TOLERANCE LIMITS

TOLERANCE LIMITS

Analysis Command

Generates normal and non-parameteric tolerance intervals.

Tolerance intervals calculate a confidence interval that contains a fixed percentage (or proportion) of the data. This is related to, but distinct from, the confidence interval for the mean.

There are two numbers for the tolerance interval:

1. The coverage probability is the fixed percentage of the data to be covered.
2. The confidence level.

Tolerance limits are given by

where is the sample mean, s is the sample standard deviation, and k is determined so that one can state with (1-)% confidence that at least % 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".

Dataplot computes the tolerance interval for three confidence levels (90%, 95%, and 99%) and five coverage percentages (50.0, 75.0, 90.0, 95.0, 99.9).

In addition, Dataplot computes non-parametric tolerance intervals. These may be preferred if the data are not adequately approximated by a normal distribution. In this case, the tables have been developed based on the smallest and largest data values in the sample.

TOLERANCE LIMITS <y>             <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable,
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax generates both the normal and the non-parametric tolerance limits.

NORMAL TOLERANCE LIMITS <y>
                        <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable,
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax generates only the normal tolerance limits.

NONPARAMETRIC TOLERANCE LIMITS <y>
                        <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable,
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax generates only the non-parametric tolerance limits.

TOLERANCE LIMITS Y1
TOLERANCE LIMITS Y1 SUBSET TAG > 2
NORMAL TOLERANCE LIMITS Y1 SUBSET TAG > 2
NONPARAMETRIC TOLERANCE LIMITS Y1 SUBSET TAG > 2

None

None

CONFIDENCE LIMITS	= Generate the confidence limits for the mean.
T-TEST	= Perform a t-test.

"Experimental Statistics: NBS Handbook 91", Natrella, National Institute of Standards and Technology (formerly National Bureau of Standards), October, 1966, pp. 2-13 - 2-15.

Confirmatory Data Analysis

1998/12
2006/3: Allow only the normal or only the non-parametric limits to be generated

SKIP 25
READ ZARR13.DAT Y
TOLERANCE LIMITS Y


The following output is generated:

      **************************
      **  TOLERANCE LIMITS Y  **
      **************************
 
 
2-SIDED NORMAL TOLERANCE LIMITS: XBAR +- K*S
 
             REFERENCE--CRC HANDBOOK, PAGES 32-35
             REFERENCE--GARDINER AND HULL, TECHNOMETRICS, 1966, PAGES 115-122
 
             NUMBER OF OBSERVATIONS    =    195
             SAMPLE MEAN               =   9.2614620
             SAMPLE STANDARD DEVIATION =   .22788810E-01
 
 
CONFIDENCE =    90.%
     COVERAGE (%)         LOWER LIMIT         UPPER LIMIT
             50.0        9.244962            9.277963
             75.0        9.233320            9.289604
             90.0        9.221224            9.301701
             95.0        9.213515            9.309409
             99.0        9.198452            9.324472
             99.9        9.180970            9.341954
 
CONFIDENCE =    95.%
     COVERAGE (%)         LOWER LIMIT         UPPER LIMIT
             50.0        9.244638            9.278286
             75.0        9.232769            9.290155
             90.0        9.220434            9.302490
             95.0        9.212575            9.310349
             99.0        9.197216            9.325708
             99.9        9.179391            9.343534
 
CONFIDENCE =    99.%
     COVERAGE (%)         LOWER LIMIT         UPPER LIMIT
             50.0        9.244002            9.278922
             75.0        9.231684            9.291241
             90.0        9.218884            9.304041
             95.0        9.210728            9.312197
             99.0        9.194788            9.328136
             99.9        9.176290            9.346635
 
 
----------------------------------------
 
 
2-SIDED DISTRIBUTION-FREE TOLERANCE LIMITS:
 
            REFERENCE--WILKS, ANNALS, 1941, PAGE 92
            REFERENCE--MOOD AND GRABLE, PAGES 416-417
 
 
INVOLVING X(3) =    9.207325     AND X(N-2) =    9.310506
    CONFIDENCE (%)       COVERAGE (%)
          100.0        .5000000E+02
          100.0        .7500000E+02
          100.0        .9000000E+02
           92.8        .9500000E+02
           36.2        .9750000E+02
            1.4        .9900000E+02
             .0        .9950000E+02
             .0        .9990000E+02
             .0        .9995000E+02
             .0        .9999000E+02
 
INVOLVING X(2) =    9.206343     AND X(N-1) =    9.320067
    CONFIDENCE (%)       COVERAGE (%)
          100.0        .5000000E+02
          100.0        .7500000E+02
          100.0        .9000000E+02
           98.9        .9500000E+02
           72.0        .9750000E+02
           13.3        .9900000E+02
            1.7        .9950000E+02
             .0        .9990000E+02
             .0        .9995000E+02
             .0        .9999000E+02
 
INVOLVING XMIN =    9.196848     AND XMAX =    9.327973
    CONFIDENCE (%)       COVERAGE (%)
          100.0        .5000000E+02
          100.0        .7500000E+02
          100.0        .9000000E+02
           99.9        .9500000E+02
           95.7        .9750000E+02
           58.2        .9900000E+02
           25.5        .9950000E+02
            1.7        .9990000E+02
             .4        .9995000E+02
             .0        .9999000E+02