Upper specification limit

Improve the control strategy for the product transition in Example 14.7. Ignore mixing time constraints, flow rate limitations on the addition of component C, and any constraints on the allowable value for The concentration of Q can exceed its steady-state value of 8mol/m but must not be allowed to go outside the upper specification limit of 9mol/m. ... 

Figure 4.34. The confidence limits of the mean of 2 to 10 repeat determinations are given for three forms of risk management. In panel A the difference between the true mean (103.8, circle ) and the limit L is such that for n = 4 the upper confidence limit (CLu, thick line) is exactly on the upper specification limit (105) the compound risk that at least one of the repeat measurements yi >105 rises from 23 n = 2) to 72% (n = 10). In panel B the mean is far enough from the SLj/ so that the CLu (circle) coincides with it over the whole range of n. In panel C the mean is chosen so that the risk of at least one repeat measurement being above the SLu is never higher than 0.05 (circle, corresponds to the dashed lines in panels A and B).

Ermer and coworkers [15, 38], recommended that the acceptance criteria for the standard deviation of the determinations should be lower than 1/6 of the specification range (upper specification limit, USL minus lower specification limit, LSL), or calculated using the following equation ... 

Upper specification limit in IOO+B% Number of individual injections... 

Figure 2 demonstrates how trend analysis would be used. The standard deviation of data for a series of batches is plotted against their control (or batch) number. The graph resulting from the dotted points indicates a trend toward the upper specification limit for the test parameter, but the trend later returns to the mean level. If one merely looked at the tabular form of the data, one would not necessarily conclude that there is a problem. It is only when the data are graphically represented that the trend is seen. This would lead to an investigation into the possible causes of the trend. There is another very helpful application to... 

Process Capability Indices Also known as process capability ratios, these provide a measure of w hether an in-control process is meeting its product specifications. Suppose that a quality variable x must have a volume between an upper specification limit (USL) and a lower specification limit (LSL) in order for product to satisfy customer requirements. The capability index Cp is defined as... 

Based on this, the Kiosk Configurators determined that the kiosk should display the refinancing terms within two minutes (120 seconds) for all users. In essence, the team set an upper specification limit (USL) at 120 seconds. There is no lower specification limit (LSL) because an instantaneous response is still acceptable (although very unlikely). 

A common capability metric for continuous data is the sigma level, or the number of standard deviation (cr) units that lie between the mean and the upper specification limit (USL). In our case, with a mean of 95, a USL of 120 and a standard deviation... 

Specification limits can be one-sided or two-sided. For two-sided specifications, you combine the capability of the lower specification limit (LSI) and the upper specification limit (USL) to derive an overall sigma level. Extensions to unstable processes, two-sided specifications, and distributions that are not normally distributed require additional analysis. 

These limits are obtained from customer input, regulatory requirements, or design functional requirements. Upper specification limit (USL) refers to the maximum allowable value for the parameter, whereas lower specification limit (LSL) indicates the minimum allowable value. 

One-tailed or two-tailed confidence limits for the mean content, activity, purity, or residual moisture may also be calculated. For each batch produced, the 99.9999% confidence limits for the mean should be found to be within specifications. For a well-controlled process, 99.9999% one-tailed limits may typically lie in the range of 50-75% of the upper specification limit. 

With regard to the upper specification limit for moisture, this increase was marginal, and it was calculated that there was no risk to breach the specification limit at the relative humidity of the clean room, assuming a cumulation of worst cases. 

As stated earlier, a process capability analysis assesses the process performance relative to product specifications. Specification limits are denoted as LSL for the lower specification limit, and as USL for the upper specification limit. In some cases, there is only a single specification limit, either a lower limit or an upper limit. 

The first digram (Fig. 4) shows an optimal process for the continuous two-step hydrosilylation as described above. The process runs for about 12 h well below the upper specification limit of 3 mol% Si-H (gray line in the diagram). 

USL = upper specification limit LSL = lower specification limit... 

Example 1. The following data have been collected from your process. In particular, you produce a child s toy. You have collected 90 values of a critical performance measurement that reflects surface quality for the manufactured product. The upper specification limit (USL) and the lower specification limit (LSL) are known to be 54 and 47, respectively. It is desired to demonstrate the natural tendency, variability, and relationship to the specification limits of the process by constructing a histogram of the data. With the collected data, the histogram is calculated by accumulating the number of observations within prescribed bands. The number of observations can be used to determine the relative frequency of each cell as demonstrated below. 

Once the process has generated sufiBcient data to support the conclusion that it is stable or in a state of statistical process control, it is desirable to judge the process s abihty to meet customer specifications, that is, the upper specification limit (USL) and lower specification limit (LSL). Within most industries, process capability ratios rtfe used to measure a given process s abihty to meet specifications. The effort employed to make this judgment is known as process capabdity analysis (PCA). 

Figure 10.3 Typical scenarios arising when measurements of the concentration of analyte are used to assess compliance with an upper specification limit. The vertical lines show the expanded uncertainty (7 on each result (see main text) and the associated curve indicates the inferred probability density function for the value of the measured concentration, emphasizing that there is a larger probability of the value of the measured concentration lying near the centre of the expanded uncertainty interval than near the ends. For a full discussion see Eurachem-CITAC Guide (2007) www.eurachem.ul.pt...

The desired separation can be achieved with 50 theoretical stages using a reflux ratio of 3.22, which is 1.34 times the minimum reflux ratio. This would meet upper specification limits (USLs) of 1,000 ppm n-heptane in the distillate and 1,000 ppm cyclohexane in the bottoms. However, the average key impurity concentrations in the products need to run with average impurity concentrations that are some distance below... 

The distance between the average key impurity concentration and the upper spec limit is the subject of product quality performance in Chapter 7. If the standard deviation (o) is 10% of the upper specification limit, then the standard deviation for an upper specification limit of 1,000 ppm impurity is 100 ppm. A distillation column would need to produce an average key impurity concentration of 700 ppm impurity to keep the average DNS (distance from the nearest specification limit) at 3a. 

One measure of the quality of distillate and bottoms from a distillation column is the concentration of impurities present. The rectification section of a distillation column above the feed point is primarily for removing heavy impurities from the distillate. So, the quality of the distillate stream can be measured by the concentration of heavy key impurity. The distillate quality specification can be an upper specification limit (USL) of heavy key impurity in the stream. If there are lighter components present, they will essentially all appear in the distillate. 

When samples of distillate and bottoms are taken once every 8-hour shift, there are 21 samples per week and 1,095 samples per year. If the samples follow a normal distribution and the average impurity concentration is 2g, that is, DNS = two standard deviations, below the upper specification limit (USL) there would be one shift sample out of spec about every 2 weeks. If the average were 3cr below the upper specification limit, there would be one shift sample out of spec about every 9 months from common cause variability. If the average were 4a below the upper specification limit, there would be one shift sample out of spec about every 27 years. 

One of the best ways of improving product quality at both ends of the distillation column is to reduce variability, as shown in Figure 7.5 that will reduce the failure rate. Robinson described the benefits from improved dryer control, such as reduced variability in product moisture content and reduced energy consumption because the average concentration of moisture in the product could be run closer to the upper specification limit. 

The distillate and bottoms streams from a distillation column can be sampled and analyzed once per shift, and then an expert system can be used to recommend adjustments in setpoints for the separation power base and the MRT using a set of backward chaining logic rules. For the case of an upper specihcation limit of 1,000 ppm heavy key impurity in the distillate stream and a standard deviation of 100 ppm impurity, the desired impurity concentration may be 700 ppm, that is, 3 standard deviations below the upper specification limit. The expert decision rules can be set to make adjustments only if the impurity concentrations are outside of the range from 0.6 to 0.8 times the upper specification limit (USL). For example, the hrst priority is to check the key impurity separation power. If the key heavy impurity concentration in the distillate is above 0.8 times its upper specification limit and the key light impurity in the bottoms is above 0.8 times its upper specification limit, then increase the separation power base (Rule 1 in Table 7.2). An initial guideline is to increase the separation power base, steam/feed, or reflux/feed by 1%. 

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