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
- Spares Calculator can forecast [Stock-Out-Risk], [Mean Time Between Stock-Out] and [Probability of Availability]
- 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.