Process sigma

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]. 

FIGURE 2 Graphical illustration of the correspondence between the defects per million opportunity (DPMO) process capability (Cpk) and process sigma (assuming normally distributed quality variation). 

Manuf./Distrib. Aldrich Fiuka Grain Processing Sigma Trade Names Geo-Meg ... 

For example, we calculate a sigma value of 0.02 inches for a sample distribution. The process sigma is then ... 

Process sigma = [Process Tolerance/(2 x Process Sigma)]... 

Sigma (s-) receptors Signal flares Signaling smokes Signal modulators Signal processing... 

Battin, L. 1988 Six Sigma Process by Design - Design and Dimensions. Group Mechanical Technology, 1(1), Government Electronics Group, Motorola Inc., Scottsdale, Arizona. 

Figure 3.7 shows the growth of R. rubrum in a batch fermentation process using a gaseous carbon source (CO). The data shown follow the logistic model as fitted by (3.14.2.11) with the solid lines, which also represent an unstructured rate model without any lag phase. The software Sigma Plot was used to fit model (3.14.2.11) to the experimental data. An increase in concentration of acetate in the prepared culture media did not improve the cell dry weight at values of 2.5 and 3 gT-1 acetate, as shown in Figure 3.7. However, the exponential growth rates were clearly observed with acetate concentrations of 0.5-2 g-F1 hi the culture media.

TABLE 3. Sigma values for SO Me and S02Me based on the ionization of benzoic acids and related processes... 

More recent examples include Ampac Fine Chemicals (AFC) in California, who implemented a multipurpose continuous small-scale plant for the production of several hundred tons of API per year [31], and Sigma-Aldrich s Fine Chemicals, which has been adding continuous-process technology within its Buch facility [32]. 

In petrochemical and bulk commodity chemical manufacture, real-time process control has been a fact of life for many years. There is considerable understanding of processes and control of process parameters is usually maintained within tight specifications to ensure statistical process control to within six sigma, or the occurrence of one defect in a million. This has been enabled through the use of real-time analytical capability that works with programmable logic circuits to make small changes to various process inputs and physical parameters as required. 

In batch chemical operations, this level of real-time process control is rarely achieved, although there are increasing attempts in recent years to achieve greater statistical process control, the industry is generally only able to operate at about three or occasionally four sigma, or one defect in 1000-10 000. 

Metrics for this might include number of excursions from statistical process control, but one very useful metric for controllability is process capability, or more accurately, process capability indices. Process capability compares the output of an in-control process to the specification limits by using capability indices. The comparison is made by forming the ratio of the spread between the process specifications (the specification width ) to the spread of the process values. In a six-sigma environment, this is measured by six standard deviation units for the process (the process width ). A process under control is one where almost all the measurements fall inside the specification limits. The general formula for process capability index is ... 

Health and Safety Manual, Lawrence Livermore National Laboratory, 1991-1996 Lange s Handbook of Chemistry, JA Dean, J Dean, McGraw Hill, 13th edition, 1985 Loss Prevention in the Process Industries, FP Leed, Butterworth-Heinemann, 1992 Material Safety Data Sheets (MSDS) CD-ROM, Sigma-Aldrich-Fluka, 1995 (subscription)... 

However, coal reactivity as measured by total conversion to liquids and gases becomes less dependent on coal parameters as processing severity increases. The effect of process temperature in the hot-rod reactor was studied using three coals of varying properties. These were Waterberg, Sigma and Landau. At 650°C the conversion yields of these coals were 89, 90 and 88 per cent of the coal (dmmf) respectively. Within experimental error the conversion yields had converged to the same value, whereas at 500°C the conversion yields were 85, 75 and 65 per cent respectively. 

Another domino process starting with a [2,3] sigma tropic rearrangement allows transformation of the propargylic alcohol 4-315 into the conjugated tetraenes 4-316 on treatment with phenylsulfenyl chloride, as described by Lera and coworkers (Scheme 4.69) [107]. 

---