My Learning curve
1. Problem definition.
It has been now 5 weeks since we have kicked off the Takatuf PMI program. The workload has increased exponentially and so is the individual learning curve. In order to properly plan the upcoming work-, a workload histogram was analyzed in my WK2- blog post. For this blog post, the information obtained from wk-2 blog post will be used to analyze the actual work done and the Learning curve as an outcome of the work performed.
2. Identify the feasible alternative.
To identify a feasible alternative, it is essential first to understand what is learning curve?
Here are some definitions of learning curve:
Investopedia’s definition:
A concept that describes how new skills or knowledge can be quickly acquired initially, but subsequent learning becomes much slower [1]. In a visual representation of a learning curve, a steeper curve indicates faster, easier learning and a flatter curve indicates slower, more difficult learning
Graham Steven indicates that the effect of learning on the unit cost is not due to the economics of scale, but due to the repetitive action of an individual of making a product or providing a service. As the time required reduces the more times it is made. It should be noted that the learning curve is not a cost reduction technique. It is a naturally occurring human phenomenon. As Learning occurs because people are resourceful, learn from errors and are interested in finding routes to complete tasks in less time in the future [2]
Learning Curve Equation:
Learning curves are identified as the relationship between cumulative quantities and cumulative average times i.e (total cumulative time divided by cumulative quantity). This has developed to the following Mathematical equation
Z_{u} = K (u^{n})
Where u = the output unit number;
Zu = the number of input resources unit needed to produce output unit u;
K = the number of input resources unit needed to produce the first output unit;
s = the learning curve slope parameter expressed as a decimal (learning rate.)
n = the learning curve exponent= log(s)/log 2
There are two types of learning curves models:
- Unit learning curve
- Cumulative average learning curve
Both of the above models will be utilized to analyze the data and produce the outcomes
3. Development of the outcome for alternative.
As per the Takatuf-PMI program the active projects for the team were the weekly blog posting and the report. Therefore for the purpose of this analysis the blog posting project will be taken as the study case. See table 1 for Blog posting historical data
Hours/ tasks | |||||
Weeks | 1 | 2 | 3 | 4 | 5 |
Blog posting Hours | 3 | 3 | 3 | 2 | 2 |
Table 1: Blog Posting Historical data
Utilizing the Excel Regression data analysis , the following outputs were derived. This step was mainly to accumulate data that will be used later in the above equation to analyze the learning curve.
Number of Tasks (u) | Unit Hours(Zu) | Cumilitive total (Cu) | Cumulative Average time (Cav.u) | ln(u) | ln(Zu) | ln(Cavu) |
1 | 3 | 3 | 3 | 0 | 1.099 | 1.099 |
2 | 3 | 6 | 3 | 0.693 | 1.099 | 1.099 |
3 | 3 | 9 | 3 | 1.099 | 1.099 | 1.099 |
4 | 2 | 11 | 2.75 | 1.386 | 0.693 | 1.012 |
5 | 2 | 13 | 2.6 | 1.609 | 0.693 | 0.956 |
Table 2: Data development
Unit Learning Curve | Cumulative Average learning Curve | |||||||
K | n | slope | R^{2} | K | n | slope | R^{2} | |
Blog posting | 3.334 | -0.271 | 83% | 0. 6025 | 2.905 | -0.081 | 95% | 0.605 |
Table 3: Input Data for the Analysis
Observations:
As per Martin, J.R. Learning curves usually range between 70% to 100%. The higher the percentage the lower the learning. i.e. A 100% learning curve indicates no learning at all [4]. Therefore when analyzing the above table Unit learning Curve illustrates a learning curve of 83% whereas the cumulative average illustrates a substantial difference in learning curve scoring a 95 % (Meaning almost no learning).
4. Analysis and comparison of the alternatives:
The above equation which is Zu = K (un), is then used to analyze the best fit alternative between the Unit learning curve and the Cumulative average learning curve. This is done by using the data from table 3 and the equation of the learning curve to estimate the hours for future blog posting. See table 4.
Unit | Unit Hours | Cumulative Total | Cumulative Average Unit learning | Cumulative average of Average Learning Curve |
1 |
3.334 | 3.334 | 3.334 | 2.905 |
2 |
2.763 | 6.096 | 3.048 |
2.746 |
3 |
2.475 | 8.571 | 2.857 |
2.512 |
4 |
2.289 | 10.860 | 2.715 |
2.245 |
5 |
2.155 | 13.015 | 2.603 |
1.971 |
6 |
2.051 | 15.066 | 2.511 |
1.705 |
7 | 1.967 | 17.032 | 2.433 |
1.456 |
8 |
1.897 | 18.929 | 2.366 |
1.230 |
9 |
1.837 | 20.766 | 2.307 |
1.030 |
10 |
1.785 | 22.551 | 2.255 |
0.855 |
11 | 1.740 | 24.291 | 2.208 |
0.704 |
12 | 1.699 | 25.990 | 2.166 |
0.575 |
Table 4: Data Analysis and forecast for future blog posting
Table 5: Chart illustration for Future time requirement for Blog posting
5. Selection of the preferred alternatives
According to the statistical parameters, the higher value of R^{2} is usually the best fit value. Therefore, as per the data from table 3 when comparing the R^{2 }value of Unit learning curve and the Cumulative average learning curve it is clear that the Cumulative average learning curve scores higher. However, realistically the data shown from the unit learning curve illustrate a more feasible production time. Also based on the forcast in table 4 , the predictive weekly hours for blog posting in unit learning curve values ranges between 2.1-3.3 whereas the forecasted production time for the blog posting In Cumulative average learning ranges between 0.6-2.9.
As per the above the chosen criteria will the unit learning curve method with the range of 2.1-3.3.
7. Performance Monitoring and the Post Evaluation of Result.
The outcome of this analysis will be used to re-baseline the actual planned schedule for the blog posting (more realistic figure if 3 hours). This then will be used to periodically evaluate be the learning curve as the program progresses.
8. References:
- Investopedia US (2014). Learning Curve. [ONLINE] Available at: http://www.investopedia.com/terms/l/learning-curve.asp. [Last Accessed July 9, 2014].
- Steven G, (2010). The Learning Curve, The key to future management . CIMA, Research executive summary series . 6 (16), pp. Retrieved on July 9, 2014 from http://www.cimaglobal.com/Documents/Thought_leadership_docs/Learning_curve.pdf
- Asro, Y. (2014). W12.1_YAW_My Learning Curve. Retrieved on July 9, 2014 from http://kristalaace2014.wordpress.com/2014/05/14/w12-1_yaw_my-learning-curve/
- Martin J R (). The Learning Curve of Experience Curve. [ONLINE] Available at: http://maaw.info/LearningCurveSummary.htm. [Last Accessed July 9, 2014].
- Syafri, AF. (2013) W3_AFS_ Learning Curve . Retrieved on July 9, 2014 from http://simatupangaace2014.wordpress.com/2013/09/18/w3_afs_-learning-curve/
- Brookfield B, (2005). Management Accounting-Decision Management. e.g. Jet Powered Motors. 2 (), pp.44-47 retrieved on July 9, from http://www.cimaglobal.com/documents/importeddocuments/fm_april_05_p44-47.pdf
Absolutely AWESOME, Ms. Mahfoodah!!! Wonderful blog posting. I am impressed.
Interestingly enough, the historic (long term) values are closer to the Cumulative Average. Extrapolated out to W15, you probably will be closer to 0.75 to 1.25 hours per blog.
Very intriguing and interesting topic and one that is incredibly useful and important whenever tracking any work which is repetitive in nature.
For your W blog posting, what I would urge you to do is also run a Statistical Process Control analysis on your data. (See Memory Jogger 2, pages 53 – 70, pages 182 – 187 and then compare it to see if your process is capable or not. (pages 173-177)
NORMALLY what you should do is perform the Statistical Process Control analysis FIRST and throw out any outliers which fall +/- 3 Sigma from the mean. THEN run your learning curve analysis on the data minus the outliers.
Great case study, well analyzed and looking forward to see whether your SPC analysis will change the outcome any.
Excited to see where you take us with this interesting and valuable topic. (BTW, you WILL see questions on SPC on your PMP exam so this effort will not be wasted!!)
BR,
Dr. PDG, Jakarta