Lagging indicators, defined

Relevant Goals must relate to the performance challenge at hand. This includes a focus on leading indicators, which are harder to define and riskier to achieve than the more commonly reUed-on lagging indicators around financial performance (i.e. revenue, profits). 

It is difficult to identify effective lagging indicators for use with process safety. The most obvious problem is that major PSIs do not occur frequently enough to develop a statistically significant trend such as that shown in Figure 2.3. If many facilities and companies pool their data it may be possible to that some trending results can be developed. However, such results are always open to doubt, not least because different organizations define terms differently. For example, the Baker report (Baker, 2007) provides a list of events that fall under the term fire. That list includes a fault in a motor control center. It is questionable as to how many organizations would call such an event a fire unless it resulted in actual flames. 

Some companies define various key performance indicators (KPIs) as lagging indicators to be watched particularly closely on a monthly, quarterly, or annual basis. One oil company, for example, has set the following KPIs for itself ... 

One key to truly understanding the effectiveness of a safety and health intervention program is to understand the mathematical relationship between the leading indicators (the quantity and quahty of the incident prevention activities) and the lagging indicators (the incident rate). Once one has defined this relationship, the safety and health program can be engineered to produce predictable results. 

Several examples have been selected from the related literature supporting the premise that clarity has not yet been achieved in defining and applying leading and lagging indicators. Within an organization, doing so is vital for success. 

The presence of a lag period in many coupled assays and difficulties in determining the linear portion of a curve present the main problems in the calculation of enzyme activity using reaction rate analysers. In the simplest instruments the slope of the curve in the first few seconds of the reaction is extrapolated into a straight line or, if the reaction is known to show a lag period, the rate of reaction after a defined period of time can be measured. The more sophisticated instruments use microcomputers to determine the linear portion of the curve and calculate the enzyme activity directly from the slope. The second derivative of the reaction progress curve (rate of change of the slope) can be monitored by the computer and when a value of zero is held for a period of time (10—15 seconds) this indicates a linear section of the graph. From the value for the slope, the enzyme activity can be calculated. 

The most important observation in the pre-steady-state kinetics of the CN system is that after a short lag (100 msec) there is a phase (lasting about 3 sec) where the evolution of H2 is linear and only after these 3 sec does CN reduction occur. This long lag prior to CN reduction would correspond to 18 to 20 electron transfer steps from the Fe protein. More realistically this delay probably involves a CN -induced modification of the enzyme, such as a ligand substitution reaction (this modified state of the enzyme is designated as. E in Figure 21). However, this modification step is too slow to be part of the steady-state cycle for CN reduction. Also, it cannot be a slow activation of the enzyme prior to turnover, since the onset of H2 evolution is the same in both the presence and the absence of CN . Steady-state observations indicate that cyanide binds to a more oxidized form of the MoFe protein than binds N2, but that state cannot be defined because of the long lag phase. 

However, urine has no great relevance in quantitative analysis because the analyte concentrations vary depending on the dose, means of administration, physiological status (urinary pH, sex, age, weight, etc.), the time lag between intake and analysis, the addition of adulterants. So the analytical data of urine may only indicate the presence of a substance up to a defined cutoff point the monitoring window (time interval in which a substance can be detected by ordinary analytical methods) varies from a few days for cocaine, amphetamine, methoxyamphetamine to 2-3 weeks for cannabinoids. 

If the drug stratum corneum/product partition coefficient K is defined as Csc(o)/C)>, CJc is assumed to be much less than Csc(o), and the permeability coefficient (kp) is KD/h, equation 4 is equivalent to equation 3. The lag time is normally defined by Fick s law as h2/6D. The importance of equation 4 is well illustrated by the work of Rougier and Lotte (1993) in which it was shown that the in vivo percutaneous absorption (= Js) of a series of compounds was directly related to their concentration in stripped stratum corneum, irrespective of their structure, concentration or site of application. In theory, drug transport could go via a polar pathway, with a permeability coefficient kp pojar, as well as through the intercellular lipid pathway, with a permeability coefficient kp iipi(1, although the existence of a polar pathway remains controversial. As indicated previously, for lipophilic drugs, an aqueous boundary layer is likely to be present at the stratum corneum-viable epidermis interface... 

Fig. 22. Single-cell calcium response. Shown is the concentration of intracellular free calcium in a single cell as a function of time. The cell is stimulated with 10 gM PhE at a time indicated by the first arrow. The second arrow represents the time of maximum rate of calcium increase as determined by a nonlinear fit of the data. The time lag between the addition of PhE and the time of maximum rate of calcium increase is defined as the calcium response latency. The experimental methods used to derive the data of this figure and Fig. 23 are described in detail in Mahama and Linderman (1993a, b).

The lagging or trailing indicators as used in the process industries for safety and reliability have been defined as,... 

Since a near miss is an actual event or discovery of a potentially unsafe situation, this metric could be defined as a lagging metric. A large number or increasing trend in such events could be viewed as an indicator of a higher potential for a more significant event therefore, many companies use Near Miss metrics as a surrogate for a Leading metric. 

Thus, the AC current has a phase constant of 90° ahead of the driving potential. Similar to capacitive circuits, a phase constant of -90° for an inductive circuit can be obtained, indicating the current lags the potential by one quarter cycle. An equivalent inductive reactance Xl in a circuit only containing an inductor can be defined as... 

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