Either you want to develop new products or wish to expand the production lines, for that it is very important to understand your available equipment can take a load of the extra processes?
You need a more equipment that performs extra tasks? Or you can be reliable on present equipment?
OK!
But how to determine your equipment is reliable?
Exactly, for that, we are going to discuss herein about the reliability calculation of equipment.
Why does our manufacturing equipment require reliability calculation?
What things we require for that?
and how it perform?
Usually, most of the manufacturing units conduct reliability calculation to understand the equipment capability for production, its reliability.
Now, the question may arise in everyone’s mind, what things that we consider as we ensure the equipment is reliable? and what are reasons that we perform reliability calculations?
There are couple of reasons that we need to reliability calculation for equipment are:
Most of the manufacturing units expect to improve the equipment performance to increase the productivity of overall production lines. It is actually a proactive measure.
There is one of the important things in any manufacturing unit is Safety! Reducing the risk of accidents during equipment operations is very important.
As we all know that the business is run for profit, cost saving is one of the important reasons that a reliability calculator is required.
The reliability calculator may provide driven data that can help the business to take decisions about appropriate requirements. Such as maintenance, repair, or replacement for equipment.
There are also several other reasons that most of the manufacturing units are performing calculation of reliability for equipment. In short, if you wish to ensure your equipment performs all the tasks you assign over the time, you have to definitely conduct reliability calculation for your equipment.
What is a reliability calculator?
A Reliability Calculator is a tool that measures the probability of a system or equipment. It helps to ensure the equipment will perform its tasks without failure over a given time period. The reliability of equipment is usually considered in the percentage. Which represents the probability of failure based on input data.
The management can take the right decisions based on the results achieved from the reliability calculator.
Using this calculator, business can get to better understand the significant problems in the equipment.
Reliability calculators mean:
“Improved equipment reliability and reduced downtime”
“Increased productivity and efficiency”
“Cost savings and improved safety”
The results from the reliability calculator can be direction for the management. They can review the existing condition of equipment to identify potential issues and deploy possible actions in case required.
Most frequent question that I always facing is:
What initial data do I need to make a reliability calculation?
Actually, it’s all depending on up to you!
To make a reliability calculator, you need some basic data such as:
- What type of equipment is?
- Describe the details of the equipment age. Actually, this is important!
- Information about the operating conditions of the equipment is very important to get accurate results from the reliability calculator. Such as temperature, vibration levels, pressure etc.
- Collect all details about maintenance history of the equipment. Most important information is describing frequency of repair, type of maintenance, all the previous repairs and replacement details.
- Complete details of failure in case occurred in specific time of period. You can also include the causes of the failure, and what repair or replacement was done.
- This can impact on its reliability; you have to include operating hours, that is actually total operating hours of the equipment.
- Include performance Metrics of the equipment. The performance metrics mean output, efficiency, and quality, which can be used to determine the impact of a failure on the equipment.
When you are expecting accurate results from the reliability calculator that estimate for specific time frame. You have to input all the necessary details that have a direct impact on equipment reliability.
Reliability Calculator Formula with Examples
Not all reliability calculators can be used for all equipment or systems. In fact, different types of reliability calculators are used depending on the type of equipment or system. Thus, the type of reliability calculator that is important for each is used.
When you think of using a reliability calculator for an instrument, the question arises how to calculate it? Also, what would be the formula for that?
So here we will describe some of the most common types of reliability calculators, along with the formulas for each. We will also include examples to understand these formulas properly.
So, let us see how these formulas work.
[ 1 ] MTBF (Mean Time Between Failures) : Reliability Calculator
This is a type of metric, that measures the average time between two consecutive failures of a system or product. Which is very popular to ensure the reliability of equipment. The MTBF is calculated by dividing the total operating time of a system or product by the number of failures occurring during that time.
Through MTBF we can get an estimate of equipment failure before failure occurs. Which makes it easy to determine the expected reliability of the instrument.
A higher MTBF value indicates a higher level of reliability, while a lower MTBF value indicates a lower level of reliability.
In short, MTBF can be used to monitor system performance over time and track improvements in reliability over time.
Formula: MTBF = Total Operating Time / Number of Failures
Example:
One manufacturing unit is going to find MTBF for Equipment “A”.
Suppose the equipment’s total operating time is: 1,000 Hours and has experienced 5 failures. So, let us calculate it:
MTBF = 1,000 hours / 5 failures = 200 hours
[ 2 ] MTTR (Hrs/Cases) Avg. Repair Time : Reliability Calculator
Average repair time. it is applied to repair systems (systems and machines to be used while repairing).
MTTR (hours/cases)
= total repair time / total number of failures
Example
The usage progress of a system is as follows. How many MTTR? (3+2+4) ÷3 = 3 Answer 3 (hours/case)
Example
Table shows the number of failures of a device and the repair time per device. How many MTTR is there?
| REPAIR TIME PER INCIDENT (HOURS) | NUMBER |
|---|---|
| 5 | 2 |
| 10 | 3 |
(5×2 + 10×3) ÷ (3 + 2 )= 8 answers 8 (hours/cases) There is a following relationship between MTTR and repair rate.
The μ is the repair rate.
Example
The repair rate for a system was 0.1 (cases per hour). How many MTTR is there? Answer 10 (hours/case)
[ 3 ] Repair rate (cases/hours) : Reliability Calculator
A measure of how many repairs were made within the unit time
Example
What is the repair rate of device A that resulted as below?
| NUMBER OF TIME | REPAIR TIME HOURS |
|---|---|
| 1st | 2 |
| 2nd | 3 |
| 3rd | 4 |
Repair rate (case/hour) = 3 (cases) ÷ (2+3+4) (hours) = 0.33333 (cases/hour) answer 0.33 (cases/hour) when rounding the third decimal place.
There is a following relationship between the repair rate and MTTR.
The μ is the repair rate.
Example
What is the repair rate with MTTR of 0.50 (hours/case)? Answer 2 (case/hour)
[ 4 ] Integrity : Reliability Calculator
The degree of maintenance is “the number of machines repaired during the unit time / the number of machines to be repaired”, while the repair rate is “the number of machines completed / the time required to repair”.
What is the degree of maintenance of the resulting device A after 3 hours?
| NUMBER OF TIME | REPAIR TIME HOURS |
|---|---|
| 1st | 2 |
| 2nd | 3 |
| 3rd | 4 |
After 3 hours, the first and second times have been repaired, but the third time has not been repaired, so 2 (case) / 3 (case) = 2/3 answer 2/3
There is a relationship between the degree of maintenance and the repair rate as follows.
M=1-e-μt
M is the degree of maintenance, and the μ is the repair rate.
Example
What is the degree of maintenance 10 hours after the start of repair of a system with a repair rate of 0.1 (cases per hour)?
M=1-e-μt=1-e-0.1×10=1-e-1=1-0.37=0.63
Answer 0.63
[ 5 ] Availability (occupancy)
The percentage of systems, machines, etc. that are ready to be used.
Availability and MTBF and MTTR have the following relationships:
Example
What is the availability when MTBF is 9 hours and MTTR is 1 hour? Answer 0.9
availability and occupancy rates are related to the following:
Availability = 1 – occupancy rate
This means that, on average, the equipment has experienced a failure in every 200 hours of operation.
[ 6 ] Distrust
Distrust =1-confidence
Example
what is the distrust of the following system?
0.9 x 0.9 = 0.81 1 – 0.81 = 0.19 Answer 0.19 distrust is synonymous with failure rate B.
when it was called the failure rate, it was usually interpreted that the failure rate (the unit is “matter / time”) is said, and the failure rate (unit none) is called distrust
[ 7 ] Failure Rate
This formula calculates the rate at which a system or component fails and is often used to estimate the reliability of equipment over time.
The failure rate is calculated based on the total operating time of the equipment and the number of failures. In fact, this gives a measure of the reliability of an equipment, that is the failure rate of an equipment within a certain period of time.
This is taken as a key input in many reliability calculations. It also includes calculation of mean time between failures (MTBF) and probability of failure. In short, the calculator uses this information to estimate the expected number of failures and expected downtime for the equipment.
Formula: Failure Rate = Number of Failures / Total Operating Time
Example:
One manufacturing unit is going to find a failure rate for Equipment “A”.
Suppose the equipment’s total operating time is: 1,000 Hours and has experienced 5 failures. So, let’s calculate failure rate:
Failure Rate = 5 failures / 1,000 hours = 0.005 failures per hour
This means that the equipment experiences 0.005 failures per hour of operation.
[ 8 ] Weibull Distribution
It is a statistical model that is very helpful in reliability calculations to describe the lifetime or failure time distribution of equipment. Product reliability or failure rate prediction is possible based on the Weibull distribution model. Thus, the calculator uses parameters of the Weibull distribution, such as the shape parameter and the scale parameter, to be useful for estimating the probability of failure at a given time.
This is very popular, as the Weibull distribution is very useful in reliability analysis and life testing. As it can model both increasing and decreasing failure rates. However, it can handle both early failure and late failure in the same model.
Formula: f(t) = (k / λ) * (t / λ)^(k-1) * e^(-(t / λ)^k)
Example:
Suppose you have data on the lifetimes of 100 light bulbs, and you want to use the Weibull distribution to model the failure behavior of these light bulbs. You estimate the scale parameter λ to be 1000 hours and the shape parameter k to be 2.
Using the CDF of the Weibull distribution, you can calculate the probability of failure before a given time. For example, to find the probability of failure before 500 hours:
F(500) = 1 – e^(-(500 / 1000)^2) = 1 – e^(-0.25) = 1 – 0.777 = 0.223
So, the probability of failure before 500 hours is 0.223, or 22.3%. This means that if 100 light bulbs are used continuously, it is estimated that 22.3 of them will fail before 500 hours.
This is a simple example to illustrate the use of the Weibull distribution in a reliability calculator. In practice, the parameters of the distribution may need to be estimated using more sophisticated methods and the results may need to be validated using additional data and statistical methods.
[ 9 ] Bathtub Curve
The Bathtub Curve is not a mathematical formula for a reliability calculator, but rather a visual representation of the expected pattern of equipment failures over time. It is not possible to calculate the Bathtub Curve as it is a representation of the general trend in failure rates over time, rather than a specific numerical calculation.
Here’s an example to help illustrate the Bathtub Curve:
Suppose we have a population of 100 identical machines that are used continuously. During the first month of operation, five machines failed due to manufacturing defects. During the next year, the failure rate decreases, with only one machine failing per month due to normal wear and tear. After several years of operation, the machines start to reach the end of their useful lives, and the failure rate begins to increase again, with two machines failing per month.
This pattern of increasing and decreasing failure rates over time can be plotted on a graph, resulting in the characteristic bathtub-shaped curve. The upward slopes on either side of the flat region represent the increasing and decreasing failure rates, while the flat region represents the period of time where the failure rate is relatively constant.
Note that the Bathtub Curve is a general representation, and the specific shape and timing of the curve will vary depending on the population of machines and the specific operating conditions.
Each type of reliability calculator has its own unique strengths and weaknesses, and it is important to select the appropriate calculator for each specific application. By using the right type of reliability calculator, it is possible to obtain a more accurate estimate of the reliability of equipment and systems, which can help organizations make more informed decisions about equipment procurement and maintenance.
[ 10 ] Reliability
This calculator helps to calculate the probability of the equipment where it identifies performance for a specific time period without failures.
Formula: Reliability = e^(-λt)
where λ is the failure rate and t are the time period.
e value = 2.71828
Example:
Suppose the equipment with a failure rate of 0.0005 failures per hour and a time period of 1,000 hours. The reliability of this equipment would be calculated as follows:
Reliability = e^ (-0.0005 * 1,000) = 0.6065
This means that the equipment has a 60.65% probability of functioning without failure for 1,000 hours.
Conclusion
In manufacturing units, equipment is very important for the running production line smoothly. Hence, the reliability of equipment is being automatically importance. Reliability in terms of reducing downtime, productivity and efficiency, cost saving etc. is associated with the word. The reliability calculator is prime tool that help the management to identify the potential issues, Obstacles, and possibilities for improvement.
The management decisions concerning the equipment can depend upon the reliability calculator. Hence, it is regular and proactive steps are necessary in most cases.
Using the reliability calculator, which equipment needs repairing, which equipment performance is being down over time etc., information can be possible to retrieve.
In short, the reliability calculator is much appreciated helpful to avoiding failures and minimize the impact of the failure of equipment during the operations.