Spares Calculator provides the scientific justification needed to support a military spare parts order worth more than $3,000,000.

A supplier of military equipment was asked to bid for a large naval retrofit program. During the tender evaluation process the supplier received a clarification request from the customer which stated:

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.

Spares Calculator helps a global manufacturer to optimize their spare parts deployments, maximize system availability and minimize their through life costs.

Is it possible to maximize system availability and minimize through life costs? According to a Fortune-500 global manufacturing company it can. A few years ago the company’s 6-sigma team became aware of Spares Calculator and decided to run a trial. The results showed that all of their sites were over-stocking on certain line items and under-stocking on others.

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.

Mathematical Models

Spares Calculator optimizes spare parts using a logorithmic poisson distribution as prescribed by Dr Sherbrooke and Dr Feeney in their work for the US DoD in the 1960’s. These models are now the industry standard and are used in nearly every spare parts program on the market today. The following papers describe more about mathematical models used within Spares Calculator.

Reference papers:

1. A System Approach to Base Stockage of Recoverable Items, G. J. Feeney and Craig C. Sherbrooke, The Rand Corporation, 1965.
2. METRIC: A Multi-Echelon Technique for Recoverable Item Control Sherebrooke, The Rand Corporation, 1967.

Assumptions

Spares Calculator returns accurate results provided the input data is accurate and the equipment is in the level section of the reliability bath-tub curve. This is also known as the active life region. The equipment must not be in the infant mortality or wear out region of life and the MTBF must be stable. At this point failures are said to occur stochastically (randomly) and can be forecast using statistics. Fortunately, advances in statistical process control, reliability engineering and production screening mean that it is usually correct to assume that equipment released from quality control has a stable MTBF.

Validation

Spares Calculator was first launch in 2002. Prelaunch the Spares Calculator models were validated in thousands of trials against credible reference texts such as those listed below. Since that time the program has undergone hundreds of real-life company trials and is used globally in numerous industries by the biggest and most successful companies in the world.

References:

1. U.S. Navy, Reliability Engineering Handbook, NAVAIR 01-1A-32
2. B L Hansen, Quality Control, Prentice Hall Inc. Englewood Cliffs
3. U.S. Navy, Maintainability Design Criteria Handbook for Designers of Shipboard Electronic Equipment, NAVSHIPS 94324

Training Objective

At the end of this tutorial you will have a general understanding of the spare parts optimization process in a single tier logistic system using Spares Calculator Professional.

Project Brief

A national mobile phone operator is about to deploy a new generation of power amplifiers and before they go into service they need to find out how many spare parts they need to buy, how much it will cost and what’s the risk.

Transcript

A Fictional US Mobile Phone Operator 

Part 1 

Consider the following example.

We work for a company called vPhone and vPhone are a national US mobile phone operator.

vPhone are about to upgrade their system by deploying improved power amplifiers and before they go into service they’re going to need to find out exactly how many spare parts they are going to need to buy.

vPhone have divided their support system into 50 regional stores. One in each state across the United States of America.

Now, for simplicity we are going to assume that each regional store supports 1000 antenna towers.

In real life they would support varying numbers, but this will make this example much easier.

Each antenna tower operates 24-hours per day and is equipped with 6 power amplifiers.

Each has a guaranteed MTBF 250,000 hours, a NFF ratio of 5% and cost $2,100 USD each.

Finally, vPhone has agreed a 30 day collect-repair policy with the supplier.

This means that broken units will be collected by the manufacturer using a courier and returned to the store within 30 days.

Part 2

Let’s enter this data into Spares Calculator.

To save time I’m going to open up a file that I saved earlier.

Let’s start with the project data.

We’re calling the project the vPhone PAU – PAU stands for Power Amplifier Upgrade.

And we are looking at one single Generic Regional Store.

The equipment is a Tower Mounted Power Amplifier

And this has a part number of AN-98-76 and it’s made by a manufacturer called Anderson.

Now let’s take a look at the logistic data.

Each antenna tower is equipped with 6 power amplifiers and we’ve got 1000 antenna towers in service.

Each power amplifier operates 24-hours per day and has a repair turnaround time of 30 days.

The MTBF is 250,000 hours and the NFF ratio is 5%.

Finally, each unit costs $2,100 US dollars.

Part 3

OK, so that’s our logistic data taken care of.

The next thing we need to do is to set the optimization goal and here we have three options:

We can either set an Availability Goal, or we can set a Stock-Out-Risk goal, or we can set a Mean-Time-Between-Stock-Out goal.

So, which one of these three should we choose?

Well, this is usually specified in the contract.

For example, the contract might say something like:

“The supplier shall provide sufficient spare parts to exceed an availability goal of 99% measured in a 30-day resupply period”.

So if this was the case, then we would select the Availability tool and enter 99% in this box here.

Alternatively, the contract might specify a Stock-Out-Risk goal.

And the contract might say something like:

“The supplier shall provide spare parts sufficient to reduce the probability of stock-out to less than 5% measured in a 30-days resupply period”.

In this case then, we would select the Stock-Out-Risk tool and enter 5% in this box here.

Finally, the contract might specify a Mean-Time-Between-Stock-Out goal.

And it might say something like:

“The supplier shall provide spare parts sufficient to meet a Mean-Time-Between-Stock-Out of greater than 10 years”.

In this case then we would select the Mean-Time-Between-Stock-Out tool and enter 10 years into this box here.

It’s worth noting that when you specify a goal, Spares Calculator converts all of the other goals so that they are equivalent.

So a few seconds ago I set the Mean-Time-Between-Stock-Out to 10-years.

Spares Calculator then converted this into an Availability of goal of 99.18%

It also changed the Stock-Out-Risk goal to 0.82%.

If I change the Stock-Out-Risk goal to 1% you will see that Spares Calculator converts the Availability goal to 99%.

It also converts the Mean-Time-Between-Stock-Out goal to 8.21 years.

Part 4

Let’s put this back to 10-years and turn our attention now to the reports:

In the Mean-Time-Between-Stock-Out report we can see a log linear chart showing the number of spares on the x-axis and Mean-Time-Between-Stock-Out on the y-axis.

We’ve also got a Results Summary panel that shows the project data along with the recommended spare parts and the projected performance figures.

At the bottom we’ve got the tabular results and this shows us the Availability, Stock-Out-Risk and Mean-Time-Between-Stock-Out figures all in one combined report.

Let’s take a look at the Availability Calculator.

You can see here that the chart now shows Spare Parts on the x-axis and Availability on the y-axis.

You can also see that the Summary Panel now shows the Availability Goal along with the Expected Availability performance.

The same goes for the Stock-Out-Risk Calculator.

We’ve got the chart with Spare Parts on the x-axis and Stock-Out-Risk on the y-axis, and a Summary Panel that now shows the Stock-Out-Risk Goal and Expected Stock-Out-Risk performance.

Part 5

Now obviously you can take screenshots of these things and incorporate them into your proposals, contracts and tendering documents.

But with Spares Calculator that’s not really necessary.

And that’s because Spares Calculator produces really nice PDF reports.

Let’s take a look at one now.

The first section shows who produced the report and when.

The next section shows the Project Data – so things like the project name, store and equipment.

After that we’ve got the Input Logistic Data – this includes things like the equipment MTBF, NFF Ratio and Daily Operating Hours.

Next we’ve got the summary of the results.

This includes the recommended number of spares, the costs and the expected logistic performance for a combined set of goals.

So in this example we have a Mean-Time-Between-Stock-Out goal of 10 years and we are expecting to achieve an actual Mean-Time-Between-Stock-Out of 12.45 years.

To achieve this we will need to procure 29 spare parts at a cost of £60,900 US Dollars.

The next section shows the tabular data.

Then we have the Stock-Out-Risk chart.

The Availability chart.

And the Mean-Time-Between-Stock-Out chart.

Finally, we have a glossary of terms in Appendix 1.

And a short introduction to Spares Calculator in Appendix 2.

So all we need to do now is to print off this report and append it to our proposal.

So that brings us to the end of this short introduction to Spares Calculator I hope you found it useful and if you have any questions then please feel free to contact us.

Thanks for watching.

Spare parts obsolescence and redundancy are an important factor in managing the lifecycle of a typical high value system.

Electronic components typically have short production lifecycles, typically 2-5 years and even military suppliers have difficulty maintaining production past this point without special government funding. 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?

Problem Analysis

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.

Sample Calculation

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?

Logistic Data

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

Step 1: Calculate the Units System

[6 LRUs Per Aircraft] x [12 Chips Per LRU] = 72

Step 2: Refactor the Expected Life into a pseudo Repair-Turn-Around-Time

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

Step 3: Model the data in Spares Calculator

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.

Here is an example of a recent question that we were asked by a client.

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.

Many items in a typical inventory do not actually get repaired and they are simply discarded on failure.

These are known as items with a Discard on Failure Repair Policy.

A customer recently asked:

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

Discussion

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.

Sample Calculation

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

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.

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 great question and it raises a really important point: What is the purpose of Spare Parts Optimization?

What is the Goal of Spare Parts Optimization?

The goal of Spare Parts Optimization is to maximize Operational Availability whilst minimizing Life Cycle Costs.

We achieve this by modelling the logistic performance of systems and equipment in an operational scenario and selection the optimum level of spare parts so that the goals are achieved.

Spare Parts Logistic Parameters

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

• Total 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 optimize each of these parameters to maximise our Operational Availability and minimize our Life Cycle Costs.

Total Units in Service

The Units in Service are controlled by operational needs and we have no control over this parameter.

Daily Operating Hours

The Daily Operating Hours are also controlled by operational needs and we have no control over this parameter.

MTBF (Mean Time Between Failure)

MTBFs can have a massive impact on the operational and logistic performance of a system. Therefore, it is imperative that high quality LRUs and components are selected.  Spares Calculator can be used to produce an A:B cost comparison between different LRUs and suppliers.

NFF Ratio (No Fault Found Ratio)

Logistically, the NFF ratio is of equal importance to the MTBF. NFF ratios can be reduced by introducing local filtering equipment, improved diagnostics and by providing high quality maintenance training. Spares Calculator can be used to compare the cost of additional training and test equipment to the cost of additional spare parts.

Repair Turn-Around-Time

The Repair Turn-Around-Time has a massive impact on the quantity of spare parts and it might be possible to achieve some kind of expedited repair policy in extreme circumstances. This is sometimes called a crisis resupply policy. Spares Calculator can be used to model the normal and crisis situations so that you can define optimum stock levels.

Unit Cost

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

Summary

In summary, Spare Parts Optimization is the process of maximizing Operational Availability whilst minimizing Life Cycle Costs. The operational parameters are fixed but we can influence the MTBF, 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.

In this article we show how to convert the Probability of Availability to Stock-Out-Risk or Mean-Time-Between-Stock-Out for Spare Parts inventory.

Problem

1. Spares Calculator can forecast [Stock-Out-Risk],  [Mean Time Between Stock-Out] and [Probability of Availability]
2. Analysts need to understand the relationship between these three parameters

Background

There is no accepted best practice for setting goals for spare parts inventory. Some contracts specify [Probability of Availability], others prefer [Stock-Out-Risk] and others prefer the [Mean Time Between Stock-Out]. Thankfully, there is a mathematical relationship between each of the goals and in this article we will show you how you can manually convert between each value?

Proof 1

[Stock-Out-Risk] and [Probability of Availability]

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].

Proof 2

[Mean Time Between Stock-Out] and [Probability of Availability]

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)

Example 1

Convert [Probability of Availability] to  [Stock-Out-Risk]

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.

Example 2

Convert [Probability of Availability] to  [Mean Time Between Stock-Out]

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.