Confidence Types
Confidence measures the statistical accuracy of estimated values. It is the relative frequency that the statistically-derived interval estimate contains the true unknown value being estimated. To calculate confidence, you specify the bounds, a level, and a method.
A confidence bound is a range of potential values within which the parameters for a selected distribution are likely to fall with a given percentage of certainty. Bounds may be set above and/or below the resulting parameters, or they may consist of an interval, which is bounded above and below. A confidence level is a percentage value known as the degree of confidence.
• A one-sided confidence bound defines the point at which a certain percentage of the population is either higher than or lower than a defined point. Two types of one-sided confidence bounds exist: upper confidence bound and lower confidence bound.
• A two-sided confidence bounds defines a closed interval between which a certain percentage of the population is likely to fall. A two-sided confidence bounds is also known as a confidence interval. In the Weibull module, the choices for a two-sided confidence bounds are Upper and Lower to distinguish it from the related concept of a double confidence bounds. For a two-sided confidence bounds, two independent one-sided bounds are calculated at the specified confidence level.
• A double confidence bounds defines an interval within which some of the values fall above and some fall below a specified point. Numerically, a 90 percent double confidence bounds matches a 95 percent upper and lower confidence bounds.
The following table describes supported confidence types and indicates the types of life data analysis (LDA) to which they apply, including special cases. For more information, see Special Cases of Life Data Analysis (LDA). When a confidence type and level is selected for a data set, its probability plot displays one or more lines above and/or below the best-fit line. The lines indicate the selected confidence bounds within which the estimated values of X and Y are most likely to fall.
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Confidence Type
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Description
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Analysis Applicability
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Lower Confidence
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Defines a value above which a specified percentage of the population is likely to fall. For example, for a one-sided lower confidence bound of 90 percent, 90 percent of the population falls above the stated value. In the probability plot, the lower bound appears below the best-fit line. Thus, the one-sided lower bound reports that the true parameter values are less than or equal to the reported parameter values at the specified level of confidence.
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• All but degradation analysis
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Double Confidence
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Defines an interval within which some values fall above and some fall below the reported value. For example, for a double confidence bounds of 90 percent, 45 percent of the expected parameter values fall above, and 45 percent fall below, the reported parameter. Thus, the double confidence bounds report an interval for which the true parameter values are likely to fall above and below the reported value at the specified level of confidence. In the probability plot, the lower bound appears below the best-fit line, and the upper bound appears above the best-fit line.
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• All but degradation analysis
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Upper Confidence
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Defines a value below which a specified percentage of the population is likely to fall. For example, for a one-sided upper confidence bound of 90 percent, 90 percent of the population falls below the stated value. In the probability plot, the upper bound appears above the best-fit line. Thus, the one-sided upper bound reports that the true parameter values are greater than or equal to the reported parameter values at the specified level of confidence.
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• All but degradation analysis
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Upper and Lower
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Defines a closed interval between which a specified percentage of the population is likely to fall. For example, for a given interval of 90 percent confidence between two values X and Y, 90 percent of the population falls within the interval between X and Y, with 10% of the population falling outside the bounds (5 percent below Y and 5 percent above Y). Thus, the two-sided bounds (upper and lower), which are also known as confidence intervals, report a closed interval within which the true parameter values are likely to fall at the given interval of some specified level of confidence. In the probability plot, the lower bound appears below the best-fit line, and the upper bound appears above the best-fit line.
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• All but reliability growth and degradation analysis
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Confidence = Reliability
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Indicates that the reliability value is used as the confidence value. Sometimes, choosing the best confidence level is difficult. Ideally, you want the confidence level to be high. Unfortunately, the higher the confidence level, the lower reliability value. To obtain a higher reliability value, you might use a lower confidence level. For example, at 95 percent confidence, the reliability value might be 0.90, but at 90 percent confidence, the reliability value might be 0.99. In other words, you might choose to decrease the confidence level to increase the reported reliability. In such a case, you can report the confidence level at the reliability value. For example, at 92 percent confidence, the reliability value is 0.92, thereby ensuring a reliability value that is equal to the confidence value.
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• Only parametric LDA and warranty analysis
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Confidence bounds are also applicable for additional data set calculations performed using the General Statistics and Summary Calculators. For more information, see General Statistics Calculator and Summary Calculator.
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