "Lambda" Reliability Analysis - Predictions, Testing and Standards 2
B Problem with Reliability and Availability Formula Reliability Analysis - Predictions, Testing and Standards 8
C Purpose of using different Distributions to solve Reliability Problems? Reliability Analysis - Predictions, Testing and Standards 2
H What's the meaning of "a minimum 95% reliability target"? General Measurement Device and Calibration Topics 14
S Reliability Conference Suggestions Reliability Analysis - Predictions, Testing and Standards 5