Confidence and Tolerance

Equipment failure rate data points carry varying degrees of uncertainty expressed by two measures, confidence and tolerance. Confidence, the statistical measurement of uncertainty, expresses how well the experimentally measured parameter represents the actual parameter. Confidence in the data increases as the sample size is increased. 

Tolerance uncertainty arises from the physical and the environmental differences among members of differing equipment samples when failure rate data are aggregated to produce a final generic data set. Increasing the number of sources used to obtain the final data set will most likely increase the tolerance uncertainty. 

Confidence that the calculated failure rate is a good estimate of the true rate can be increased by lengthening the study or sample time. Adding another population of the same equipment under the identical circumstances to the original population will reduce uncertainties and increase confidence in the calculated failure rates. 

Plant-specific data are frequently unavailable or are low in their level of confidence. Further, this source of data cannot provide information on equipment not in use at the plant, nor can it do more than suggest how plant equipment might behave under different circumstances. Since data collection is very difficult, using shared or generic data is one way of resolving these problems without the expense of extensive data collection systems. 

Frequently, the only way to gather sufficient data for a CPQRA is to build a data set using inputs from other plants within the company or from other available resources. Generic data provide less specific and detailed data, but can draw upon a much larger 

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Uncertainty A measure of doubt that considers confidence and tolerance. 

Proschan F. Confidence and tolerance intervals for the normal distribution. Journal of the American Statistical Association 1953 48 550-564. 

Confidence and tolerance bounds on predictions that use the Weibull distribution function. 

The PET systems of the aminoalkyl aromatic type discussed so far display a very simple behavior in that luminescence intensity (or quantum yield) is the only variable. Such systems are very user-friendly as a result and tolerate a wide variety of communication wavelengths. However these simple systems could be adapted to include an additional absorptiometric sensing channel which can confirm the results of ion density (pH say) obtained via luminescence. Of course, such increased user-confidence is only attained with a proportionate reduction in simplicity. Now excitation needs to be done at the isosbestic wavelength. These systems, e.g. 11 and 12, use a push-pull fluorophore with electron donor and acceptor substituents which give rise to internal charge transfer (ICT) excited states. In contrast, the simple PET systems employed aromatic hydrocarbon fluorophores with essentially pure nn excited states. The charge separation in ICT states can cause electrostatic... 

To establish the confidence that fully automatic hot air sterilizing and depyrogenation tunnel and auxiliary systems perform in accordance with the manufacturer specifications and with GMP principles, and are capable of operating within established limits and tolerances. 

Installation Qualification After equipment selection, it is necessary to assure that the equipment is installed well. The IQ document describes and validates the procedure of the equipment installation. It establishes confidence that the process equipment and ancillary systems are capable of consistently operating within established limits and tolerances [10]. The equipment manufacturer and pharmaceutical company must agree and check the IQ, which must be approved by the pharmaceutical company at the end. This document certifies that equipment was installed as specified by the manufacturer and the purchaser. 

Tables I and II provide additional statistical data that can be used to qualify the estimates derived from the fitting process. C is the standard deviation of y, its numerical value is largely determined by the sampling error arising from the selection of test specimens. C is the standard deviation of the S fs, which is a measure of theSinhomogeneity of the lot of SRM material. C is the standard deviation of the residuals from the fit, which is a measure of the extent to which individual data values depart from the model in equation 6. We have chosen not to construct the usual confidence or tolerance intervals because we do not have enough data on the distribution of the S s.

Installation qualification Establishing confidence that process equipment and ancillary systems are capable of consistently operating within established limits and tolerances (FDA). 

Originally limited to ellipsoids, the use of Mahalonobis distances allows the use of more variables as the confidence ellipsoid can be transformed to a confidence or tolerance hypersphere. These ideas were examined using the microecosystem test method developed by Kersting for the examination of multispecies systems. These three-compartment microecosystems are comprised of an autotrophic, herbivore, and decomposer subsystems that are connected by tubing and pumps. Although relatively simple and small, these systems are operable over a number of years. 

The determination of the sample size is intimately related to the trial objectives, the inferences the researcher wants to be able to make and the error probabilities in the case of hypotheses testing or the confidence and precision in the case of estimation that the researcher is willing to tolerate. The following example illustrates the process of determining the required sample size for a clinical trial. 

Kevin and his friends are learning that cocaine use can be costly. Some first-time cocaine users feel a rush of energy, confidence, and euphoria while others, like Kevin, have violent reactions. People vary in their ability to tolerate cocaine, and for some, even small amounts can prove harmful or even fatal. Experiencing the positive effects of cocaine once does not guarantee a similar experience in the future since tolerance to the drug can change over time. 

One can calculate the acceptance criteria for the particle size distribution median and standard deviation by use of a technique described by Hahn and Meeker (11). Their work describes three types of statistical interval confidence, prediction, and tolerance. The authors maintain that the choice of the appropriate statistical interval to use depends on the nature of the parameters to be estimated. The confidence interval is used when hying to find bounds on a population parameter—for example, the population mean or standard deviation. The confidence interval is the most commonly appearing of the three intervals and is the interval... 

Devices are assembled typically from 15 to 20 individual components, and each will be produced on a multicavity mould with four or eight moulds. Until this stage is reached, with devices being assembled from these production moulds, and then tested, the final variability between devices cannot be fully established. However, during development, appropriate engineering and tolerance analyses can give good confidence. The device will be delivered from the moulders with a minimum number of subassemblies and will be filled with the formulation at the pharmaceutical company. In the case of unit dose devices, the capsule or blister will usually be filled at the pharmaceutical company. 

Chew V Confidence, prediction and tolerance regions for the multivariate normal distribution. JoumalofAnjerijg Statistics Association 1966 61 605-617. 

BMW Group Standard GS 95003 Electrical/Electronic Assemblies in Motor Vehicles. lEC 600 50(191) (lEV) Dependability and quality of sevices. lEC 60605-4 Equipment reliability testing Part 4 Statistical procedures for exponential distribution Point estimates, confidence intervals, prediction intervals and tolerance intervals. 

For external method evaluation results from interlaboratory studies may be presented in tables and figures including mean, standard deviation, ratio/recoveiy, relative mean square error, a histogram of all results, and plots of the method evaluation function, Youden, and Z score. Furthermore, limits for acceptance of the performance characteristics parameters after which the methods have to be evaluated, e.g., tolerance limits as well as confidence and/or prediction intervals are essential. 

The first target is interpreted to mean that for, say SOO years accumulated operation of a PLC, it is tolerable for a design error to result in one failure. The period of 500 years is somewhat arbitrary, but is chosen such that this type of failure could be claimed not to dominate system unreliability. It is therefore claimed that 5000 years accumulated experience should provide a sufficient basis to claim an tqrpropriale level of reliability. No specific justification for this is provided except that the period for which experience is required is some 10 times the target MTBF. This factor is judged to be appropriate to give some confidence in the claim (if the failures occurred at random intervals, such a period would lead to betto than 85% confidence) and to make some allowance for the lack of maturity of software reliability modelling. 

The reading on an instrument will be affected by imperfections in components in the instrument. If it is an electromechanical device, these errors will be due to magnetic hysteresis, friction, and tolerances on the sizes, assembly, and purity of the components. Likewise, for an electronic instrument, tolerances on components, assembly, and hysteresis of operation of the various circuits will affect the operation. In both types of instrument, ai r changes in the environment (temperature, humidity, and possibly pressure) will have an effect on the performance. Since many materials change their properties slightly with age (and continual use), it is necessary to consider the effect of age on the performance of an instrument. Since this is difficult to predict, it is essential that instruments be checked (calibrated) at regular intervals, for example, once a year, but preferably every 6 months. From the records (history) of instruments, confidence in the performance of a particular instrument is maintained. 

If the random errors are higher than can be tolerated to meet the goals of the test, the errors can be compensated for with rephcate measurements and a commensurate increase in the laboratory resources. Measurement bias can be identified through submission and analysis of known samples. Establishing and justifying the precision and accuracy reqrtired by the laboratory is a necessary part of estabhshing confidence. 

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