Mutual exclusivity

If maintenance is performed, there are two principal maintenance strategies preventive and breakdown maintenance. These are not mutually exclusive, and may be combined even in the same piece of equipment. Take for example a private motor car. The owner performs a mixture of preventive maintenance (by adding lubricating oil, topping up the battery fluid, hydraulic fluid and coolant) with breakdown maintenance (e.g. only replacing the starter motor when it fails, rather than at regular intervals). 

If a Pfaff differential expression DF = Xdx + Tdy+Zdz has the property that every arbitrary neighbourhood of a point P(x, y, z) contains points that are inaccessible along a path corresponding to a solution of the equation DF = 0, then an integrating denominator exists. Physically this means that there are two mutually exclusive possibilities either a) a hierarchy of non-intersecting surfaces (x,y, z) = C, each with a different value of the constant C, represents the solutions DF = 0, in which case a point on one surface is inaccessible... 

The vibrations of acetylene provide an example of the so-called mutual exclusion mle. The mle states that, for a molecule with a centre of inversion, the fundamentals which are active in the Raman spectmm (g vibrations) are inactive in the infrared spectmm whereas those active in the infrared spectmm u vibrations) are inactive in the Raman spectmm that is, the two spectra are mutually exclusive. Flowever, there are some vibrations which are forbidden in both spectra, such as the torsional vibration of ethylene shown in Figure 6.23 in the >2 point group (Table A.32 in Appendix A) is the species of neither a translation nor a component of the polarizability. 

It is clear from Figure 7.18 that progressions and sequences are not mutually exclusive. Each member of a sequence is also a member of two progressions. However, the distinction is usefiil because of the nature of typical patterns of bands found in a band system. Progression members are generally widely spaced with approximate separations of cOg in absorption and co" in emission. In contrast, sequence members are more closely spaced with approximate separations of cOg — co". 

For example, if the invention has cleaning properties it may be a composition of matter, process, or machine, all of which are patentable subject matter. If the invention performs work, it may be a process, article of manufacture, or machine, which are all patentable subject matter. It may also be that the development of a new composition results in a composition of matter and a process of using the composition, both of which are distinct, yet patentable inventions. The various types of patentable subject matter are not mutually exclusive and may be disclosed in a single patent. 

Mutual Exclusion (MUTEX). The idea of multiple entities all working on the same piece of work raises this issue of coordination and communication among the individual processes. A weU-known example from banking is instmctive. Consider two bank tellers simultaneously performing withdrawals from the same bank account. Both read the account balance and determine that the balance is 100, and so a withdrawal of 100 is allowed. Both then withdraw 100 from the account. Clearly this process needs some means by which the actions of the independent processes can be synchronized and coordinated. 

Incremental Criteria. When mutually exclusive ventures having different levels of investment are compared, an attractive concept is that each increment of investment must itself yield a satisfactory return. This concept has led to a variety of incremental approaches for profitabiUty analysis. Because the risk can vary with investment level and cloud the meaning of satisfactory, any incremental approach to multiyear investment analysis should be viewed with caution. 

Clearly, these groupings are not mutually exclusive. The chief distinctions are between homogeneous and heterogeneous reactions and between batch and flow reactions. These distinctions most influence the choice of equipment, operating conditions, and methods of design. 

These methods of classification are not mutually exclusive. Thus filters usually are divided first into the two groups of cake and clarifying equipment, then into groups of machines using the same land of driving force, then further into batch and continuous classes. This is the scheme of classification underlying the discussion of filters of this subsection. Within it, the other aspects of operating cycle, the nature of the sohds, and additional factors (e.g., types and classification of filter media) will be treated explicitly or implicitly. 

These procedures are not mutually exclusive and are divided here as a matter of convenience for discussion. The identification, measurement treatment, and interpretation are tvpicaUy embodied into a single effort with testing and retesting as analysts search for the cause of the observed symptoms. 

Figure 7.1 Possible reactive chemical hazards (consequences are not mutually exclusive)...

The function of pH adjustment is to neutralize acids and bases and to promote the formation of precipitates (especially of heavy metal precipitates) which can subsequently be removed by conventional settling techniques. These purposes are not mutually exclusive, precipitates can be formed as the result of neutralizing a waste. Conversely, neutralization of the waste stream can result when adjusting the pH to effect chemical precipitation. Typically, pH adjustment is effective in treating inorganic or... 

The physical reason for the third term on the right of equation 2.4-7 is to correct t or a mating the overlap twice as seen in Figure 2.2-1. The technique of Venn diagrams is used in some PRAs to calculate mutually exclusive power states from non-mutually exclusive states... 

PREPROCESSOR - Modifies the FTAP punch file output for common cause and dependent analyses (conditional probabilities), removes complemented events, and corrects for mutually exclusive events. 

Eliminating min cut sets with mutually exclusive events. 

MEX and SLIB are optional commands. MEX command must precede the SUB command. The MEX command sets to false, basic events that are pairwise mutually exclusive. For the SUB command, the user identifies sets of basic events within cutsets (original sets) that are to be rejilaced by another set of basic events (substituted sets). The SUB command accounts for basic events within cutsets that have either a common cause or statistical dependency. 

After selecting the MEX command (selection 5) the comma delimited input consists of groups of basic events that are pairwise mutually exclusive. To extend the group to the next and subsequent lines, the first field must be blank. Up to 100 names per group are allowed with a new group starting when a non-blank character is encountered in the first field. The number of pairs that are mutually exclusive is n /[(n-2) 2 ], where n is the number of basic events in the group. An example for the plant blackout fault tree is DG-A-M,DG-B-M,DG-C-M (where means enter). 

Conducting common cause and dependent event analysis Dropping complemented events and performing the subsequent minimization Generating block files (i.e., a set of Boolean equations) for subsystems Eliminating mincutsets with mutually exclusive events... 

Quality, service, cost, and technology are not mutually exclusive. One can t distinguish between a quality improvement and a service or technology improvement. It was necessary only to mention quality and cost, as an improvement in service must be an improvement in either the quality or cost of the service - all other factors come within the definition of quality. Improvements in technology are also improvements in quality or cost. Such improvements may improve the quality of design, quality of conformance, or quality of use (see Part 1 Chapter 1 under Quality parameters) or may cause a reduction in cost while not providing any change in product or service characteristics. 

When events A and B liave no elements in common tliey are said to be mutually exclusive. A set having no elements is called tlie null set and is designated by < ). Thus if events A and B are mutually exclusive then AB = < ). 

Note that tlie union of A and B consists of tliree mutually exclusive events AB, AB, AB. 

Consider n mutually exclusive events A, A2,. .., A whose union is tlie sample space S. Let B be any given event. Then Bayes theorem states... 

Suppose that an explosion at a chemical plant could have occurred as a result of one of tliree mutually exclusive causes equipment nialfimction, carelessness, or sabotage. It is estimated tliat such an explosion could occur witli probability 0.20 as a result of equipment malfunction, 0.40 as a result of carelessness, and 0.75 as a result of sabotage. It is also estimated tliat tlie prior probabilities of the tliree possible causes of the explosion are, respectively, 0.50,0.35, and 0.15. Using Bayes tlieorem, deteniiine tlie most likely cause of the explosion. 

Consider n independent performances of a random experiment witli mutually exclusive outcomes that can be classified "success or failure . Tlie words success and failure are to be regarded as labels for two mutually exclusive categories of outcomes of the random experiment. They do not necessarily have tlie ordinary connotations of success or failure. Assume tliat p, tlie probability... 

For a set of mutually exclusive alternatives, the project with the smallest LCC is the most cost-effective. 

Capital investments can also be selected on the basis of other measures of performance such as return on investment, internal rate of return, and benefit-cost ratio (or savings-to-investment ratio). Flowever, care must be taken in the application of these methods, as an incremental analysis is required to ensure consistent comparison of mutually exclusive alternatives. Also, rather than requiring a separate value to be calculated for each alternative, as in the case of the life-cycle cost method, these other methods incorporate the difference between two mutually exclusive alternatives within a single measure. For example, the net benefits measure directly pressures the degree to which one alternative is more economically desirable than another. 

Note, however, that the frequency/malfunction relationship is not mutually exclusive and a specific mechanical problem cannot definitely be attributed to a unique frequency. While frequency is a very important piece of information with regard to isolating machinery malfunctions, it is only one part of the total picture. It is necessary to evaluate all data before arriving at a conclusion. 

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