Chance failure

Exponential distribution The exponential distribution is the simplest component life distribution. It is suited to model chance failures when the rate at which events occur remains constant over time. It is often suitable for the time between failures for repairable equipment. 

The slope downwards on the left represents the decrease in faults (increase in reliability) during the commissioning, ramp-up, run-in or teething period. The flat base represents the period of sustained low fault operation (chance failure). The upward curve on the right represents the steady increase in faults (decrease in reliability) as equipment or a system reaches the end of its useful life. Obviously design, planned inspection, maintenance or parts replacement can have an impact on various parts of the curve. 

Causes of early failure include poor policy, planning, training, and system design as well as resistance to change. Factors in chance failure m include drop in employee skill level lack of maintenance overload environment, e.g. dust no performance monitoring lack of effective controls or no planned reviews. Weaiout failure is more likely where financial planning is poor and resources are switehed, there is failure to retrain employees, onty parts of a system are eorrected, outdated methods of work persist, or staff are not consulted. 

The CFR region is the useful life period, which is characterized by an essentially constant failure rate. This is the period dominated by chance failures. Chance failures are those failures that result from strictly random or chance causes. They cannot be eliminated by either lengthy burn-in periods or good... 

Cases 3 and 4 are both exploration prospects, since the volumes of potential oil present are multiplied by a chance factor which represents the probability of there being oil there at all. For example, case 3 has an estimated probability of oil present of 65%, i.e. low risk of failure fo find oil (35%). However, even if there is oil present, the volume is small no greater than 130 MMstb. This would be a low risk, low reward prospect. 

The expected life is sometimes used as an iadicator of system rehabihty however, it can be a false iadication and should be used with caution. In most test situations the chance of surviving the expected life is not 50% and depends on the undedyiag failure pattern. For example, considering the exponential as used ia equation 10, the expected life would be... 

Conditional Failure Probability. The concept of conditional piobabihty of faiuie is useful to predict the chances of survival for a device that has been in operation for a period of time and is not in a failed state. Such information is helpful for maintenance planning. 

Example 3. A centrifugal pump moving a corrosive Hquid is known to have a time-to-failure that is well approximated by a normal distribution with a mean of 1400 h and a standard deviation of 120 h. A particular pump has been in operation for 1080 h. In order to plan maintenance activities the chances of the pump surviving the next 48 h must be deterrnined. 

From equation 8 it was shown that the chance of surviving the mean life was 36.8% for the exponential distribution. However, this fact must be used with some degree of rationaHty in appHcations. For example, in the above situation the longest surviving MPU that was observed survived for 291.9 hours. The failure rate beyond this time is not known. What was observed was only a failure rate of A = 1.732 x lO " failures per hour over approximately 292 hours of operation. In order to make predictions beyond this time, it must be assumed that the failure rate does not increase because of wearout and... 

Poor reputation. In the past, electric tracing has been less than reliable. Due to past failures, some operating personnel are unwilling to take a chance on any electric tracing. 

Elimination of defect-related failures has a limited chance of success once equipment is installed. The key to successful elimination is to prevent defective components from being installed in the first place. This is accomplished in one of two ways ... 

Use staggered proof testing to reduce chances of common cause failure... 

Most equipment failures occur under abnonnal conditions, especially elevated pressures and temperatures. The design of equipment presents internal and external constraints. External limits may arise from physical laws, while internal limits may depend on tlie process and materials. In any case, if these limits are exceeded, tlie chance of an accident is greatly increased. 

The rate of failure declines when tlie equipment is under normal operation. At tliis point, failures are chance occurrences. 

A random variable is a real-valued function defined over the sample space S of a random experiment (Note that tliis application of probability tlieorem to plant and equipment failures, i.e., accidents, requires tliat the failure occurs randomly, i.e., by chance). The domain of tlie function is S, and tlie real numbers associated witli tlie various possible outcomes of the... 

So, for a project that has five innovative aspects each with a 90% degree of certainty, the overall probability of project success, P = 0.9 = 59%. For avoidance of doubt, to put it another way, the project has a 41% chance of failure This does not make for a good investment case. 

Biguanides such as metformin are thought to inhibit mitochondrial oxidation of lactic acid, thereby increasing the chance of lactic acidosis occurring. Fortunately, the incidence of lactic acidosis in clinical practice is rare. Patients at greatest risk for developing lactic acidosis include those with liver disease or heavy alcohol use, severe infection, heart failure, and shock. Thus, it is common practice to evaluate liver function prior to initiation of metformin. 

The limit of detection (LoD) has already been mentioned in Section 4.3.1. This is the minimum concentration of analyte that can be detected with statistical confidence, based on the concept of an adequately low risk of failure to detect a determinand. Only one value is indicated in Figure 4.9 but there are many ways of estimating the value of the LoD and the choice depends on how well the level needs to be defined. It is determined by repeat analysis of a blank test portion or a test portion containing a very small amount of analyte. A measured signal of three times the standard deviation of the blank signal (3sbi) is unlikely to happen by chance and is commonly taken as an approximate estimation of the LoD. This approach is usually adequate if all of the analytical results are well above this value. The value of Sbi used should be the standard deviation of the results obtained from a large number of batches of blank or low-level spike solutions. In addition, the approximation only applies to results that are normally distributed and are quoted with a level of confidence of 95%. 

---