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Process Capability: Engineering and Statistical Issues

batch-to-batch variability, specimen-to-specimen variability, operator-to-operator variability, etc.

• Identify fiirther potential sources of variability, and estimate them using a

componcnts of variance model.

• Evaluate the underlying probability distribution of the process. The

underlying distribution, its functional form, shape, etc., should be carefully examined. Goodness-of-fit tests should be conducted to test beliefs about the distribution.

Following an exhaustive study focusing on the above points, it would then make sense to assess the capability of the process. However, the calculation of a process capability index without going through a thorough process analysis cannot be considered proper statistical practice and should be avoided.

Process Capability and Performance Assessment

When a control chart is employed in the analysis, and we think one should always be, estimates of the process mean and variability are directly available. If the process is judged to be in-control and any anomalous “out-of-control” data points deleted or “edited out,” the process parameters can be estimated from the control chart summary statistics. Below, we refer to this approach as “procedurę 1.”

•Process Mean p: Use the average X from an individuals chart or the grand average (the average of the sample averages) from the X -chart. •Process Standard Deviation ct: If an individuals chart was used, use the average moving rangę MR . For charts with subgrouping, use the average rangę R or average standard deviation S . The subgroup sample size is typically smali and hence the estimates of a should be: MR/d₂,R/d₂ and S/c₄ respectively.

Capability indices calculated from these summary statistics indicate what is achievable rather than what is currently being achieved. The editing of data prior to the calculation of the indices has been criticized by some practitioners.

The concept of process performance indices (Bigelow 1992) was created in response to the above criticism. Process performance indices (p_P,p„,.p_P>.p_P*,) are calculated using the same formulas for process capability

indices. The difference is that process performance indices do not assume that