## DFSS

#### benchmarking

Maps technical benchmarking data to a percentage scale of performances.

Collection benchmarking(Collection data, Collection opt, Collection best)

• data: is the table of benchmarking data
• opt: is the vector of optimization directions
• best: is the vector of "best in class" values

#### best

Returns the best value according to a given direction for optimization

Object best(Collection x, Collection opt)

• x: Is the container with the input values
• opt: is the container with the direction for optimization

#### BOMConceptCost

Calculates the cost of all parts needed for different concepts

Collection BOMConceptCost(Collection quantity, Collection costperunit, Collection conceptselection)

• quantity: is the quantity (per concept)
• costperunit: is the unit cost
• conceptselection: is the concept selection table

#### consistencyRatio

computes the consistency ratio

Collection consistencyRatio(Collection matrix, Collection importance, Collection ri=nothing, Collection =nothing)

• matrix: is the ahp matrix
• importance: is the vector containing the importance in group for the ahp
• ri:
• :

#### criticality

Determines if a combination of difficulty and importance values is critical. Returns a range from 0...4.

Collection criticality(Collection difficulty, Collection importance, float d_crit=0.0, float i_crit=0.0)

• difficulty: is the difficulty
• importance: is the importance
• d_crit: is the threshold for the critical difficulty
• i_crit: is the threshold for the critical importance

#### csi

Maps a vector from one tree to another by applying the independent scoring method. Mathematically, the independent scoring method can be expressed as a linear transformation.

Collection csi(Collection matrix, Collection x)

• matrix: is the QFD correlation matrix.
• x: is the vector in the source tree you want to map.

#### gap

returns the absolute of the difference between x and y. Only existing matrix values are handled.

Object gap(Object x, Object y)

• x: is the first value
• y: is the second value

#### independentScore

Maps a vector from one tree to another by applying the independent scoring method. Mathematically, the independent scoring method can be expressed as a linear transformation.

Collection independentScore(Collection matrix, Collection x, integer sign=all, Object total=0.0, integer grouphandling=autodetect)

• matrix: is the QFD correlation matrix.
• x: is the vector in the source tree you want to map.
• sign: sets a filter for the matrix relations: all, pos(itive only), neg(ative only)
• total: total sum for normalization. Use 0 in order to skip normalization.
• grouphandling: group handling mode: shallow (leafs only), sums (accumulate hierarchically), levels (calculate system level and paramater level separately).

#### opportunity

Calculates the difference of an importance and a performance value if importance>performance>0

Collection opportunity(Collection importance, Collection performance)

• importance: is the importance value
• performance: is the performance value

#### pairedComparison

Returns the result of a paired comparison. The result is calculated as the Eigenvector corresponding to the largest Eigenvalue of the matrix.

Collection pairedComparison(Collection matrix)

• matrix: The matrix containing the comparisons. Must be a reciprocal matrix with 1's on the diagonal. Use mirrorInv() to create a reciprocal matrix from an upper or lower triangular matrix.

#### proportionalScore

Maps a vector from one tree to another by applying the proportional scoring method.

Collection proportionalScore(Collection matrix, Collection x, integer sign=all, Object total=0.0, integer grouphandling=autodetect)

• matrix: is the QFD correlation matrix.
• x: is the vector in the source tree you want to map.
• sign: sets a filter for the matrix relations: all, pos(itive only), neg(ative only)
• total: total sum for normalization. Use 0 in order to skip normalization.
• grouphandling: group handling mode: shallow (leafs only), sums (accumulate hierarchically), levels (calculate system level and paramater level separately).

#### pughSum

Returns the Pugh sum for a container. The Pugh sum is a measure for the number of positive and negative effects of a number of alternatives.

Object pughSum(Collection x, Collection value, Object param1=nothing, Object param2=nothing, Object param3=nothing, Collection , Collection , Object =nothing, Object =nothing, Object =nothing)

• x: is the container for which you want to calculate the Pugh sum.
• value: is the Pugh value, i.e.the value being counted. Normally, this argument should be one of -1, 0 +1 to count negative, neutral or positive relationships in the given container.
• param1: is the first parameter (7.5 for positive, 5 for neutral, 2.5 for negative pugh sum)
• param2: is the second parameter (10 for positive, 0 for negative pugh sum)
• param3:
• : is the container for which you want to calculate the Pugh sum.
• : is the Pugh value, i.e.the value being counted. Normally, this argument should be one of -1, 0 +1 to count negative, neutral or positive relationships in the given container.
• : is the first parameter (7.5 for positive, 5 for neutral, 2.5 for negative pugh sum)
• : is the second parameter (10 for positive, 0 for negative pugh sum)
• :

#### pughSumEx

Object pughSumEx(Collection x, Collection concepts, Collection mode, Object param1=nothing, Object param2=nothing, Object param3=nothing)

• x:
• concepts:
• mode:
• param1:
• param2:
• param3:

#### ranking

Calculates rank numbers for a sequence according to the values in a vector. If the reverse parameter is false, the item with the highest value will get rank number 1. If the reverse parameter is true, the item with the lowest value will get rank number 1.

Collection ranking(Collection vector, boolean reverse=false)

• vector: a vector of values to be compared to each other
• reverse: indicates the sort direction

#### scaleBenchmarking

Maps technical data to a given scale of performances using a data-to-performance mapping table

Collection scaleBenchmarking(Collection data, Collection map, Collection scores, Collection opt=nothing, boolean limit=true, Collection accumulate=nothing)

• data: is the table of benchmarking data
• map: is the data-to-performance mapping table
• scores: is the vector of performance scale values
• opt: is the vector of optimization directions
• limit: if true, result is limited to the scaled range
• accumulate:

#### scaleBenchmarkingEx

Maps technical data to a given scale of performances using a data-to-performance mapping table

Collection scaleBenchmarkingEx(Collection data, Collection map, Collection scores, Collection opt=nothing, Collection limit=nothing)

• data: is the table of benchmarking data
• map: is the data-to-performance mapping table
• scores: is the vector of performance scale values
• opt: is the vector of optimization directions
• limit: if true, result is limited to the scaled range

#### scaleMax

Re-scales argument x from 0..maximum(x) to the new range given by min and max

Collection scaleMax(Collection x, Object min=1, Object max=10, Object mode=levels)

• x: is the vector of values to be re-scaled
• min: is the new minimum
• max: is the new maximum
• mode: is the calculation mode: shallow: calculate in the dimension of x, levels: calculate for both the system and the parameter level of x

Returns the spectral radius of the comparison matrix. The spectral radius is the largest Eigenvalue of the comparison matrix.

• matrix: The matrix containing the comparisons. Must be a reciprocal matrix with 1's on the diagonal. Use mirrorInv() to create a reciprocal matrix from an upper or lower triangular matrix.

#### topsis

Concept selection function TOPSIS

Collection topsis(Collection decisionMatrix, Collection importance, Collection optimization, Collection best=nothing, Collection worst=nothing, boolean useBestWorst=false)

• decisionMatrix: the decision matrix with quantified performance data
• importance: the vector of decision criteria weights
• optimization: the vector of decision criteria optimization directions
• best: the vector of best-in-class performance
• worst: the vector of worst in class performance
• useBestWorst: if true always use best and worse for calculation

#### topsisEx

Concept selection function TOPSIS

Collection topsisEx(Collection decisionMatrix, Collection importance, Collection map, Collection scores)

• decisionMatrix: the decision matrix with quantified performance data
• importance: the vector of decision criteria weights
• map: is the data-to-performance mapping table
• scores: is the vector of performance scale values

#### totalImportance

Calculates the total importance from one or more scoring methods, e.g. AHP, result of a questionnaire...

Collection totalImportance(Collection table, float total=1.0)

• table: is the table containing the results of the different methods
• total: the intended total sum for the result, 1.0 for percentage

#### worst

Returns the worst value according to a given direction for optimization

Object worst(Collection x, Collection opt)

• x: Is the container with the input values
• opt: is the container with the direction for optimization