By and large, we come across situations where we favor the mean value of the outcome of a process (central tendency) to be focused around a specified targeted value with as less variation as possible (dispersion). There are situations where the variation assumes relatively higher importance than the central tendency; mostly because higher variations are more intolerable than some shifts in central tendency. Interestingly, there may be certain situations where variation or controlled variation is advantageous as well.
Study of Process Potential:
The process potential index Cp is used to study the variation, or spread of a process with respect to specified limits. While we study process potential, we are interested in the variation and not in the central tendency. The underlying idea is that if the process is able to maintain the variation within specified limits, it is considered to possess the required potential. The centering of mean can always be achieved by setting adjustments. Or in other words, if Cp is not satisfactory, Cpk (process capability) can never be achieved, since Cpk can never exceed Cp; it can at best equal Cp.
Many examples where the variation is generally considered unfavorable to the outcome:
1. Analysis of Variance
While evaluating whether there is a significant difference between means (central tendency) for multiple sets of trials as in ANOVA, the variation between sets and within sets are compared using F tests. Thus in such situations, the variation comparison assumes high importance.
2. Relative grading systems
For many competitive examinations, the concept of ‘percentile’ is used, which is actually a relative grading system. Here, more than the absolute mark by a student, the relative variation from the highest mark is more important, thus the relative variability becomes key decisive factor.
3. Control chart analysis
While studying a process variation using a control chart, first the instability and variation are given the importance. Only if we have control on these parameters we will be able to meaningfully study the ‘Off-target’ i.e. the central tendency.
4. Temperature variation in a mold
While performing certain compression molding process, temperature variation across different points on the surface of the mold does more harm than the mean temperature. Here the mean temperature is permitted to have a wider tolerance, but the variation across mold does more warping of the product.
5. Voltage fluctuations
Many electrical appliances get damaged due to high variation (fluctuation) in the voltage, although the mean voltage (central tendency) is maintained.
Controlled variation is favorable:
1. Load distribution in a ship
While loading a ship the mean value of the load can vary, but the distribution of the load is more important to maintain the balance of the ship on water.
2. Science of music
Those who understand the science of music would agree that more than the base note, the appropriate variation of the other notes with respect to the base note is extremely important to produce good music.
Some examples where variation is favorable:
Systematic Investment plans (SIPs) take advantage of the variation in the NAVs to accumulate wealth. Here even an adverse shift of the central tendency is compensated by the variation!
Law of physics states that Force = Mass x Acceleration (F = ma). Thus, if we consider speed as the variable, it is the variation of speed that decides the force and the mean speed (central tendency) appears to have little relevance.