Forecasting a last time buy quantity for a service part using a low-pass filter approach

1. A method for forecasting a Last Time Buy quantity for a service part using a low-pass filter approach, comprising:

accessing input data comprising:

a service lifespan beginning at the end of mass production of a product associated with the service part;

data reflecting past accumulated production of the associated product for at least a first period beginning at the end of mass production of the associated product; and

an order data series reflecting past quantities of the service part ordered in each of a succession of periods beginning with a second period that immediately follows the first period and ending with a current period;

applying a low-pass filter to at least a portion of the order data series to extract low frequency components representing a smoothed order data series;

performing exponential forecasting according to the smoothed order data series for a local maximum in the smoothed order data series;

generating an estimated Last Time Buy quantity for the service part over all remaining periods of the service lifespan following the current period, wherein the Last Time Buy quantity is calculated using the following equation:

Last

⁢

⁢

Time

⁢

⁢

Buy

=

∑

i

=

c

+

1

N

⁢

⁢

O

^

i

=

O

~

c

*

⁢

η

*

⁢

θ

⁡

(

N

-

c

)

+

O

~

c

*

⁢

μ

⁡

(

1

-

θ

)

*

⁢

(

N

-

c

)

;

wherein Ô i is defined as a forecasted smoothed order data series, wherein Õ c is defined as a smoothed order data series, θ is defined as a fixed constant value representing a division of the Last Time Buy period, N is the total number of periods in the service lifespan, c is defined as the current period, η is defined as the total number of periods in the service lifespan minus the current period, and μ is defined as a fixed constant value that represents a declining rate of service part demand; and

making the estimated Last Time Buy quantity for the service part available for use in connection with one or more business analyses.

2. The method of claim 1 , wherein the data reflecting past accumulated production of the associated product comprises such data for each of a succession of periods beginning with the first period and ending with the current period.

3. The method of claim 1 , wherein the input data further comprises a data series reflecting past demand rates for the service part for each of the succession of periods beginning with the first period and ending with the current period, the demand rate for a period being the past quantity of the service part ordered in the period divided by the past accumulated production of the associated product for the first period.

4. The method of claim 1 , wherein the input data further comprises a number of remaining periods in the service lifespan.

5. The method of claim 1 , wherein the low-pass filter operates according to a smoothing parameter having a predetermined value that is independent of periods associated with the input data.

6. The method of claim 1 , further comprising deleting all leading zeros, if any, from the order data series prior to application of the low-pass filter.

7. The method of claim 1 , wherein the local maximum is selected to reveal recent trending in the smoothed order data series and is more than three periods prior to the current period to ensure that sufficient data exists for the exponential forecasting.

8. The method of claim 1 , wherein exponential forecasting comprises:

generating an exponential trend curve reflecting estimated future demand for the service part in each remaining period of the service lifespan; and

summing the estimated future demand for the service part over all remaining periods of the service lifespan to generate the estimated Last Time Buy quantity for the service part.

9. The method of claim 1 , wherein the smoothed order data series reveals an upward trend from the first period to the current period, the smoothed order data series contains data for a sufficient number of periods, and a value of a first parameter is not less than a predetermined threshold for the share parameter, the method further comprises:

solving a non-linear equation to disaggregate the estimated LTB quantity;

generating an estimated future order quantity for the service part in each of a succession of periods beginning with a first remaining period and ending with a last period of the service lifespan; and

summing the estimated future order quantities over all remaining periods to generate the estimated LTB quantity.

10. The method of claim 9 , wherein the smoothed order data series contains data for a sufficient number of periods if the current period is in the second half of the service lifespan.

11. The method of claim 9 , wherein according to the value of the first parameter, the upward trend will fade out over remaining periods of the service lifespan and that part substitution effects on future demand for the service part will dominate part failure rate effects on future demand for the service part over the remaining periods of the service lifespan.

12. The method of claim 1 , wherein the smoothed order data series reveals an upward trend from the first period to the current period and the smoothed order data series contains data for a sufficient number of periods, the method further comprises:

calculating estimated demand for each period within the first half of the service lifespan;

calculating estimated demand for each period within the second half of the service lifespan; and

summing the estimated demand for the first half of the service lifespan and the estimated demand for the second half of the service lifespan to generate an estimated Last Time Buy quantity for the service part.

13. The method of claim 12 , wherein according to the value of the first parameter it is assumed that the upward trend will fade out over remaining periods of the service lifespan and that part substitution effects on future demand for the service part will not dominate part failure rate effects on future demand for the service part over the remaining periods of the service lifespan.

14. The method of claim 1 , wherein the smoothed order data series does not contain data for a sufficient number of periods, the method further comprises:

performing a discriminant analysis to identify another service part having a demand pattern similar to that of the service part; and

using, in place of the order data series for the service part, a data series reflecting past demand rates for the other service part for each of the succession of periods beginning with the first period and ending with the current period, the demand rate for a period being the past quantity of the other service part ordered in the period divided by the past accumulated production of a product associated with the other service part for the first period.

15. The method of claim 14 , wherein the smoothed order data series contains data for a sufficient number of periods if the current period is in the second half of the service lifespan.

16. The method of claim 1 , wherein a business analysis comprises one of service part risk management analysis and inventory control analysis.

17. A system for forecasting a Last Time Buy quantity for a service part using a low-pass filter approach, comprising:

a database operable to store input data comprising:

a service lifespan beginning at the end of mass production of a product associated with the service part;

data reflecting past accumulated production of the associated product for at least a first period beginning at the end of mass production of the associated product; and

an order data series reflecting past quantities of the service part ordered in each of a succession of periods beginning with a second period that immediately follows the first period and ending with a current period;

one or more processors collectively operable to:

access the input data;

apply a low-pass filter to at least a portion of the order data series to extract low frequency components representing a smoothed order data series;

perform exponential forecasting according to the smoothed order data series for a local maximum in the smoothed order data series;

generate an estimated Last Time Buy quantity for the service part over all remaining periods of the service lifespan following the current period, wherein the Last Time Buy quantity is calculated using the following equation:

Last

⁢

⁢

Time

⁢

⁢

Buy

=

∑

i

=

c

+

1

N

⁢

⁢

O

^

i

=

O

~

c

*

⁢

η

*

⁢

θ

⁡

(

N

-

c

)

+

O

~

c

*

⁢

μ

⁡

(

1

-

θ

)

*

⁢

(

N

-

c

)

;

wherein Ô i is defined as a forecasted smoothed order data series, wherein Õ c is defined as a smoothed order data series, θ is defined as a fixed constant value representing a division of the Last Time Buy period, N is the total number of periods in the service lifespan, c is defined as the current period, η is defined as the total number of periods in the service lifespan minus the current period, and μ is defined as a fixed constant value that represents a declining rate of service part demand; and

make the estimated Last Time Buy quantity for the service part available for use in connection with one or more business analyses.

18. Software for forecasting a Last Time Buy quantity for a service part using a low-pass filter approach, the software being embodied in computer-readable media and when executed operable to:

access input data comprising:

a service lifespan beginning at the end of mass production of a product associated with the service part;

data reflecting past accumulated production of the associated product for at least a first period beginning at the end of mass production of the associated product; and

an order data series reflecting past quantities of the service part ordered in each of a succession of periods beginning with a second period that immediately follows the first period and ending with a current period;

apply a low-pass filter to at least a portion of the order data series to extract low frequency components representing a smoothed order data series;

perform exponential forecasting according to the smoothed order data series for a local maximum in the smoothed order data series;

generate an estimated Last Time Buy quantity for the service part over all remaining periods of the service lifespan following the current period, wherein the Last Time Buy quantity is calculated using the following equation:

Last

⁢

⁢

Time

⁢

⁢

Buy

=

∑

i

=

c

+

1

N

⁢

⁢

O

^

i

=

O

~

c

*

⁢

η

*

⁢

θ

⁡

(

N

-

c

)

+

O

~

c

*

⁢

μ

⁡

(

1

-

θ

)

*

⁢

(

N

-

c

)

;

wherein Ô i is defined as a forecasted smoothed order data series, wherein Õ c is defined as a smoothed order data series, θ is defined as a fixed constant value representing a division of the Last Time Buy period, N is the total number of periods in the service lifespan, c is defined as the current period, η is defined as the total number of periods in the service lifespan minus the current period, and μ is defined as a fixed constant value that represents a declining rate of service part demand; and

make the estimated Last Time Buy quantity for the service part available for use in connection with one or more business analyses.

19. The software of claim 18 , wherein the data reflecting past accumulated production of the associated product comprises such data for each of a succession of periods beginning with the first period and ending with the current period.

20. The software of claim 18 , wherein the input data further comprises a data series reflecting past demand rates for the service part for each of the succession of periods beginning with the first period and ending with the current period, the demand rate for a period being the past quantity of the service part ordered in the period divided by the past accumulated production of the associated product for the first period.

21. The software of claim 18 , wherein the input data further comprises a number of remaining periods in the service lifespan.

22. The software of claim 18 , wherein the low-pass filter operates according to a smoothing parameter having a predetermined value that is independent of periods associated with the input data.

23. The software of claim 18 , further operable to delete all leading zeros, if any, from the order data series prior to application of the low-pass filter.

24. The software of claim 18 , wherein the local maximum is selected to reveal recent trending in the smoothed order data series and is more than three periods prior to the current period to ensure that sufficient data exists for the exponential forecasting.

25. The software of claim 18 , wherein exponential forecasting comprises:

generating an exponential trend curve reflecting estimated future demand for the service part in each remaining period of the service lifespan; and

summing the estimated future demand for the service part over all remaining periods of the service lifespan to generate the estimated Last Time Buy quantity for the service part.

26. The software of claim 18 , wherein the smoothed order data series reveals an upward trend from the first period to the current period, the smoothed order data series contains data for a sufficient number of periods, and a value of a first parameter is not less than a predetermined threshold for the share parameter, the software is further operable to:

solve a non-linear equation to disaggregate the estimated LTB quantity;

generate an estimated future order quantity for the service part in each of a succession of periods beginning with a first remaining period and ending with a last period of the service lifespan; and

sum the estimated future order quantities over all remaining periods to generate the estimated LTB quantity.

27. The software of claim 26 , wherein the smoothed order data series contains data for a sufficient number of periods if the current period is in the second half of the service lifespan.

28. The software of claim 26 , wherein according to the value of the first parameter, the upward trend will fade out over remaining periods of the service lifespan and that part substitution effects on future demand for the service part will dominate part failure rate effects on future demand for the service part over the remaining periods of the service lifespan.

29. The software of claim 18 , wherein if a local maximum is not found, if the smoothed order data series reveals an upward trend from the first period to the current period and if the smoothed order data series contains data for a sufficient number of periods, then the software is further operable to:

calculate estimated demand for each period within the first half of the service lifespan;

calculate estimated demand for each period within the second half of the service lifespan; and

sum the estimated demand for the first half of the service lifespan and the estimated demand for the second half of the service lifespan to generate an estimated Last Time Buy quantity for the service part.

30. The software of claim 29 , wherein according to the value of the first parameter it is assumed that the upward trend will fade out over remaining periods of the service lifespan and that part substitution effects on future demand for the service part will not dominate part failure rate effects on future demand for the service part over the remaining periods of the service lifespan.

31. The software of claim 18 , wherein the smoothed order data series does not contain data for a sufficient number of periods, the software is further operable to:

perform a discriminant analysis to identify another service part having a demand pattern similar to that of the service part; and

use, in place of the order data series for the service part, a data series reflecting past demand rates for the other service part for each of the succession of periods beginning with the first period and ending with the current period, the demand rate for a period being the past quantity of the other service part ordered in the period divided by the past accumulated production of a product associated with the other service part for the first period.

32. The software of claim 31 , wherein the smoothed order data series contains data for a sufficient number of periods if the current period is in the second half of the service lifespan.

33. The software of claim 18 , wherein a business analysis comprises one of service part risk management analysis and inventory control analysis.