Hierarchical methodology for productivity measurement and improvement of complex production systems

• US 20040034555A1
• Filed: 03/14/2003
• Published: 02/19/2004
• Est. Priority Date: 03/18/2002
• Status: Abandoned Application

• Current Assignee: University of Toledo
• Original Assignee: University of Toledo
• Inventors: Su, Qi, Mittal, Rahul, Dismukes, John P., Kothamasu, Ranganath, Razzak, Mousalam A., Huang, Samuel H., Doshi, Milan H., Miller, Lawrence K.
• Application Number:
  US10/388,921
• Publication Number:
  US 20040034555A1
• Time in Patent Office: Days
• US Class Current: 705/7
• CPC Class Codes: G06Q 10/06 Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling

Abstract

A hierarchical method, computer system, and computer product for causally relating productivity to a complex manufacturing system to provide an integrated analysis of the system which measures, monitors, analyzes and, optionally, simulates performance of the complex manufacturing system based on a common set of productivity metrics for throughput effectiveness, throughput, cycle time effectiveness, and inventory.

Claims

1. A hierarchical method for causally relating productivity to a production system to provide an integrated productivity analysis of the system, comprising:

a) identifying an array of production operations including any one or more of the following;

process, transportation, storage, cost, building of simulation model, and time;

b) modeling the system as an interconnected array of unit production processes (UPP) reflecting actual or desired material flow sequence through the system;

c) applying at least one set of UPP interconnections to factor the system into at least one set of UPP complex manufacturing subsystems (CMS) for description and analysis;

d) assessing each UPP and each subsystem (CMS) to calculate at least one productivity metric of each UPP, UPP subsystem (CMS) and the system;

e) determining a quantity of Operating Sequences (OSs) describing the material flow sequence of products through the complex manufacturing subsystem (CMS);

f) determining product throughout or input, P_a, good product output, P_g, and defective product, P_a-P_g, for a total time, T_T, of measurement or simulation;

g) determining each OS in the complex manufacturing subsystem (CMS), and determining Overall Equipment Effectiveness (OEE) for each of the UPPs;

h) determining availability efficiency (A_eff) or yield of each UPP; and

i) determining Overall Throughput Effectiveness (OTE) of the complex manufacturing subsystem (CMS) by the relations,

OTE_CMS=[P_th(CMS)/P_tha(CMS)] and P_tha(CMS)=R_thavg(CMS)*T_T

where, quantity P_tha(CMS) is theoretical actual product output units from the complex manufacturing subsystem (CMS) in total time, and R_thavg(CMS) is defined as the average theoretical processing rate for total product output from the complex manufacturing subsystem (CMS) during the period of total time T_T, and, optionally

j) collecting the total costs the system including at least one of Direct Manufacturing Costs (DMC);

Process Labor (PL), Process Energy and Utilities (PE &

U), Process Tooling (PT), Process Materials (PM), Equipment Depreciation (ED), and Direct Materials (DM);

k) defining all direct manufacturing activities at each UPP activity, including at least one of;

Manufacturing Operations (MO), Engineering Operations (EO), Quality Assurance Operations (QAO), Material Handling Operations (MHO), and Production Management (PM);

l) allocating the DMC from each of the set of 6 (six) DMC Categories in step j) above to each of the 5 direct manufacturing activities defined in step k) at the respective UPP activity centers based on second stage cost driver factors;

m) obtaining a dollar value of costs of each of the activities of the respective UPP-activity center using Equations (15-2) and (15-3),

$\begin{array}{cc}A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>2\right)\\ A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_i^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>3\right)\end{array}$

where

AC^UPP_ij=the jth activity cost component contributed to UPP activity center i

AC^UPP_i=total activity cost of UPP activity cost center

DMC_k=kth direct manufacturing cost component

DCD_ijk=direct resource cost driver which allocates kth direct manufacturing cost to jth activity component of UPP activity center i;

n) allocating the costs of each of the five general sets of activities of the respective UPP-activity center to three products based on third stage cost-driver factor as follows;

$\frac{\text{Manufacturing Operations Labor Hrs of}\text{UPP}\text{-1 on Product-1}}{\text{Total Manufacturing Operations Labor Hours for All}\text{UPP}\text{'"'"'s}}=\mathrm{xx}$

and,

o) determining the total unit direct manufacturing cost (TDMC_k, $/unit) for each product type, k, from Equation (15-4), where the numerator represents the total dollar cost of product contributed by each UPP activity center, and P_g(k) represents the number of good product units of product type k

$\begin{array}{cc}{\mathrm{TDMC}}_k=\frac{\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{P_{g<br><br>\left(k\right)}}& \left(15<br><br>\text{-}<br><br>4\right)\end{array}$

 

and further optionally,

p) determining the total direct manufacturing cost of a unit of good product averaged over all product types, k, during the period, T_T, from Equation 15-(5),

$\begin{array}{cc}\begin{array}{c}{\mathrm{TDMC}}_{\mathrm{AVG}}=\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\underset{k}{\sum <br><br>}<br><br>P_{g<br><br>\left(k\right)}}\\ =\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\mathrm{OTE}\times <br><br>R_{\mathrm{avg}<br><br>\left(F\right)}^{\left(\mathrm{th}\right)}\times <br><br>T_T}\end{array}& \left(15<br><br>\text{-}<br><br>5\right)\end{array}$

where

ACD_ijk=activity center cost driver, which traces the jth activity cost of UPP activity center i to product type k

OTE=unit-based overall throughput effectiveness of the factory

R^(th)_avg(F)=theoretical average processing rate in time T_T for products through the factory,

thereby establishing a relation of the average product cost to productivity (OTE).

2. The method of claim 1, in which the manufacturing subsystem comprises a plurality of integrated processing modules linked together.

3. The method of claim 2, in which the manufacturing subsystem comprises fixed-sequence cluster tools.

4. The method of claim 2, in which the manufacturing subsystem comprises flexible-sequence cluster tools.

5. The method of claim 2, in which each UPP comprises input transport rates from an upstream UPP, and output transport rates to a downstream UPP, input and output storage buffers for work in process, and a unit process step.

6. The method of claim 1, in which algorithms are applied to calculate the productivity metrics of unit based overall equipment effectiveness (OEE), cycle time effectiveness (CTE), production throughput of good product (P_g) and UPP inventory level (L_upp), based on any one or more of the following:

factory data for equipment time parameters, theoretical cycle time, actual cycle time, arrival and departure rates, and input and output buffer levels.

7. The method of claim 1, in which algorithms are applied to calculate UPP subsystem and/or system level productivity metrics of overall throughput effectiveness (OTE_F), cycle time effectiveness (CTE_F), production throughput of good product (P_G(F)) and UPP subsystem or factory inventory level (L_F), based on factory data and the productivity metrics for each UPP.

8. The method of claim 1, in which measurement, monitoring and quantitative calculation of the productivity metrics for the UPPs, the UPP subsystems, and/or production system is conducted using spreadsheet analysis tools which represent an actual factory architecture or the system.

9. The method of claim 8, in which measurement, monitoring and quantitative calculation of the productivity metrics for the UPPs, the UPP subsystems, and systems is conducted using a flowchart tool and a graphical user interface for data input and metrics output in appropriate spreadsheet or chart format.

10. The method of claim 9, comprising:

creating UPPs required to represent the generic subsystem types,

creating data input and metrics output boxes for standard input and output of data and results,

linking the UPPs to represent the experimental material flow sequence, or system architecture, with recognition algorithms applied to identify generic subsystem types, and

calculating productivity metrics for each UPP, UPP subsystem, and the overall system.

11. The method of claim 10, in which the UPPs include regular, assembly and expansion.

12. The method of claim 1, further comprising building an automated simulation model comprising importing data in spreadsheet form from a flowcharting and measurement tool, and representing interconnectivity of the system and actual and theoretical performance characteristics.

13. The method of claim 12, in which the simulation model comprises a rapid what-if scenario analysis of existing production facilities or systems, wherein specific changes needed for bottleneck removal and productivity improvement are identified.

14. The method of claim 13, in which the scenario analysis is linked to market demand.

15. The method of claim 13, in which the simulation model comprises rapid assessment and development of new factory designs optimized for specific manufacturing performance.

16. The method of claim 1, wherein the UPP includes any one or more of the following:

equipment, subsystem, product line, factory, transportation system, and supply chain (which includes transportation systems and manufacturing systems).

17. The method of claim 1, wherein measurement and analysis of the system are conducted using a spreadsheet analysis and a visual flowcharting and measurement tool coded with the algorithms for unit-based productivity measurement at the equipment, subsystem and system level.

18. The method of claim 17, wherein the measurement and analysis of the system is conducted for single and/or multiple product types.

19. The method of claim 17, wherein data representing interconnectivity of the system and intrinsic performance characteristics are transferred from the flowcharting and measurement tool via at least one or more spreadsheets to set up an equivalent manufacturing array in a discrete event simulation software package.

20. The method of claim 19, wherein development and implementation of a dynamic simulation is used to assess scenarios for eliminating bottlenecks and tailoring performance, and to develop new designs optimized for specific requirements in the production system.

21. The method of claim 19, wherein the production system includes any one or more of the following:

equipment, subsystem, product line, manufacturing process, factory, transportation system, and supply chains (which includes transportation systems and manufacturing systems).

22. The method of claim 1, wherein the method is used to analyze overall equipment effectiveness.

118. The method of claim 1, wherein step (g) comprises calculating average theoretical processing rates of chamber and pseudo-chambers in a Series-Connected subsystem for all operation sequences (OSs) by using the following equation

119. The method of claim 118 wherein (R_avg(CT)^(th)) is used to calculate P_a(CT)^(th), theoretical total product output/processes (units) from the subsystem in a total time T_T,

P_a(CT)^(th)=(R_avg(CT)^(th))(T_T) 

 

(2b)

and the overall throughput effectiveness is defined as

120. The method of claim 118, comprising determining the overall throughput effectiveness (OTE) of step (i) by determining the product of the available efficiency, the performance efficiency, and the quality efficiency

OTE_(CT)=(A_eff(CT))(P_eff(CT))(Q_eff(CT)) 

 

(10b).

121. The method of claim 120, wherein the available efficiency for the subsystem is defined as

23. A method for hierarchical representation of a production system for measuring, monitoring, analyzing and/or simulating production performance of the production system based on a common set of productivity metrics for throughput effectiveness, cycle time effectiveness, overall throughput effectiveness, and inventory, comprising:

a) identifying an array of production operations including any one or more of the following;

process, transportation, storage, cost, building of simulation model, and time;

b) providing a description of the production system as an interconnected array of unit production processes (UPP) reflecting an actual material flow sequence through the system;

c) applying at least one set of UPP complex manufacturing subsystems (CMS) to factor an overall system flowchart into UPP complex manufacturing subsystems (CMS), and combining the subsystems to represent the overall production system;

d) analyzing productivity metrics of each UPP, each UPP complex manufacturing subsystem (CMS), and the overall system;

e) determining a quantity of Operating Sequences (OSs) describing the material flow sequence of products through the complex manufacturing subsystem;

f) determining product throughout or input, P_a, good product output, P_g, and defective product, P_a-P_g, for a total time, T_T, of measurement or simulation;

g) determining each OS in the complex manufacturing subsystem (CMS), and determining Overall Equipment Effectiveness (OEE) for each of the UPPs;

h) determining availability efficiency (A_eff) or yield of each UPP; and

i) determining Overall Throughput Effectiveness (OTE) of the complex manufacturing subsystem (CMS) by the relations,

OTE_CMS=[P_tha(CMS)/P_tha(CMS)] and P_tha(CMS)=R_thavg(CMS)*T_T or, OTE_CMS=A_(CMS)·

P_(CMS)·

Q_(CMS)

where, quantity P_tha(CMS) is theoretical actual product output units from the complex manufacturing subsystem (CMS) in total time, and R_thavg(CMS) is defined as the average theoretical processing rate for total product output from the complex manufacturing subsystem (CMS) during the period of total time T_T, and converting the overall system flowchart to a discrete event simulation description, and enabling comparative performance assessment of various production scenarios useful for performance improvement and system design and, optionally

j) collecting the total costs the system including at least one of Direct Manufacturing Costs (DMC);

Process Labor (PL), Process Energy and Utilities (PE &

U), Process Tooling (PT), Process Materials (PM), Equipment Depreciation (ED), and Direct Materials (DM);

k) defining all direct manufacturing activities at each UPP activity, including at least one of;

Manufacturing Operations (MO), Engineering Operations (EO), Quality Assurance Operations (QAO), Material Handling Operations (MHO), and Production Management (PM);

l) allocating the DMC from each of the set of 6 (six) DMC Categories in step j) above to each of the 5 direct manufacturing activities defined in step k) at the respective UPP activity centers based on second stage cost driver factors;

m) obtaining a dollar value of costs of each of the activities of the respective UPP-activity center using Equations (15-2) and (15-3),

$\begin{array}{cc}A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>2\right)\\ A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_i^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>3\right)\end{array}$

where

AC^UPP_ij=the jth activity cost component contributed to UPP activity center i

AC^UPP_i=total activity cost of UPP activity cost center

DMC_k=kth direct manufacturing cost component

DCD_ijk=direct resource cost driver which allocates kth direct manufacturing cost to jth activity component of UPP activity center i;

n) allocating the costs of each of the five general sets of activities of the respective UPP-activity center to three products based on third stage cost-driver factor as follows;

$\frac{\text{Manufacturing Operations Labor Hrs of}\text{UPP}\text{-1 on Product-1}}{\text{Total Manufacturing Operations Labor Hours for All}\text{UPP}\text{'"'"'s}}=\mathrm{xx}$

and,

o) determining the total unit direct manufacturing cost (TDMC_k, $/unit) for each product type, k, from Equation (15-4), where the numerator represents the total dollar cost of product contributed by each UPP activity center, and P_g(k) represents the number of good product units of product type k

$\begin{array}{cc}{\mathrm{TDMC}}_k=\frac{\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{P_{g<br><br>\left(k\right)}}& \left(15<br><br>\text{-}<br><br>4\right)\end{array}$

 

and further optionally,

p) determining the total direct manufacturing cost of a unit of good product averaged over all product types, k, during the period, T_T, from Equation 15-(5),

$\begin{array}{cc}\begin{array}{c}{\mathrm{TDMC}}_{\mathrm{AVG}}=\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\underset{k}{\sum <br><br>}<br><br>P_{g<br><br>\left(k\right)}}\\ =\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\mathrm{OTE}\times <br><br>R_{\mathrm{avg}<br><br>\left(F\right)}^{\left(\mathrm{th}\right)}\times <br><br>T_T}\end{array}& \left(15<br><br>\text{-}<br><br>5\right)\end{array}$

where

ACD_ijk=activity center cost driver, which traces the jth activity cost of UPP activity center i to product type k

OTE=unit-based overall throughput effectiveness of the factory

R^(th)_avg(F)=theoretical average processing rate in time T_T for products through the factory,

thereby establishing a relation of the average product cost to productivity (OTE).

24. The method of claim 23, in which the manufacturing subsystem comprises a plurality of integrated processing modules linked together.

25. The method of claim 24, in which the manufacturing subsystem comprises fixed-sequence cluster tools.

26. The method of claim 24, in which the manufacturing subsystem comprises flexible-sequence cluster tools.

27. The method of claim 23, in which each UPP comprises input transport rates from an upstream UPP, and output transport rates to a downstream UPP, input and output storage buffers for work in process, and a unit process step.

28. The method of claim 23, in which algorithms are applied to calculate the productivity metrics of unit based overall equipment effectiveness (OEE), cycle time effectiveness (CTE), production throughput of good product (P_g) and UPP inventory level (L_upp), based on any one or more of the following:

factory data for equipment time parameters, theoretical cycle time, actual cycle time, arrival and departure rates, and input and output buffer levels.

29. The method of claim 23, in which algorithms are applied to calculate UPP subsystem and/or system level productivity metrics of overall throughput effectiveness (OTE_F), cycle time effectiveness (CTE_F), production throughput of good product (P_G(F)) and UPP subsystem or factory inventory level (L_F), based on factory data and the productivity metrics for each UPP.

30. The method of claim 23, in which measurement, monitoring and quantitative calculation of the productivity metrics for the UPPs, the UPP subsystems, and/or production system is conducted using spreadsheet analysis tools which represent an actual factory architecture or the system.

31. The method of claim 30, in which measurement, monitoring and quantitative calculation of the productivity metrics for the UPPs, the UPP subsystems, and systems is conducted using a flowchart tool and a graphical user interface for data input and metrics output in appropriate spreadsheet or chart format.

32. The method of claim 31, comprising:

creating UPPs required to represent the generic subsystem types,

creating data input and metrics output boxes for standard input and output of data and results,

linking the UPPs to represent the experimental material flow sequence, or system architecture, with recognition algorithms applied to identify generic subsystem types, and

calculating productivity metrics for each UPP, UPP subsystem, and the overall system.

33. The method of claim 32, in which the UPPs include regular, assembly and expansion.

34. The method of claim 23, further comprising building an automated simulation model comprising importing data in spreadsheet form from a flowcharting and measurement tool, and representing interconnectivity of the system and actual and theoretical performance characteristics.

35. The method of claim 23, in which the simulation model comprises a rapid what-if scenario analysis of existing production facilities or systems, wherein specific changes needed for bottleneck removal and productivity improvement are identified.

36. The method of claim 23, in which the scenario analysis is linked to market demand.

37. The method of claim 23, in which the simulation model comprises rapid assessment and development of new factory designs optimized for specific manufacturing performance.

38. The method of claim 23, wherein the UPP includes anyone or more of the following:

equipment, subsystem, product line, manufacturing process, factory, transportation system, and supply chains (which includes transportation systems and manufacturing systems).

39. The method of claim 23, wherein measurement and analysis of the system are conducted using a spreadsheet analysis and a visual flowcharting and measurement tool coded with the algorithms for unit-based productivity measurement, for single or multiple product types, at the equipment, subsystem and system level.

40. The method of claim 39, wherein the measurement and analysis of the system is conducted for single and multiple product types.

41. The method of claim 39, wherein data representing interconnectivity of the system and intrinsic performance characteristics are transferred from the flowcharting and measurement tool via at least one spreadsheet to set up an equivalent manufacturing array in a discrete event simulation software package.

42. The method of claim 41, wherein development and implementation of a dynamic simulation used to assess scenarios for eliminating bottlenecks and tailoring performance, and to develop new designs optimized for specific requirements in the production system.

43. The method of claim 23, wherein the production system includes any one or more of the following:

equipment, subsystem, product line, manufacturing process, factory, transportation system, and supply chains (which includes transportation systems and manufacturing systems).

44. The method of claim 23, wherein the method is used to analyze overall equipment effectiveness.

45. The method of claim 23, wherein the system layout or architecture is determined by factoring the system into unique combinations of UPP subsystems.

122. The method of claim 23 wherein step (g) comprises calculating average theoretical processing rates of chamber and pseudo-chambers in a Series-Connected subsystem for all operation sequences (OSs) by using the following equation

123. The method of claim 122 wherein (R_avg(CT)^(th)) is used to calculate P_a(CT)^(th), theoretical total Product output/processes (units) from the subsystem in a total time T_T,

P_a(CT)^(th)=(R_avg(CT)^(th))(T_T) 

 

(2b)

and the overall throughput effectiveness is defined as

124. The method of claim 122, comprising determining the overall throughput effectiveness (OTE) of step (i) by determining the product of the available efficiency, the performance efficiency, and the quality efficiency

OTE_(CT)=(A_eff(CT))(P_eff(CT))(Q_eff(CT)) 

 

(10b.

125. The method of claim 124, wherein the available efficiency for the subsystem is defined as

46. A method for analysis of system level productivity comprising:

a) establishing a unique layout or architecture for arranging at least one set of unit production processes (UPPs) in a complex manufacturing subsystem;

b) calculating overall equipment effectiveness (OEE) and, optionally, other parameters of individual UPP'"'"'s;

c) calculating overall throughput effectiveness (OTE_F) of the UPP complex manufacturing subsystems and the system;

d) calculating good production output (P_G(F)) of the UPP complex manufacturing subsystem and the system;

e) calculating cycle time efficiency (CTE_F) of the UPP complex manufacturing subsystem and the system; and

f) calculating factory level inventory (L_F) of the UPP complex manufacturing subsystem and the system,

g) determining each OS in the complex manufacturing subsystem (CMS), and determining Overall Equipment Effectiveness (OEE) for each of the UPPs;

h) determining availability efficiency (A_eff) or yield of each UPP; and

i) determining Overall Throughput Effectiveness (OTE) of the complex manufacturing subsystem (CMS) by the relations,

OTE_CMS=[P_tha(CMS)/P_tha(CMS)] and P_tha(CMS)=R_thavg(CMS)*T_T

where, quantity P_tha(CMS) is theoretical actual product output units from the complex manufacturing subsystem (CMS) in total time, and R_thavg(CMS) is defined as the average theoretical processing rate for total product output from the complex manufacturing subsystem (CMS) during the period of total time T_T, and, optionally

j) collecting the total costs the system including at least one of Direct Manufacturing Costs (DMC);

Process Labor (PL), Process Energy and Utilities (PE &

U), Process Tooling (PT), Process Materials (PM), Equipment Depreciation (ED), and Direct Materials (DM);

k) defining all direct manufacturing activities at each UPP activity, including at least one of;

Manufacturing Operations (MO), Engineering Operations (EO), Quality Assurance Operations (QAO), Material Handling Operations (MHO), and Production Management (PM);

l) allocating the DMC from each of the set of 6 (six) DMC Categories in step j) above to each of the 5 direct manufacturing activities defined in step k) at the respective UPP activity centers based on second stage cost driver factors;

m) obtaining a dollar value of costs of each of the activities of the respective UPP-activity center using Equations (15-2) and (15-3),

$\begin{array}{cc}A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>2\right)\\ A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_i^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>3\right)\end{array}$

where

AC^UPP_ij=the jth activity cost component contributed to UPP activity center i

AC^UPP_i=total activity cost of UPP activity cost center

DMC_k=kth direct manufacturing cost component

DCD_ijk=direct resource cost driver which allocates kth direct manufacturing cost to jth activity component of UPP activity center i;

n) allocating the costs of each of the five general sets of activities of the respective UPP-activity center to three products based on third stage cost-driver factor as follows;

$\frac{\text{Manufacturing Operations Labor Hrs of}\text{UPP}\text{-1 on Product-1}}{\text{Total Manufacturing Operations Labor Hours for All}\text{UPP}\text{'"'"'s}}=\mathrm{xx}$

and,

o) determining the total unit direct manufacturing cost (TDMC_k, $/unit) for each product type, k, from Equation (15-4), where the numerator represents the total dollar cost of product contributed by each UPP activity center, and P_g(k) represents the number of good product units of product type k

$\begin{array}{cc}{\mathrm{TDMC}}_k=\frac{\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{P_{g<br><br>\left(k\right)}}& \left(15<br><br>\text{-}<br><br>4\right)\end{array}$

 

and further optionally,

p) determining the total direct manufacturing cost of a unit of good product averaged over all product types, k, during the period, T_T, from Equation 15-(5),

$\begin{array}{cc}\begin{array}{c}{\mathrm{TDMC}}_{\mathrm{AVG}}=\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\underset{k}{\sum <br><br>}<br><br>P_{g<br><br>\left(k\right)}}\\ =\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\mathrm{OTE}\times <br><br>R_{\mathrm{avg}<br><br>\left(F\right)}^{\left(\mathrm{th}\right)}\times <br><br>T_T}\end{array}& \left(15<br><br>\text{-}<br><br>5\right)\end{array}$

where

ACD_ijk=activity center cost driver, which traces the jth activity cost of UPP activity center i to product type k

OTE=unit-based overall throughput effectiveness of the factory

R^(th)_avg(F)=theoretical average processing rate in time T_T for products through the factory,

thereby establishing a relation of the average product cost to productivity (OTE).

47. The method of claim 46, wherein the system layout or architecture is determined by factoring the complex system into unique combinations of UPP subsystems.

48. The method of claim 47, in which the manufacturing subsystem comprises a plurality of integrated processing modules linked together.

49. The method of claim 48, in which the manufacturing subsystem comprises fixed-sequence cluster tools.

50. The method of claim 48, in which the manufacturing subsystem comprises flexible-sequence cluster tools.

51. The method of claim 46, in which each UPP comprises input transport rates from an upstream UPP, and output transport rates to a downstream UPP, input and output storage buffers for work in process, and a unit process step.

52. The method of claim 46, in which algorithms are applied to calculate the productivity metrics of unit based overall equipment effectiveness (OEE), cycle time effectiveness (CTE), production throughput of good product (P_g) and UPP inventory level (L_upp), based on any one or more of the following:

factory data for equipment time parameters, theoretical cycle time, actual cycle time, arrival and departure rates, and input and output buffer levels.

53. The method of claim 46, in which algorithms are applied to calculate UPP subsystem and/or system level productivity metrics of overall throughput effectiveness (OTE_F), cycle time effectiveness (CTE_F), production throughput of good product (P_G(F)) and UPP subsystem or factory inventory level (L_F), based on factory data and the productivity metrics for each UPP.

54. The method of claim 46, in which measurement, monitoring and quantitative calculation of the productivity metrics for the UPPs, the UPP subsystems, and/or production system is conducted using spreadsheet analysis tools which represent an actual factory architecture or the system.

55. The method of claim 54, in which measurement, monitoring and quantitative calculation of the productivity metrics for the UPPs, the UPP subsystems, and systems is conducted using a flowchart tool and a graphical user interface for data input and metrics output in appropriate spreadsheet or chart format.

56. The method of claim 55, comprising:

creating UPPs required to represent the generic subsystem types,

creating data input and metrics output boxes for standard input and output of data and results,

linking the UPPs to represent the experimental material flow sequence, or system architecture, with recognition algorithms applied to identify generic subsystem types, and

calculating productivity metrics for each UPP, UPP subsystem, and the overall system.

57. The method of claim 56, in which the UPPs include regular, assembly and expansion.

58. The method of claim 46, further comprising building an automated simulation model comprising importing data in spreadsheet form from a flowcharting and measurement tool, and representing interconnectivity of the system and actual and theoretical performance characteristics.

59. The method of claim 46, in which the simulation model comprises a rapid what-if scenario analysis of existing production facilities or systems, wherein specific changes needed for bottleneck removal and productivity improvement are identified.

60. The method of claim 46, in which the scenario analysis is linked to market demand.

61. The method of claim 46, in which the simulation model comprises rapid assessment and development of new factory designs optimized for specific manufacturing performance.

62. The method of claim 46, wherein the UPP includes any one or more of the following equipment, subsystem, product line, manufacturing process, factory, transportation system, and supply chains (which includes transportation systems and manufacturing systems).

63. The method of claim 46, wherein measurement and analysis of the system are conducted using a spreadsheet analysis and a visual flowcharting and measurement tool coded with the algorithms for unit-based productivity measurement at the equipment, subsystem and system level.

64. The method of claim 46, wherein the measurement and analysis of the system is conducted for single and/or multiple product types.

65. The method of claim 63, wherein data representing interconnectivity of the system and intrinsic performance characteristics are transferred from the flowcharting and measurement tool via at least one or more spreadsheets to set up an equivalent manufacturing array in a discrete event simulation software package.

66. The method of claim 65, wherein development and implementation of a dynamic simulation is used to assess scenarios for eliminating bottlenecks and tailoring performance, and to develop new designs optimized for specific requirements in the production system.

67. The method of claim 46, wherein the production system includes any one or more of the following:

equipment, subsystem, product line, manufacturing process, factory, transportation system, and supply chains (which includes transportation systems and manufacturing systems).

68. The method of claim 46, wherein the method is used to analyze overall equipment effectiveness.

69. The method of claim 46, wherein the system layout or architecture is determined by factoring the system into unique combinations of UPP subsystems.

70. A computer system for relating productivity to a production system to provide an integrated productivity analysis of the system comprising:

a) identifying an array of production operations including any one or more of the following;

process, transportation, storage, cost, building of simulation model, and times;

b) modeling the system as an interconnected array of unit production processes (UPP) reflecting actual or desired material flow sequence through the system;

c) applying at least one set of UPP interconnections to factor the system into at least one set of UPP complex manufacturing subsystems for description and analysis;

d) assessing each UPP and each complex manufacturing subsystem to calculate at least one productivity metric of each UPP, UPP complex manufacturing subsystem and the system;

e) determining a quantity of Operating Sequences (OSs) describing the material flow sequence of products through the complex manufacturing subsystem;

f) determining product throughout or input, P_a, good product output, P_g, and defective product, P_a-P_g, for a total time, T_T, of measurement or simulation;

g) determining each OS in the complex manufacturing subsystem (CMS), and determining Overall Equipment Effectiveness (OEE) for each of the UPPs;

h) determining availability efficiency (A_eff) or yield of each UPP; and

i) determining Overall Throughput Effectiveness (OTE) of the complex manufacturing subsystem (CMS) by the relations,

OTE_CMS=[P_tha(CMS)/P_tha(CMS)] and P_tha(CMS)=R_thavg(CMS)*T_T

where, quantity P_tha(CMS) is theoretical actual product output units from the complex manufacturing subsystem (CMS) in total time, and R_thavg(CMS) is defined as the average theoretical processing rate for total product output from the complex manufacturing subsystem (CMS) during the period of total time T_T and, optionally

j) collecting the total costs the system including at least one of Direct Manufacturing Costs (DMC);

Process Labor (PL), Process Energy and Utilities (PE &

U), Process Tooling (PT), Process Materials (PM), Equipment Depreciation (ED), and Direct Materials (DM);

k) defining all direct manufacturing activities at each UPP activity, including at least one of;

Manufacturing Operations (MO), Engineering Operations (EO), Quality Assurance Operations (QAO), Material Handling Operations (MHO), and Production Management (PM);

l) allocating the DMC from each of the set of 6 (six) DMC Categories in step j) above to each of the 5 direct manufacturing activities defined in step k) at the respective UPP activity centers based on second stage cost driver factors;

m) obtaining a dollar value of costs of each of the activities of the respective UPP-activity center using Equations (15-2) and (15-3),

$\begin{array}{cc}A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>2\right)\\ A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_i^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>3\right)\end{array}$

where

AC^UPP_ij=the jth activity cost component contributed to UPP activity center i

AC^UPP_i=total activity cost of UPP activity cost center

DMC_k=kth direct manufacturing cost component

DCD_ijk=direct resource cost driver which allocates kth direct manufacturing cost to jth activity component of UPP activity center i;

n) allocating the costs of each of the five general sets of activities of the respective UPP-activity center to three products based on third stage cost-driver factor as follows;

$\frac{\text{Manufacturing Operations Labor Hrs of}\text{UPP}\text{-1 on Product-1}}{\text{Total Manufacturing Operations Labor Hours for All}\text{UPP}\text{'"'"'s}}=\mathrm{xx}$

and,

o) determining the total unit direct manufacturing cost (TDMC_k, $/unit) for each product type, k, from Equation (154), where the numerator represents the total dollar cost of product contributed by each UPP activity center, and P_g(k) represents the number of good product units of product type k

$\begin{array}{cc}{\mathrm{TDMC}}_k=\frac{\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{P_{g<br><br>\left(k\right)}}& \left(15<br><br>\text{-}<br><br>4\right)\end{array}$

 

and further optionally,

p) determining the total direct manufacturing cost of a unit of good product averaged over all product types, k, during the period, T_T, from Equation 15-(5),

$\begin{array}{cc}\begin{array}{c}{\mathrm{TDMC}}_{\mathrm{AVG}}=\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\underset{k}{\sum <br><br>}<br><br>P_{g<br><br>\left(k\right)}}\\ =\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\mathrm{OTE}\times <br><br>R_{\mathrm{avg}<br><br>\left(F\right)}^{\left(\mathrm{th}\right)}\times <br><br>T_T}\end{array}& \left(15<br><br>\text{-}<br><br>5\right)\end{array}$

where

ACD_ijk=activity center cost driver, which traces the jth activity cost of UPP activity center i to product type k

OTE=unit-based overall throughput effectiveness of the factory

R^(th)_avg(F)=theoretical average processing rate in time T_T for products through the factory,

thereby establishing a relation of the average product cost to productivity (OTE).

71. The computer system of claim 70, in which the manufacturing subsystem comprises a plurality of integrated processing modules linked together.

72. The computer system of claim 71, in which the manufacturing subsystem comprises fixed-sequence cluster tools.

73. The computer system of claim 71, in which the manufacturing subsystem comprises flexible-sequence cluster tools.

74. A computer system of claim 70, in which each UPP comprises input transport rates from an upstream UPP, and output transport rates to a downstream UPP, input and output storage buffers for work in process, and a unit process step.

75. A computer system of claim 70, in which algorithms are applied to calculate the productivity metrics of unit based overall equipment effectiveness (OEE), cycle time effectiveness (CTE), production throughput of good product (P_g) and UPP inventory level (L_upp) based on any one or more of the following:

factory data for equipment time parameters, theoretical cycle time, actual cycle time, arrival and departure rates, and input and output buffer levels.

76. A computer system of claim 70, in which algorithms are applied to calculate UPP subsystem and/or system level productivity metrics of overall throughput effectiveness (OTE_F), cycle time effectiveness (CTE_F), production throughput of good product (P_G(F)) and UPP subsystem or factory inventory level (L_F), based on factory data and the productivity metrics for each UPP.

77. A computer system of claim 70, in which measurement, monitoring and quantitative calculation of the productivity metrics for the UPPs, the UPP subsystems, and/or production system is conducted using spreadsheet analysis tools which represent an actual factory architecture or the system.

78. A computer system of claim 70, in which measurement, monitoring and quantitative calculation of the productivity metrics for the UPPs, the UPP subsystems, and systems is conducted using a flowchart tool and a graphical user interface for data input and metrics output in appropriate spreadsheet or chart format.

79. A computer system of claim 77, comprising:

creating UPPs required to represent the generic subsystem types,

creating data input and metrics output boxes for standard input and output of data and results,

linking the UPPs to represent the experimental material flow sequence, or system architecture, with recognition algorithms applied to identify the generic subsystem types, and

calculating productivity metrics for each UPP, UPP subsystem, and the overall system.

80. A computer system of claim 78, in which the UPPs include regular, assembly and expansion.

81. A computer system of claim 70, further comprising building an automated simulation model comprising importing data in spreadsheet form from a flowcharting and measurement tool, and representing interconnectivity of the system and actual and theoretical performance characteristics.

82. A computer system of claim 70, in which the simulation model comprises a rapid what-if scenario analysis of existing production facilities or systems, wherein specific changes needed for bottleneck removal and productivity improvement are identified.

83. A computer system of claim 70, in which the scenario analysis is linked to market demand.

84. A computer system of claim 70, in which the simulation model comprises rapid assessment and development of new factory designs optimized for specific manufacturing performance.

85. A computer system of claim 70, wherein the UPP includes any one or more of the following:

equipment, subsystem, product line, manufacturing process, factory, transportation system, and supply chains (which includes transportation systems and manufacturing systems).

86. A computer system of claim 70, wherein measurement and analysis of the system are conducted using a spreadsheet analysis and a visual flowcharting and measurement tool coded with the algorithms for unit-based productivity measurement at the equipment, subsystem and system level.

87. A computer system of claim 86, wherein the measurement and analysis of the system is conducted for single and/or multiple product types.

88. A computer system of claim 70, wherein data representing interconnectivity of the system and intrinsic performance characteristics are transferred from the flowcharting and measurement tool via at least one or more appropriate spreadsheets to set up an equivalent manufacturing array in a discrete event simulation software package.

89. A computer system of claim 88, wherein development and implementation of a dynamic simulation is used to assess scenarios for eliminating bottlenecks and tailoring performance, and to develop new designs optimized for specific requirements in the production system.

90. A computer system of claim 70, wherein the production system includes any one or more of the following:

equipment, subsystem, product line, manufacturing process, factory, transportation system, and supply chains (which includes transportation systems and manufacturing systems).

91. A computer system of claim 70, wherein the method is used to analyze overall equipment effectiveness.

126. The computer system of claim 70, wherein step (g) comprises calculating average theoretical processing rates of chamber and pseudo-chambers in a Series-Connected subsystem for all operation sequences (OSs) by using the following equation

127. The computer system of claim 126 wherein (R_avg(CT)^(th)) is used to calculate P_a(CT)^(th), theoretical total product output/processes (units) from the subsystem in a total time T_T,

P_a(CT)^(th)=(R_avg(CT)^(th))(T_T) 

 

(2b)

and the overall throughput effectiveness is defined as

128. The computer system of claim 126, comprising determining the overall throughput effectiveness (OTE) of step (i) by determining the product of the available efficiency, the performance efficiency, and the quality efficiency

OTE_(CT)=(A_eff(CT))(P_eff(CT))(Q_eff(CT)) 

 

(10b).

129. The computer system of claim 128, wherein the available efficiency for the subsystem is defined as

92. A computer system for hierarchical representation of a production system for measuring, monitoring, analyzing and/or simulating production performance of the production system based on a common set of productivity metrics for throughput effectiveness, cycle time effectiveness, throughput and inventory, comprising:

a) identifying an array of production operations including any one or more of the following;

process, transportation, storage, cost, building of simulation model, and time;

b) providing a description of the production system as an interconnected array of unit production processes (UPP) reflecting an actual material flow sequence through the system;

c) applying at least one set of UPP subsystems to factor an overall system flowchart into UPP complex manufacturing subsystems, and combining the subsystems to represent the overall production system;

d) analyzing productivity metrics of each UPP, each UPP complex manufacturing subsystem, and the overall system;

e) determining a quantity of Operating Sequences (OSs) describing the material flow sequence of products through the complex manufacturing subsystem;

f) determining product throughout or input, P_a, good product output, P_g, and defective product, P_a-P_g, for a total time, T_T, of measurement or simulation;

g) determining each OS in the complex manufacturing subsystem (CMS), and determining Overall Equipment Effectiveness (OEE) for each of the UPPs;

h) determining availability efficiency (A_eff) or yield of each UPP; and

i) determining Overall Throughput Effectiveness (OTE) of the complex manufacturing subsystem (CMS) by the relations,

OTE_CMS=[P_tha(CMS)/P_tha(CMS)] and P_tha(CMS)=R_thavg(CMS)*T_T or, OTE_CMS=A_(CMS)·

P_(CMS)·

Q_(CMS).

where, quantity P_tha(CMS) is theoretical actual product output units from the complex manufacturing subsystem (CMS) in total time, and R_thavg(CMS) is defined as the average theoretical processing rate for total product output from the complex manufacturing subsystem (CMS) during the period of total time T_T; and

, optionally

j) collecting the total costs the system including at least one of Direct Manufacturing Costs (DMC);

Process Labor (PL), Process Energy and Utilities (PE &

U), Process Tooling (PT), Process Materials (PM), Equipment Depreciation (ED), and Direct Materials (DM);

k) defining all direct manufacturing activities at each UPP activity, including at least one of;

Manufacturing Operations (MO), Engineering Operations (EO), Quality Assurance Operations (QAO), Material Handling Operations (MHO), and Production Management (PM);

l) allocating the DMC from each of the set of 6 (six) DMC Categories in step j) above to each of the 5 direct manufacturing activities defined in step k) at the respective UPP activity centers based on second stage cost driver factors;

m) obtaining a dollar value of costs of each of the activities of the respective UPP-activity center using Equations (15-2) and (15-3),

$\begin{array}{cc}A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>2\right)\\ A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_i^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>3\right)\end{array}$

where

AC^UPP_ij=the jth activity cost component contributed to UPP activity center i

AC^UPP_i=total activity cost of UPP activity cost center

DMC_k=kth direct manufacturing cost component

DCD_ijk=direct resource cost driver which allocates kth direct manufacturing cost to jth activity component of UPP activity center i;

n) allocating the costs of each of the five general sets of activities of the respective UPP-activity center to three products based on third stage cost-driver factor as follows;

$\frac{\text{Manufacturing Operations Labor Hrs of}\text{UPP}\text{-1 on Product-1}}{\text{Total Manufacturing Operations Labor Hours for All}\text{UPP}\text{'"'"'s}}$

and,

o) determining the total unit direct manufacturing cost (TDMC_k, $/unit) for each product type, k, from Equation (15-4), where the numerator represents the total dollar cost of product contributed by each UPP activity center, and P_g(k) represents the number of good product units of product type k

$\begin{array}{cc}{\mathrm{TDMC}}_k=\frac{\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{P_{g<br><br>\left(k\right)}}& \left(15<br><br>\text{-}<br><br>4\right)\end{array}$

 

and further optionally,

p) determining the total direct manufacturing cost of a unit of good product averaged over all product types, k, during the period, T_T, from Equation 15-(5),

$\begin{array}{cc}\begin{array}{c}{\mathrm{TDMC}}_{\mathrm{AVG}}=\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\underset{k}{\sum <br><br>}<br><br>P_{g<br><br>\left(k\right)}}\\ =\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\mathrm{OTE}\times <br><br>R_{\mathrm{avg}<br><br>\left(F\right)}^{\left(\mathrm{th}\right)}\times <br><br>T_T}\end{array}& \left(15<br><br>\text{-}<br><br>5\right)\end{array}$

where

ACD_ijk=activity center cost driver, which traces the jth activity cost of UPP activity center i to product type k

OTE=unit-based overall throughput effectiveness of the factory

R^(th)_avg(F)=theoretical average processing rate in time T_T for products through the factory,

thereby establishing a relation of the average product cost to productivity (OTE), and, further

q) converting the flowchart to a discrete event simulation description, and enabling comparative performance assessment of various production scenarios useful for performance improvement and system design.

93. The computer system of claim 92, in which the manufacturing subsystem comprises a plurality of integrated processing modules linked together.

94. The computer system of claim 93, in which the manufacturing subsystem comprises fixed-sequence cluster tools.

95. The computer system of claim 93, in which the manufacturing subsystem comprises flexible-sequence cluster tools.

130. The computer system of claim 92, wherein step (g) comprises calculating average theoretical processing rates of chamber and pseudo-chambers in a Series-Connected subsystem for all operation sequences (OSs) by using the following equation

131. The computer system of claim 130 wherein (R_avg(CT)^(th)) is used to calculate P_a(CT)^(th), theoretical total product output/processes (units) from the subsystem in a total time T_T,

P_a(CT)^(th)=(R_avg(CT)^(th))(T_T) 

 

(2b)

and the overall throughput effectiveness is defined as

132. The computer system of claim 130, comprising determining the overall throughput effectiveness (OTE) of step (i) by determining the product of the available efficiency, the performance efficiency, and the quality efficiency

OTE_(CT)=(A_eff(CT))(P_eff(CT))(Q_eff(CT)) 

 

(10b).

133. The computer system of claim 132, wherein the available efficiency for the subsystem is defined as

96. A computer program product comprising a program storage device readable by a computer system tangibly embodying a program of instructions executed by the computer system to perform in a process for causally relating productivity to a production system, the process comprising:

a) identifying an array of production operations including any one or more of the following;

process, transportation, storage, cost, building of simulation model, and time;

b) modeling the system as an interconnected array of unit production processes (UPP) reflecting actual or desired material flow sequence through the system;

c) applying at least one set of UPP interconnections to factor the system into at least one set of UPP complex manufacturing subsystems for description and analysis;

d) assessing each UPP and each complex manufacturing subsystem type to calculate at least one productivity metric of each UPP, UPP complex manufacturing subsystem and the system; and

e) determining a quantity of Operating Sequences (OSs) describing the material flow sequence of products through the complex manufacturing subsystem;

f) determining product throughout or input, P_a, good product output, P_g, and defective product, P_a-P_g, for a total time, T_T, of measurement or simulation;

g) determining each OS in the complex manufacturing subsystem (CMS), and determining Overall Equipment Effectiveness (OEE) for each of the UPPs;

h) determining availability efficiency (A_eff) or yield of each UPP; and

i) determining Overall Throughput Effectiveness (OTE) of the complex manufacturing subsystem (CMS) by the relations,

OTE_CMS=[P_tha(CMS)/P_tha(CMS)] and P_tha(CMS)=R_thavg(CMS)*T_T

where, quantity P_tha(CMS) is theoretical actual product output units from the complex manufacturing subsystem (CMS) in total time, and R_thavg(CMS) is defined as the average theoretical processing rate for total product output from the complex manufacturing subsystem (CMS) during the period of total time T_T and, optionally

j) collecting the total costs the system including at least one of Direct Manufacturing Costs (DMC);

Process Labor (PL), Process Energy and Utilities (PE &

U), Process Tooling (PT), Process Materials (PM), Equipment Depreciation (ED), and Direct Materials (DM);

k) defining all direct manufacturing activities at each UPP activity, including at least one of;

Manufacturing Operations (MO), Engineering Operations (EO), Quality Assurance Operations (QAO), Material Handling Operations (MHO), and Production Management (PM);

l) allocating the DMC from each of the set of 6 (six) DMC Categories in step j) above to each of the 5 direct manufacturing activities defined in step k) at the respective UPP activity centers based on second stage cost driver factors;

m) obtaining a dollar value of costs of each of the activities of the respective UPP-activity center using Equations (15-2) and (15-3),

$\begin{array}{cc}A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>2\right)\\ A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_i^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}=\underset{j}{\sum <br><br>}<br><br>\underset{k}{\sum <br><br>}<br><br>{\mathrm{DMC}}_k\times <br><br>{\mathrm{DCD}}_{\mathrm{ijk}}& \left(15<br><br>\text{-}<br><br>3\right)\end{array}$

where

AC^UPP_ij=the jth activity cost component contributed to UPP activity center i

AC^UPP_i=total activity cost of UPP activity cost center

DMC_k=kth direct manufacturing cost component

DCD_ijk=direct resource cost driver which allocates kth direct manufacturing cost to jth activity component of UPP activity center i;

n) allocating the costs of each of the five general sets of activities of the respective UPP-activity center to three products based on third stage cost-driver factor as follows;

$\frac{\text{Manufacturing Operations Labor Hrs of}\text{UPP}\text{-1 on Product-1}}{\text{Total Manufacturing Operations Labor Hours for All}\text{UPP}\text{'"'"'s}}=\mathrm{xx}$

and,

o) determining the total unit direct manufacturing cost (TDMC_k, $/unit) for each product type, k, from Equation (154), where the numerator represents the total dollar cost of product contributed by each UPP activity center, and P_g(k) represents the number of good product units of product type k

$\begin{array}{cc}{\mathrm{TDMC}}_k=\frac{\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{P_{g<br><br>\left(k\right)}}& \left(15<br><br>\text{-}<br><br>4\right)\end{array}$

 

and further optionally,

p) determining the total direct manufacturing cost of a unit of good product averaged over all product types, k, during the period, T_T, from Equation 15-(5),

$\begin{array}{cc}\begin{array}{c}{\mathrm{TDMC}}_{\mathrm{AVG}}=\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\underset{k}{\sum <br><br>}<br><br>P_{g<br><br>\left(k\right)}}\\ =\frac{\underset{k}{\sum <br><br>}<br><br>\underset{i\in <br><br>\mathrm{OP}}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>A<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{ij}}^{\mathrm{UPP}}\times <br><br>{\mathrm{ACD}}_{\mathrm{ijk}}}{\mathrm{OTE}\times <br><br>R_{\mathrm{avg}<br><br>\left(F\right)}^{\left(\mathrm{th}\right)}\times <br><br>T_T}\end{array}& \left(15<br><br>\text{-}<br><br>5\right)\end{array}$

where

ACD_ijk=activity center cost driver, which traces the jth activity cost of UPP activity center i to product type k

OTE=unit-based overall throughput effectiveness of the factory

R^(th)_avg(F)=theoretical average processing rate in time T_T for products through the factory,

thereby establishing a relation of the average product cost to productivity (OTE).

97. The computer program product of claim 96, in which the manufacturing subsystem comprises a plurality of integrated processing modules linked together.

98. The computer program product of claim 97, in which the manufacturing subsystem comprises fixed-sequence cluster tools.

99. The computer program product of claim 97, in which the manufacturing subsystem comprises flexible-sequence cluster tools.

100. The method of claim 96, in which each UPP comprises input transport rates from an upstream UPP, and output transport rates to a downstream UPP, input and output storage buffers for work in process, and a unit process step.

101. The method of claim 96, in which algorithms are applied to calculate the productivity metrics of unit based overall equipment effectiveness (OEE), cycle time effectiveness (CTE), production throughput of good product (P_g) and UPP inventory level (L_upp), based on any one or more of the following:

factory data for equipment time parameters, theoretical cycle time, actual cycle time, arrival and departure rates, and input and output buffer levels.

102. The method of claim 96, in which algorithms are applied to calculate UPP subsystem and/or system level productivity metrics of overall throughput effectiveness (OTE_F), cycle time effectiveness (CTE_F), production throughput of good product (P_G(F)) and UPP subsystem or factory inventory level (L_F), based on factory data and the productivity metrics for each UPP.

103. The method of claim 96, in which measurement, monitoring and quantitative calculation of the productivity metrics for the UPPs, the UPP subsystems, and/or production system is conducted using spreadsheet analysis tools which represent an actual factory architecture or the system.

104. The method of claim 96, in which measurement, monitoring and quantitative calculation of the metrics for the UPPs, the UPP subsystems, and systems is conducted using a flowchart tool and a graphical user interface for data input and metrics output in appropriate spreadsheet or chart format.

105. The method of claim 101, comprising:

creating UPPs required to represent the generic subsystem types,

creating data input and metrics output boxes for standard input and output of data and results,

linking the UPPs to represent the experimental material flow sequence, or system architecture, with recognition algorithms applied to identify the generic subsystem types, and

calculating productivity metrics for each UPP, UPP subsystem, and the overall system.

106. The method of claim 105, in which the UPPs include regular, assembly and expansion.

107. The method of claim 96, further comprising building an automated simulation model comprising importing data in spreadsheet form from a flowcharting and measurement tool, and representing interconnectivity of the system and actual and theoretical performance characteristics.

108. The method of claim 96, in which the simulation model comprises a rapid what-if scenario analysis of existing production facilities or systems, wherein specific changes needed for bottleneck removal and productivity improvement are identified.

109. The method of claim 96, in which the scenario analysis is linked to market demand.

110. The method of claim 96, in which the simulation model comprises rapid assessment and development of new factory designs optimized for specific manufacturing performance.

111. The method of claim 96, wherein the UPP includes any one or more of the following:

equipment, subsystem, product line, manufacturing process, factory, transportation system, and supply chains (which includes transportation systems and manufacturing systems).

112. A computer program of claim 96, wherein measurement and analysis of the system are conducted using a spreadsheet analysis and a visual flowcharting and measurement tool coded with the algorithms for unit-based productivity measurement at the equipment, subsystem and system level.

113. The method of claim 112, wherein the measurement and analysis of the system is conducted for single and/or multiple product types.

114. A computer program of claim 112, wherein data representing interconnectivity of the system and intrinsic performance characteristics are transferred from the flowcharting and measurement tool via at least one or more spreadsheets to set up an equivalent manufacturing array in a discrete event simulation software package.

115. A computer program of claim 114, wherein development and implementation of a dynamic simulation is used to assess scenarios for eliminating bottlenecks and tailoring performance, and to develop new designs optimized for specific requirements in the production system.

116. A computer program of claim 96, wherein the production system includes any one or more of the following:

equipment, subsystem, product line, manufacturing process, factory, transportation system, and supply chains (which includes transportation systems and manufacturing systems).

117. A computer program of claim 96, wherein the method used to analyze overall equipment effectiveness.

134. The computer program product of claim 96, wherein step (g) comprises calculating average theoretical processing rates of chamber and pseudo-chambers in a Series-Connected subsystem for all operation sequences (OSs) by using the following equation

135. The computer program product of claim 134 wherein (R_avg(CT)^(th)) is used to calculate P_a(CT)^(th), theoretical total product output/processes (units) from the subsystem in a total time T_T,

P_a(CT)^(th)=(R_avg(CT)^(th))(T_T) 

 

(2b)

and the overall throughput effectiveness is defined as

136. The computer program product of claim 134, comprising determining the overall throughput effectiveness (OTE) of step (i) by determining the product of the available efficiency, the performance efficiency, and the quality efficiency

OTE_(CT)=(A_eff(CT))(P_eff(CT))(Q_eff(CT)) 

 

(10b).

137. The computer program product of claim 136, wherein the available efficiency for the subsystem is defined as