Ch10: Quantitative Techniques Flashcards
(1) High-Low Method (2) Time-Series (3) Correlation and Regression (4) Regression Analysis (5) Learning Curve Theory (6) Reservations of the Learning Curve Theory (7) Steady Rate (25 cards)
What is the High-Low Method?
A technique used for estimating the fixed and variable elements of a semi-variable cost to make more accurate forecasts of costs.
What is the process for the High-Low Method?
(1) Take the highest and lowest output levels.
(2) Find the difference.
(3) Calculate the Variable Cost Per Unit (VCPU).
(4) Calculate the Fixed Costs (FC) by substituting the VC into the highest output.
What is a Time Series?
- A series of figures or values recorded over time.
-FORMULA:
Time Series (TS) = Trend (T) + Seasonal Variations (SV) + Cyclical Variations (CV) + Random Variations (RV).
What are the components of a Time Series?
- Trend (T):
The underlying long-term movement in values over time. - Seasonal Variations (SV):
Short-term fluctuations in value caused by differing circumstances at different times. - Cyclical Variations (CV):
Medium-term changes in values resulting from factors that repeat in cycles. - Random Variations (RV):
Irregular, unpredictable variations due to rare occurrences.
What is the Moving Averages Method for Trend (T)?
A method that removes seasonal variations from data by averaging the results of a fixed number of periods.
What is the process for the Moving Averages Method?
(1) Calculate a ‘moving’ total for the number of periods in a normal cycle.
(2) Calculate a ‘moving’ average by dividing the moving total by the number of periods in a normal cycle.
(3) For an even number of periods, average the moving averages again to compare directly to a data point.
What is the Additive Model for Seasonal Variations (SV)?
A model that assumes the components of the Time Series are independent. The formula is SV = TS - T.
What is the process for the Additive Model?
For each trend value, calculate the SV.
Calculate the average SV for each period in the cycle.
Adjust the SV so that the total equals 0 if necessary.
What is the Multiplicative Model for Seasonal Variations (SV)?
A model that assumes SV will likely increase or decrease in line with the trend.
The formula is SV = TS / T.
What are the advantages of Time Series Analysis?
Advantages:
- Trend lines can be reviewed for reliability.
- Easy to understand.
- Enables future predictions based on past experiences.
What are the disadvantages of Time Series Analysis?
Disadvantages:
- Forecasts become less reliable the further into the future.
- Less data reduces reliability.
- Patterns of trends and SV cannot be guaranteed to continue.
- Random variations can upset patterns.
What is Correlation and Regression?
- Correlation measures the closeness of the relationship between two or more variables.
- Regression describes the closeness of a linear relationship between two variables and allows forecasting.
What is the formula for Regression Analysis?
R = [ ( n∑xy - ∑x∑y) / ( √ (n∑x2 - (∑x)2) (n∑y2 - (∑y)2) ]
n = the number of pairs of values
∑x = the sum of the x values
∑x2 = the sum of the squares of the x values
(∑x)2 = the square of the sum of the x values
∑y = the sum of the y values
∑y2 = the sum of the squares of the y values
(∑y)2 = the square of the sum of the y values
∑xy = the sum of the products of each pair of x and y values
What is the Correlation Coefficient (r)?
Measures the degree of linear correlation between two variables. The value must be between -1 and +1.
What is the Coefficient of Determination (r²)?
Measures the proportion of the total variation in one variable that can be explained by variations in other variables. The value must be between 0 and 1.
What are Interpolation and Extrapolation in Regression Analysis?
- Interpolation: Predicting a value within two extreme points of the observed range.
- Extrapolation: Predicting a value outside the two extreme points of the observed range.
What are the advantages of Regression Analysis?
Advantages:
- Gives a definitive line of best fit.
- Makes efficient use of data, many processes are linear.
What are the disadvantages of Regression Analysis?
Disadvantages:
- Assumes linearity between x and y.
- Observations may be unrepresentative.
- Historic data may not predict future patterns.
- Extrapolation of forecasting may be invalid.
- Limited data reduces reliability.
What is Learning Curve Theory?
Describes the speeding up of a job with repeated performance, where the workforce improves efficiency with experience.
What are the conditions required for Learning Curve Theory?
Significant manual element, no extensive breaks in production, early stage of production, consistency in the workforce, repetitive tasks, motivated workforce.
What are the two approaches to Learning Curve Theory?
- Tabular Approach
- Algebraic Approach: y = ax^b, where y is the cumulative average time, a is the time for the first unit, x is the cumulative number of units, and b=Index of Learning [logLR/Log2] [(LR:Learning Rate is GIVEN)/(Log2=0.30103)]
What are the applications of Learning Curve Theory?
Standard setting, budgeting, pricing decisions, work scheduling.
What are the reservations of Learning Curve Theory?
Learning rate for new products is unknown, only useful for continuous production, modern production is often tailor-made, breaks in production affect predictability.
What is meant by the Steady Rate?
Due to constant repetition, improvements get smaller so the learning process stops and reaches a steady rate where no further improvements needs to be made.
