**Opportunity Statements**

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).

Day No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

Gas Mileage (km/lt) | 21 | 19 | 20 | 22 | 18 | 21 | 20 | 20 | 18 | 20 | 19 | 22 | 20 | 21 | 19 | 20 | 19 | 21 | 18 | 22 |

**Root Cause**

- 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.

**Develop Alternatives**

**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.

References:

*Kiemele, Mark J., Schmidt, Stephen R. & Berdine, Ronald J. (2000), Basic Statistic, Tools for Continuous Improvement 4*^{th}*Edition, Colorado: Air Academy Press, LLC.**Sullivan, William G., Wicks, Elin M. & Koelling, C. Patrick (1942), Engineering Economy 15*^{th}*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.*

OUTSTANDING, Candra!!! Your usual excellent work!!! Very impressive and very proud of your ability to apply what you are learning to very real day to day problems.

About the only thing I see missing from your IPO Analysis would be the quality of the fuel? Do you think that using Premium vs Regular would make any significant difference in a motorcycle? Also, I think if you used diluted or contaminated fuel, that too would impact the mileage, but then again, that would probably produce an outlying condition?

Regardless, this is an excellent (and very REAL) application of SPC in our day to day lives.

Will be looking forward to your W9 posting as well!!

BR,

Dr. PDG, Jakarta