Process capability indices example

The process capability index, Cpk, is related to the so-called process sigma such that a 6a process corresponds to a Cpk of exactly 2.00, or 2.0 defective parts per billion (PPB), assuming N (0, a) quality variance distribution (can alternative calculation for process sigma estimates 3.4 defective parts per million for a 6a process). Examples of the correspondence between Cpk, process sigma, and defect rate for N(0, a) distributions are shown in Figure 2. The process capability (based on observed yield) of pharmaceutical manufacturers has been cited by some benchmark studies to be roughly 0.7 (2.1a) [28]. 

Where there are stated specifications for individual measurements y, a is sometimes turned into a kind of index comparing it to the difference in upper and lower engineering specifications. For example, one such process capability index is... 

It is important to remember that the capability and performance indices calculated from the data are only estimates and thus have uncertainty associated with them. Confidence intervals can be calculated for these indices to reflect this imprecision. For example, a 100(1 — a)% two-sided confidence interval about the estimated process capability index Cp is ... 

If the process capability index of one product characteristic is below a defined critical value— e.g. state-of-the-art value 1.33—a review of the production process should be done to improve the manufacturing steps and achieve higher capability indices. Depending on the industrial discipline there are also higher capability requirements such as Cp > 2.0 and pk >1. 67. An example for a normally distributed characteristic (drill characteristic Cl in Table 1) is shown in Eigure 3. 

For one thing, remembering again the fact that an interval from p — 3normal distribution, the figure 6a is sometimes stated as the process capability. This usage would say that in the context of the polyethylene melt index example of Table 5.4 the a = 12.1 figure from (5-10) implies a melt index process capability... 

The next step is to determine the Capability Index (Cpk) for the system. Cpk is calculated by using the smaller value of either the Upper Process Location (Z ) or Lower Process Location (ZJ. In this example, Z is the smaller value with -. 5, therefore, the Process Capability (Cpk) is calculated and interpreted as follows ... 

Since the result of -. 16 is less than 1.00, which is required, and 1.33, which is preferred, the Capability Index indicates that the air handling equipment is not capable of meeting the requirements of controlling the air contaminant levels to a sufficient level as defined by the process specifications. In approximately 37% of the samples would be expected to be outside of the desired upper and lower specification ranges. While the lower readings in this example would be beneficial, the readings above the upper level could pose increased risks. 

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