Quality Money Management : Process Engineering and Best Practices for Systematic Trading and Investment

260 CHAPTER ◆ 2 8 Perform SPC Analysis

Over time, other process-monitoring tools have been developed for different underlying

process distributions, including:

● Pareto diagrams

● Scatter diagrams

● CUSUM chart.

● EWMA charts.

A cumulative sum control chart (CUSUM) plots the cumulative sum of deviations of suc-

cessive samples from the average. An exponentially weighted moving average (EWMA)

chart plots the weighted average of current and all previous values, giving greater weight

to more recent data and decreasing weights for older data.

28.3.4. Process Capability

Process capability is a way of reporting performance with what are called C p , C pk mea-

surements. In process improvement efforts, the process capability index or process capa-

bility ratio is a statistical measure of the ability of a process to produce output within

specification limits, assuming a state of statistical control.

● C p process capability index is a measure of the capability of a process, that is, what

it could produce.

● C pk process capability index adjusts the C p index for the effect of a noncentered

distribution.

Capability statistics are basically a ratio between the width of the specification limits,

that is, the tolerance, and the actual process spread. C p estimates what the process would

be capable of producing if the process could be centered assuming the process is approxi-

mately normal.

Cp





USL LSL

6 

The upper specification limit minus the lower specification limit, called the tolerance,

divided by six times sigma is the capability of the machine. That is, the machine is

capable of operating within the specified tolerance. In a case where the process spread

is greater than the tolerance, the system must be considered to be incapable of meeting

specifications. A C p of 1 or greater means the system is capable of operating within toler-

ance. The C pk takes into account off-centeredness.

Cpk









min ,

USL  LSL





33 

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⎣

⎢

⎢

⎤

⎦

⎥

⎥

Process capability charts can have important applications to backtesting as well

since they show whether or not a process is capable of remaining in control.