Grouped Data Analysis

The original 110 data points are depicted below. The maximum of the data set is, 57.5, the minimum is 53.1, the range is 4.4, the average is 55.4, and the standard deviation is 1.113.

The process capability is a processes ability to produce a product withing the given specifications. Since the specification given is 55 +/-4.0 the the range the product must fall within the range of 51 and 59. By subtracting this information we get the numerator of our equation.  The denominator will be our standard deviation multiplied by 6. Thus the process specification will be: Cp=(59-51)/(6*1.113)=1.198
In the case that the process capability needs to be tighter we can take process centering and variability into consideration. To do this the numerator can be replaced by the difference between the maximum and the minimum.  The denominator is then replaced by 3 times the standard deviation. Thus the process specification becomes: Cpk=(57.5-55.4)/(3*1.113)=0.629

The data was grouped with a frequency distribution in increments of 0.5. Since the distribution is not tight enough that it would be impossible to make the part it had an adequate kurtosis. The histogram is also centered within the parameters showing a good skewness.