In mathematics any ratio is expressed as:

**A:B**

which is equivalent to:

** A/B**

Therefore the NFF Ratio can be expressed as:

**No Fault Found : Fault Found**

which is equivalent to:

**No Fault Found / Fault Found **

or:

**NFF/FF**

Consider the case where we receive 4 units for repair. If 3 of the units are diagnosed as NFF and 1 unit is diagnosed as a FF then we have the following NFF Ratio in percentage terms. NFF Ratio = NFF/FF = 3/1 x 100% = 3 x 100% = 300% Therefore we would have a NFF ratio of 300%.

Consider the case where we receive 4 units for repair. If 1 of the units is diagnosed as NFF and 3 units are diagnosed as a FF then we have the following NFF Ratio in percentage terms. NFF Ratio = NFF/FF = 1/3 x 100% = .3333 x 100% = 33.33% Therefore we would have a NFF ratio of 33.3% (to 1 significant figure)

]]>The number of operational units supported by the store.

A measure of how reliable a hardware product or component is. The MTBF is equal to the average number of hours that will elapse before a component fails. For most components, the measure is typically in thousands or even tens of thousands of hours between failures. For example, a hard disk drive may have a mean time between failures of 300,000 hours. The MTBF figure can be developed as the result of intensive testing, based on actual product experience, or predicted by analyzing known factors. The manufacturer may provide it as an index of a product’s or component’s reliability and, in some cases, to give customers an idea of how much service to plan for.

A measure of how many components will be returned for repair that are still serviceable (i.e. not broken). The NFF Ratio depends on a number of factors such as the experience and training of users and support staff, the accessibility of the product, and the availability of tools, test equipment and facilities for testing the component prior to return. In specialist installations where the end user is supported by a team of highly experienced well trained and well equipped engineers the NFF ratio can be as low as 2%. In consumer applications or in installations where there is a high degree of user interface or where the component is easy to remove and return to the supplier this figure could be as much as 600%. A typical figure in most industrial applications is 50%.

Learn how to calculate the NFF Ratio

A measure of how long it takes for a spare part to be dispatched to the supplier, repaired and returned to the user’s store once it has been repaired.

A measure of the number of hours the equipment operates per day.

A measure of the total number of hours that the whole fleet of equipment operates during the Repair Turn-Around-Time period.

Derived by combining the MTBF and NFF Ratio and is equal to the average number of hours that will elapse before a component is returned for repair.

The probability that a spare part will not be available in the spares pool when demanded to carry out a repair. For example a stockholding of 10 spare parts might offer a 10% stock-out-risk. This would mean that 90% of the demands for spare parts would be satisfied during the Repair Turn Around Time and 10% of the demands would not.

The average time that ought to elapse before a stock-out situation is experienced. For example a component with a 90-day repair turn-around- time and a 10% stock-out-risk should experience 1 stock-out situation in 10 repair periods. This would mean that there should be 1 stock-out situation in 900 days (i.e. 10 repair periods x 90 days). Therefore, the MTBSO would be 900 days or around 2.5 years.

The cost of the product or component being analyzed.

]]>

Often requirements documents will specify something like, “spare parts availability shall be 95%”. What does this mean? Nothing. For an availability goal to be meaningful it must combine the availability goal and the time frame. Therefore, “spare parts availability measured in any 30 day period shall be 95%” would be correct.

Most project sponsors don’t really understand what 95% spare parts availability measured in a 30-day time frame means. As I am sure you know, it actually means that on average you should expect a stock-out situation every 600 days (see calculation below). I wonder how many project sponsors actually appreciate this when they compile their requirements documents.

MTBSO is defined by the following equation:

**[Mean Time Between Stock-Out] = [Replenishment Delay] / [Probability of Unavailability]**

Using the previous example: 95% spare parts availability – 30-day time frame

MTBSO = 30 days / [1 – 0.95] = 30 / .05 = 600 days (1.67 years)

Using the MTBSO brings the following benefits:

Using the MTBSO figure there is no chance that anybody can make a mistake. The measurement period and the availability goal are combined into one easy to interpret value.

Everybody in the team can understand that in 10 years we are likely to experience 5 stock-out situations if we have a MTBSO of 2-years.

]]>

- Spares Calculator forecasts [Stock-Out-Risk] and [Mean Time Between Stock-Out]
- Many organisations prefer to specify a [Probability of Availability]
- Analysts need to understand the relationship between these parameters

Many organisations prefer to specify a [Probability of Availability] for their Spare Parts rather than [Stock-Out-Risk] or [Mean Time Between Stock-Out]. For example, a specification might state that the all parts shall have a [Probability of Availability] of 0.95 (or 95%) measured in a 30-day period. So how can you convert between the three values?

We now prove the relationship between [Stock-Out-Risk] and [Probability of Availability]

We start with the fundamental statistical axiom that the probability of a certainty is 1.

[Probability of a Certainty] = 1 (eq1)

We also know that it is certain that a part will either be Availability or Unavailability.

Therefore:

[Probability of Availability] + [Probability of Unavailability] = 1 (eq2)

By transposing we get:

[Probability of Availability] = 1 – [Probability of Unavailability] (eq3)

And:

[Probability of Unavailability] = 1 – [Probability of Availability] (eq4)

Now:

Stock-Out-Risk is defined as:

[Stock-Out-Risk] = [Probability of Unavailability] x 100% (eq5)

Or:

[Stock-Out-Risk] = (1 – [Probability of Availability]) x 100% (eq6)

By transposing we get:

[Probability of Availability] = 1 – ([Stock-Out-Risk] / 100%) (eq7)

Therefore, we have proven the relationship between the [Probability of Availability] and [Stock-Out-Risk].

We now prove the relationship between [Mean Time Between Stock-Out] and [Probability of Availability]

[Mean Time Between Stock-Out] = [Replenishment Delay] / [Probability of Unavailability] (eq8)

But:

[Probability of Unavailability] = 1 – [Probability of Availability] (eq9)

Therefore:

[Mean Time Between Stock-Out] = [Replenishment Delay] / 1 – [Probability of Availability] (eq10)

Or:

[Probability of Availability] = 1 – ( [Replenishment Delay] / [Mean Time Between Stock-Out] ) (eq11)

A procurement authority states:

All spare parts shall have a [Probability of Availability] of greater than 0.95 (or 95%) measured in a 30-day period.

Convert this into a corresponding [Stock-Out-Risk] goal:

Equation 5a states:

[Stock-Out-Risk] = (1 – [Probability of Availability]) x 100%

[Stock-Out-Risk] = (1 – 0.95) x 100%

[Stock-Out-Risk] = 5%

Therefore, we can convert the statement to read:

All spare parts shall have a [Stock-Out-Risk] of less than 5% measured in a 30-day period.

A procurement authority states:

All spare parts shall have a [Probability of Availability] of greater than 0.95 measured in a 30-day period.

Convert this into a corresponding [Mean Time Between Stock-Out] goal:

Equation 9 states:

[Mean Time Between Stock-Out] = [Replenishment Delay] / 1 – [Probability of Availability]

[Mean Time Between Stock-Out] = 30/(1-0.95)

[Mean Time Between Stock-Out] = 600 days

Therefore, we can convert the statement to read:

All spare parts shall have a [Mean Time Between Stock-Out] of greater than 600 days.

Notice that the [Mean Time Between Stock-Out] encompasses both the availability figure and the 30-day period in one single parameter.

]]>With this in mind, one of our customers recently asked:

The budgets of our customers are being continually slashed, yet they still want and need the same level of spare parts support. Is there a way of using Spares Calculator to help them spend their money more wisely so that they get the best spare parts ranging and scaling package within their budget?

This is a good question and the answer is obviously yes, but you need to be careful that you don’t end up being pressurized into promising unrealistic service levels. Here are some ideas that might help you achieve the same levels of risk at a reduced cost.

Here is a list of the key spare parts logistic parameters:

- Units in Service
- Daily Operating Hours
- MTBF (Mean Time Between Failure)
- NFF Ratio (No Fault Found Ratio)
- Repair Turn Around Time
- Unit Cost

Now let us consider how we can tune each of the key logistic parameter to maximise our Operational Availability and minimize our Life Cycle Costs.

The Units in Service are controlled by the customer and as a supplier you have no control over this parameter.

The Daily Operating Hours is another parameter that is controlled by the customer and as a supplier you have no control over this parameter.

Consider the MTBF parameter. Unless you redesign the equipment this figure is fixed.

In theory it is possible to improve upon this the NFF Ratio by introducing local filtering equipment and by providing additional maintenance training. You could use Spares Calculator to compare the additional training and test equipment costs to the spare parts cost savings.

The Repair Turn-Around-Time can have a massive impact on the required quantity of spare parts and it might be possible to offer some kind of expedited repair policy in extreme circumstances. This is sometimes called a crisis resupply policy. In this situation you would need to produce two risk calculations. The first in the normal mode of operation and the second in the crisis state.

The Unit Cost is a no brainer and it would be an insult to the reader’s intelligence to state that reducing the unit cost would reduce the overall Life Cycle Cost.

In summary, there are few parameters that you can control when optimizing your spare parts inventory. The operational parameters are fixed by the client. The supplier can influence the NFF ratio, the Repair Turn-Around-Time and the Unit Price. It’s just a matter of trading-off the cost of various logistic scenarios.

]]>How should I model with items that have a discard on failure repair policy in Spares Calculator?

The short answer to this question is that the repair policy does not affect the calculation. What matters is how long it takes to replace the part. Spares Calculator is based on the Poisson distribution which is used to forecast the projected number of events that might occur when you actually expect something else.

For example, it would be reasonable to expect an item with an MTBF of 1000 hours to fail once in 1000 hours of operation. However, in real life there is actually a 0.05% chance of 5 failures during a 1000 hour operating period.

A helicopter is equipped with a hermetically sealed low-noise GPS amplifier that has a discard on failure repair policy.

**The logistic data is as follows:**

LRU: Low-noise GPS Amplifier

Helicopters in Service: 160

LRUs per Helicopter: 2

Daily Operating Hours: 4

Mean Time Between Failures: 250,000

No Fault Found Ratio: 5%

Provisioning Delay: 180 Days (Equivalent to Repair Turn-Around-Time)

Unit Cost: $4,750

MTBSO Goal: > 100 Years

[160 Helicopters in Service] x [2 LRUs per Helicopters] = 320

By entering that data in the into Spares Calculator you can see that we would need to procure 4 spare amplifiers at a total cost of $19,000.00 to meet a MTBSO (Mean Time Between Stock-Out) goal of greater than 100 years.

]]>

I have a unit that with a lifetime of 10 years and I want zero stock-out-risk. How many spare parts should I recommend?

The short answer to this is infinity spare parts. Only infinity spare parts could achieve a zero per cent stock-out-risk. Obviously this isn’t very helpful and therefore we need to strike a compromise. But how much risk should you accept?

This depends on what effect the stock-out situation would have on your operation. If the LRU was a low-cost desktop telephone that could be replaced in 30 minutes by visiting a local electrical store then it would be reasonable to accept a very high chance of stock-out. The crisis resupply policy would be to drive to a local store and buy another.

If the LRU was a mission-critical klystron amplifier with a 2-year replenishment delay and a failure would be catastrophic then we need to make sure we minimize and mitigate any risk of outage. We could minimize our risk by making sure we have enough spare parts to cover the replenishment period and we might also agree a crisis resupply contract with the supplier and maybe a collaborative partner.

So what is the answer then? Unfortunately, there isn’t one. All a consultant can do is model the scenario and present the figures to the decision makers. It is the responsibility of the project sponsor to decide how much risk the organisation should accept and the decision should be recorded somewhere in the project documentation (possibly the project log or the minutes of a project meeting).

A common technique used in scenarios like this is called a Sensitivity Analysis (or What-If) analysis. Here we would model lots of different scenarios and measure the impact on our operation.

Thankfully, Spares Calculator simplifies this task by presenting data in graphical and tabular formats making it easy for decision makers to make the critical choice.

]]>Here is a question that was recently asked by one of our customers:

1) I have an item that will not be repaired nor is there a possibility the item can get resupplied from the vendor, nor will it get tested for faults, so I believe the No Fault Find Ratio and repair turnaround time is not relevant in my situation.

2) When the item fails a new item will be issued from stores and the failed item will not get tested nor will the item get replaced. I need to find out what the ideal sparing is based on no testing, no resupply and no repair for item.

3) Adjusting the No Fault Find Ratio and Repair Turn Around Times adjusts my recommended spares level, what should I put into the model to indicate a no testing, no resupply, no repair inventory management policy?

The client is describing what is known as a **“discard on failure repair policy”** and because there will no chance of resupply from the supplier the client will need to forecast the requirements for what is known as a **“lifetime buy”**.

* Light bulbs are examples of items that have a discard on failure repair policy.*

The client assumes that the “**No Fault Found Ratio”** is irrelevant. This is incorrect. Items will still be removed in error. Testing might not be conducted but the NFF ratio will still be present. In real-life maintenance, people remove LRUs and either discard them or send them back for repair when there isn’t anything wrong with them.

* I recently watched a maintenance engineer repair a central heating boiler under warranty and he must have removed and discarded at least four items before he fixed the fault.*

What should you do if you do not know the NFF Ratio?

In this case the Project Manager should liaise with maintenance specialists and subject matter experts to try to establish a reasonable figure. A technique called **“Qualification by Similarity”** can be adopted where other similar installations are reviewed and reasonable figures deduced. Once a figure has been established it should be recorded somewhere in the project documentation. Often logistic specialists will approximate by guessing a figure without consulting subject matter specialists. This is obviously to be discouraged.

The client also assumes that the “**Repair-Turn-Around-Time”** is irrelevant. This is also incorrect. In this case it would be better to think of a **“Replenishment Delay” **rather than a Repair-Turn-Around-Time.

Nearly all spare parts forecasting solutions use the **Poisson Distribution** to forecast the likelihood of a certain number of events occurring when something else is expected.

In this situation we are trying to establish the likelihood that we will run out of spare parts during the life of the equipment.

The Replenishment Delay in a Lifetime Buy situation is the whole life of the equipment. For example, if the system will have an operational life of 20-years then the Repair-Turn-Around-Time becomes 20-years.

Consider the following example. An aircraft Flight Management System has a special memory chip that is going out of production. The aircraft is expected to operate for a further 20-years and the operator needs to perform a Lifetime Buy. How many parts should the operator order?

Equipment: ABC Memory Chip

Aircraft in Service: 146

LRUs Per Aircraft: 6

Chips Per LRU: 12

Daily Operating Hours: 18 hours/day

Mean Time Between Failure: 600,000 hours

No Fault Found Ratio: 20%

Expected Life: 20 years

Unit Cost: $146

MTBSO Goal: > 1000 Years

[146 Aircraft in Service] x [6 LRUs Per Aircraft] x [12 Chips Per LRU] = 10,512

[20 years] x [365.25 days/year] = 7305 days expected lifetime

By entering that data in the into Spares Calculator you can see that we would need to procure 2,873 memory chips at a total cost of $419,458.00 to meet a MTBSO (Mean Time Between Stock-Out) goal of greater than 1000 years.

]]>

Spares Calculator has given us a scientific way to work out how many spare parts we need. We tested Spares Calculator on a random sample of 20 line items used in our 12 operations spread across Asia. The results were amazingly accurate. We now have an enterprise licence and use Spares Calculator to workout how many spares we need and where to deploy them.

Spares Calculator is now being used to:

- Calculate shortfalls
- Redistribute spares
- Procure additional spares
- Identify possible resale opportunities
- Justify capital investments

And the results? With minimal training users quickly identified the optimum levels of stock required by each facility and redeployed where necessary. This greatly reduced the risk on the operation leading to less outages.

In the words of the company’s SVP of Operations:

]]>By using Spares Calculator we have learned to use our existing assets more effectively. Over the past year we have worked hard to reduce the risk on our operations by deploying our spares where they are needed. We have also identified certain shortages and Spares Calculator has helped us to justify an increase in our MRO budget to cover those items. Now we have started to look at how we can dispose of some of our redundant stock to recover some capital. Spares Calculator has been an excellent investment.

Please provide a full mathematical justification on how the supplier intends to support our whole fleet with the proposed level of spares.

The supplier had recently started using Spares Calculator and they responded with a fully justified technical note showing that the proposed figures were correct. The analysis also showed that there was a fundamental flaw in the customer’s logistic model and the customer was invited to take part in a logistics planning workshop.

We first started using Spares Calculator when a military customer asked us to justify our spare parts figures. Spares Calculator showed that the customer’s logistic model was flawed and as a result they increased their Spare Parts order from $800,000 to over $3,000,000.

Spares Calculator was used as a presentation tool during the workshop and the supplier and customer worked together to define a new logistic model based on the validated statistical data that Spares Calculator provided.

And the results? With minimal training, Spares Calculator gave the supplier the accurate data needed to support the proposal and develop a long-term revenue generating relationship.

By showing the accurate risk of equipment failure and quantifying the associated costs the supplier was able to:

- Demonstrate professionalism.
- Justify the proposal with validated risk and cost data.
- Eliminate outages by identifying the correct level of spares.
- Increase repeat business by strengthening relationships.

In the words of the VP of Bids and Marketing:

]]>We are absolutely delighted with the way that Spares Calculator has helped us to improve our bid process and the way we justify our spare parts proposals.