
BASIS TOLERANCE LIMITSName:
There are two numbers for the tolerance interval:
Standard tolerance limits are given by
where \( \bar{X} \) is the sample mean, s is the sample standard deviation, and k is determined so that one can state with (1 α)% confidence that at least Φ% of the data fall within the given limits. The values for k, assuming a normal distribution, have been numerically tabulated. This is commonly stated as something like "a 95% confidence interval for 90% coverage". A and B basis values are a special case of this. Specifically, the B basis value is a 95% lower confidence bound on the tenth percentile of a specified population of measurements and the A basis value is a 95% lower confidence bound of the first percentile. Alternatively, this can be stated as the B basis value is a 95% lower tolerance bound for the upper 90% of a specified population and the A basis value is a 95% lower tolerance bound for the upper 99% of a specified population. Note that the A and B basis values are one sided intervals (the standard tolerance limits are two sided). Also, the standard tolerance limits are typically based on a normality assumption while the A and B basis values can be computed for Weibull, normal, or lognormal distributions or they can be computed nonparametrically if none of these distributions provide an adequate fit. A and B basis values were added to support the MIL17 Handbook standard (see the Reference section below). The mathematics of computing these basis values are given in the MIL17 Handbook and are not given here. A and B basis values are used for the case where the data can be considered unstructured. That is, the data are either univariate to start with or the AndersonDarling ksample test has determined that the data can be treated as coming from a common sample. Also, the appropriate distribution should be determined first. The MIL17 Handbook recommends using the AndersonDarling goodness of fit test. It also recommends trying the Weibull, then the lognormal, then the normal. If all of these fail, then the nonparametric case can be used.
where <dist> is WEIBULL, NORMAL, LOGNORMAL, or NONPARAMETRIC; <y> is the response variable, and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes B basis values.
where <dist> is WEIBULL, NORMAL, LOGNORMAL, or NONPARAMETRIC; <y> is the response variable, and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes A basis values.
BBASIS LOGNORMAL TOLERANCE LIMITS Y1 BBASIS NORMAL TOLERANCE LIMITS Y1 BBASIS NONPARAMETRIC TOLERANCE LIMITS Y1 ABASIS WEIBULL TOLERANCE LIMITS Y1 ABASIS WEIBULL TOLERANCE LIMITS Y1 SUBSET BATCH > 1
LET A = LOGNORMAL A BASIS Y LET A = WEIUBULL A BASIS Y LET A = NONPARAMETRIC A BASIS Y LET A = NORMAL B BASIS Y LET A = LOGNORMAL B BASIS Y LET A = WEIUBULL B BASIS Y LET A = NONPARAMETRIC B BASIS Y Enter HELP STATISTICS to see what commands can use these statistics.
ABASIS <dist> TOLERANCE A BASIS <dist> A BASIS <dist> TOLERANCE
The following are synonyms for BBASIS
BBASIS <dist> TOLERANCE B BASIS <dist> B BASIS <dist> TOLERANCE
2016/12: Corrected tolerance limit factor for Weibull ABasis SKIP 25 READ VANGEL31.DAT Y SET WRITE DECIMALS 4 BBASIS WEIBULL TOLERANCE LIMITS Y ABASIS WEIBULL TOLERANCE LIMITS YThe following output is generated: Weibull B Basis Tolerance Limits Summary Statistics: Number of Observations: 38 Sample Mean: 185.7895 Sample Standard Deviation: 18.5955 Sample Minimum: 147.0000 Sample Maximum: 231.0000 Tolerance Values: Confidence Value: 0.9500 Coverage Value: 0.9000 Shape Parameter: 10.5732 Scale Parameter: 194.2046 Tolerance Limit Factor: 4.8513 B Basis Value: 145.7135 Weibull A Basis Tolerance Limits Summary Statistics: Number of Observations: 38 Sample Mean: 185.7895 Sample Standard Deviation: 18.5955 Sample Minimum: 147.0000 Sample Maximum: 231.0000 Tolerance Values: Confidence Value: 0.9500 Coverage Value: 0.9900 Shape Parameter: 10.5732 Scale Parameter: 194.2046 Tolerance Limit Factor: 8.7913 A Basis Value: 109.8321  
Date created: 06/05/2001 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 