I have to start learning of Statistical Process Control (SPC) from something simple which I took using a motor cycle to go to the office everyday and one critical item to be measured is gas mileage.
I want to know whether the gas consumption is within control or not (the data is round up).
|Gas Mileage (km/lt)||21||19||20||22||18||21||20||20||18||20||19||22||20||21||19||20||19||21||18||22|
- Computing the average gas mileage over the 20 days will give me a feel for the motor cycle ‘s expected gas mileage.
- To obtain a measure of the variability in gas mileage, I can calculate the variance.
Development of the outcomes
The first step in generating a control chart is to construct a run chart as per graph below:
Mean = 20 km / ltrs.
Calculate the variance s^2:
S^2 = 1.684 hence the standard deviation = 1.3.
Minimum Acceptable requirements
The common technique which is a simple way to get visual feel for the way data is distributed is to draw a histogram which display how frequently a given outcome occurs:
Analyze and compare the alternatives
Based on the histogram above, it would appear to be symmetric and bell shaped which is about a normal curve. Now, I am using the empirical rule to develop and interprete the control chart. Most of control charts establish the upper and lower control limit +/- 3 standard deviations from the centerline. So the result is:
- Lower Control Limit = 20 – (3*1.3) = 16,1
- Upper Control Limit = 20 + (3*1.3) = 23.9
The empirical rule states that approximately 3s = 99.73% of all gas mileage value for this motor cycle should fall within these limits.
Develop preferred alternative
The graph below is showing that the gas mileage process is in control.
Scenario: What if on day 21 produced gas mileage 23.5? Nothing special has caused this value, however a value of 15 is outside the control limit and indicates that there is an extremely high chance this value was a result of some special cause affecting the operational of motor cycle. The obvious next step is to determine its cause as per fish bone diagram.
Monitor and Evaluation (Post Mortem)
Evaluate and monitor the gas mileage of motor cycle in between 16.1 – 23.9 km/ltr and always due maintenance check regularly as per manual guideline.
- Kiemele, Mark J., Schmidt, Stephen R. & Berdine, Ronald J. (2000), Basic Statistic, Tools for Continuous Improvement 4thEdition, Colorado: Air Academy Press, LLC.
- Sullivan, William G., Wicks, Elin M. & Koelling, C. Patrick (1942), Engineering Economy 15th Edition, Singapore: Prentice Hall, Inc.
- Brassard, Michael & Ritter, Diane (2010), The Memory Jogger 2nd edition, Tools for Continuous Improvement and effective planning, Canada:GOAL/QPC.