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OCR for page 20
Table 39 Results of t-test for comparison of measured and target percent retained on #18 sieve of Type 3 samples Method of No. Average% % Rejection Measurement-- of Round, Retained, Probability Sample Type Labs Measured Target Sx Computed t Critical t Decision (p) Mechanical 13 58.8 55.0 3.197 4.286 2.179 Reject 0.001 Sieve--Type 3 COM-A--Type 3 8 57.2 55.0 2.026 3.071 2.365 Reject 0.018 COM-B--Type 3 1 52.5 55.0 -- -- -- -- -- closer than the mechanical sieve measurements to the gests that computerized optical equipment is espe- target value, as indicated by the larger rejection prob- cially suitable for measuring the size distribution of ability for the COM-A data (0.018) when compared the larger-sized glass beads. with the rejection probability for the mechanical sieve data (0.001). Roundness Measurement Type 5 Samples Tables 41, 42, and 43 summarize the percent round statistics of the three sample types. The com- Table 40 compares the percent retained measure- puted and critical t-values for a 5% level of signifi- ments on the #14 sieve for the Type 5 samples by the cance are utilized to compute the rejection probabili- various measurement methods. The COM-A percent ties. A rejection probability greater than 0.05 indicates retained measurements were in very good agreement that the measured and target roundness of a sample with the target value of 55% (rejection probability of are the same. 0.167) while the mechanical sieve significantly over- estimated the percent retained (rejection probability Type 1 Samples of 0.006). Table 41 compares the percent round measure- Summary of Bias in Size Measurement ments with the target percent round on the #50 sieve for the Type 1 samples for various measur- The t-test results for the size measurement of the ing methods and parameters. Except for the rejec- glass bead samples revealed that computerized opti- tion probability for the COM-B measurements, cal methods in general provided more accurate mea- the rejection probabilities are smaller than 0.05, surements of size than the mechanical sieve. For indicating that only COM-B measured the round- Type 1 beads, COM-B provided more accurate mea- ness of Type 1 samples correctly. Despite its accu- surement than did the mechanical sieve; for the larger racy, COM-B provided the most variable measure- beads, COM-A was more accurate than the mechan- ments as indicated by the standard deviation of ical sieves. It was also indicated that the level of the laboratory means (Sx = 5.95). The least variable accuracy and precision of COM-A measurements measurement was provided by the COM-A b/l increased as the size of the beads increased. This sug- parameter. Table 40 Results of t-test for comparison of measured and target percent retained on #14 sieve of Type 5 samples Method of No. Average % % Rejection Measurement-- of Round, Retained, Probability Sample Type Labs Measured Target Sx Computed t Critical t Decision (p) Mechanical 13 58.5 55.0 3.771 3.313 2.201 Reject 0.006 Sieve--Type 5 COM-A--Type 5 7 55.5 55.0 0.876 1.571 2.447 Accept 0.167 COM-B--Type 5 1 51.9 55.0 -- -- -- -- -- 20
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Table 41 Results of t-test for comparison of measured and target percent round on #50 sieve of Type 1 samples Method of No. Average % % Rejection Measurement-- of Round, Round, Probability Sample Type Labs Measured Target Sx Computed t Critical t Decision (p) Roundometer-- 11 74.2 70.0 2.89 4.776 2.228 Reject 0.001 Type 1 COM-A-b/l-- 6 78.6 70.0 1.26 16.833 2.571 Reject 0.000 Type 1 COM-A-SPHT-- 3 84.5 70.0 1.38 18.231 4.303 Reject 0.003 Type 1 COM-B-NSP-- 4 77.3 70.0 5.95 2.435 3.182 Accept 0.093 Type 1 Type 3 Samples for the COM-B measurements because only one set of Type 5 roundness data was available. The round- Table 42 compares the percent round measure- ness measurement using the b/l parameter agreed ments with the target percent round on the #18 sieve very well with the target roundness of 90% (p = 0.08). for the Type 3 samples. No t-statistics were calculated The b/l parameter also had a very small standard devi- for the COM-B measurements since only one set ation compared to that of the roundometer (Sx = 1.13 of roundness data was available for Type 3 samples. vs. Sx = 4.14). Although both SPHT and roundometer The most accurate roundness measurement was measurements were significantly different from provided by the COM-A b/l parameter (p = 0.616). the target roundness, the results from the SPHT The roundometer also measured the roundness of parameter were closer to the target value than those the Type 3 samples correctly (p = 0.257), although from the roundometer (p = 0.036 and 0.003). The with the highest variability (Sx = 3.52). The lowest SPHT measurements were also less variable than the rejection probability (p = 0.000) in Table 42 corre- roundometer measurements (Sx = 1.13 and 4.14). sponds to the SPHT parameter, indicating that the measured roundness as judged by this parameter was Summary of Bias in Roundness Measurement significantly different from the target roundness. The one-sample t-test results on the glass bead roundness measurements indicated that the comput- Type 5 Samples erized optical methods provided more accurate mea- Table 43 compares the percent round measure- surements than did the mechanical roundometer. For ments with the target percent round on the #14 sieve Type 1 beads, the COM-B device provided the most of the Type 5 samples. No t-statistics were calculated accurate roundness measurement and for Types 3 and Table 42 Results of t-test for comparison of measured and target percent round on #18 sieve of Type 3 samples Method of No. Average % % Rejection Measurement-- of Round, Round, Probability Sample Type Labs Measured Target Sx Computed t Critical t Decision (p) Roundometer-- 8 78.5 80.0 3.52 1.233 2.365 Accept 0.257 Type 3 COM-A-b/l-- 8 80.1 80.0 0.77 0.525 2.365 Accept 0.616 Type 3 COM-A-SPHT-- 4 86.3 80.0 0.70 17.898 3.182 Reject 0.000 Type 3 COM-B-NSP-- 1 86.8 80.0 -- -- -- -- -- 21