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Process Capability: Engineering and Statistical Issues

also defines the key words of this definition, namely process, capability and reproducibility as:

Process uniąue combination of machinę, tools, methods, materials and people engaged in production.” We notę that this infers that process capability is a broader term than machinę capability, sińce it includes other potential sources of variability.

Capability “...competence, based on tested performance, to achieve measurable results."

Reproducibility: “...refers to the product uniformity resulting from a process which is in a State of statistical control, i.e., in the absence of -assignable causes of variation. Jnstantaneous reproducibility is a synonym."

Thus, what might have initially seemed like a very simple exercise of just estimating a mean and a standard deviation and calculating some index, has now raised some important, fundamental issues. For example, how does one properly account for the variability among the machines, tools, methods, materials and the people engaged in production? We defer the resolution of these important ąuestions until later. But the reader should consider these issues and how they might affect the meaning of each of the following indices.

Process capability indices relate the specifications to the process tolerance. The simplest process capability index is C_p:

_ USL-LSL ^p ~ 6a

where USL and LSL are the upper and lower specification limits, respectively, and a is the process standard deviation. The C_p index represents the ratio of

the specification width to the natural tolerance spread of the process.

Another index that measures a process' potential when the process is centered on an explicit, finite process target, T, is C_pl which is defined in terms

of C_p„ and C_ptu.

C_pl = min {C_ptlC_plu} where