Intensive Care Lab Assessing Process Capability Example 6.5 Cp = Cp = Upper specification - Lower specification 30 - 20 6(1.35) 6 = 1.23 Process Capability Ratio Does not meet 4 (1.33 Cp) target Before Process Modification Upper specification = 30.0 minutes Lower specification = 20.0 minutes Average service = 26.2 minutes  = 1.35 minutes Cpk = 0.94 Cp = 1.23 After Process Modification Upper specification = 30.0 minutes Lower specification = 20.0 minutes Average service = 26.1 minutes  = 1.2 minutes Cpk = 1.08 Cp = 1.39 © 2007 Pearson Education
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Washing and waxing a car for 45-60 minutes Vigorous, Washing windows or floors for 45-60 minutes Less More Time Playing volleyball for 45 minutes Playing touch football for 30-45 minutes Gardening for 30-45 minutes Wheeling self in wheelchair for 30-40 minutes Walking 1 3/4 miles in 35 minutes (20 min/mile) Basketball (shooting baskets) for 30 minutes Bicycling 5 miles in 30 minutes Dancing fast (social) for 30 minutes Pushing a stroller 1 1/2 miles in 30 minutes Raking leaves for 30 minutes Walking 2 miles in 30 minutes (15 min/mile) Water aerobics for 30 minutes Swimming laps for 20 minutes Wheelchair basketball for 20 minutes Basketball )playing a game) for 15-20 minutes Bicycling 4 miles in 15 minutes Jumping rope for 15 minutes Running 1 1/2 miles in 15 minutes (10 min/mile) 2.2 Shoveling snow for 15 minutes Vigorous, Stairwalking for 15 minutes More Less Time
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24 Functions are not Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods are are are are are are are are are are are are are are are are are are are are are are are are not not not not not not not not not not not not not not not not not not not not not not not not Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods are are are are are are are are are are are are are are are are are are are are are are are are not not not not not not not not not not not not not not not not not not not not not not not not Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods F are are are are are are are are are are are are are are are are are are are are are are are are not not not not not not not not not not not not not not not not not not not not not not not not Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods are are are are are are are are are are are are are are are are are are are are are are are are not not not not not not not not not not not not not not not not not not not not not not not not Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions
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Intensive Care Lab Example 6.5 The intensive care unit lab process has an average turnaround time of 26.2 minutes and a standard deviation of 1.35 minutes. The nominal value for this service is 25 minutes with an upper specification limit of 30 minutes and a lower specification limit of 20 minutes. The administrator of the lab wants to have four-sigma performance for her lab. Is the lab process capable of this level of performance? Upper specification = 30 minutes Lower specification = 20 minutes Average service = 26.2 minutes  = 1.35 minutes © 2007 Pearson Education
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Merge Sort Analysis Worst-case time complexity for applying the merge function to a size-k subarray: M(k) = 18k-7. template template Etype> void merge(Etype source[], void merge(Etype source[], Etype Etype dest[], dest[], int int lower, lower, int int middle, middle, int int upper) upper) { int int s1 s1 = = lower; lower; int // int s2 s2 = = middle middle + + 1; 1; // 1 1 TU TU int int d d = = lower; lower; do do { if if (source[s1] (source[s1] < < source[s2]) source[s2]) // // If If block: block: { // 14 { // 14 TU TU dest[d] dest[d] = = source[s1]; source[s1]; s1++; s1++; } else else { { dest[d] dest[d] = = source[s2]; source[s2]; s2++; s2++; } d++; // d++; // 1 1 TU TU } while ((s1 <= middle) && // } while ((s1 <= middle) && // k-m k-m iter. iter. (s2 // @ (s2 <= <= upper)); upper)); // @ 3 3 TU TU } } if (s1 > middle) do do { { dest[d] dest[d] = = source[s2]; source[s2]; s2++; s2++; d++; } } while while (s2 (s2 <= <= upper); upper); else else do do { { dest[d] = source[s1]; s1++; s1++; d++; d++; } } while while (s1 (s1 <= <= middle); middle); CS 340 // 1 TU // // // // // // // 6 6 1 1 1 m m TU TU TU TU TU iter. iter. @ @ 1 1 TU TU Time complexity for applying the order function to a size-k subarray: R(k), where R(1)=1 and R(k) = 5+M(k)+2R(k/2) = 18k-2+2R(k/2). This recurrence relation yields R(k) = 18klogk-logk+2. template template void order(Etype source[], Etype dest[], int lower, int upper) { int middle; if (lower != upper) { middle = (lower + upper) / 2; order(dest, source, lower, middle); order(dest, source, middle + 1, upper); merge(source, dest, lower, middle, upper); } } // 1 TU // // // // 3 TU R(k/2) TU R(k/2)+1 TU M(k) TU Time complexity for applying the mergesort function to a sizen subarray: T(n) = 8n+1+R(n) = 18nlogn+8n-logn+3. template void mergeSort(Etype A[], const int n) { Etype Acopy[n+1]; // 1 TU int size; for (int k = 1; k <= n; k++) // n iter. @ 2 TU Acopy[k] = A[k]; // 6 TU order(Acopy, A, 1, size); // R(n) TU } While While this this O(nlogn) O(nlogn) time time complexity complexity is is favorable, favorable, the the requirement requirement of of aa duplicate duplicate array array is is detrimental detrimental to to the the Merge Merge Sort Sort algorithm, algorithm, possibly possibly making making it it less less popular popular than certain alternative choices. than certain alternative choices. Page 16
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Merge Sort void order(list source, list dest, int lower, int upper); void merge(list source, list dest, int lower, int middle, int upper); void sort(list L, int n) { list Lcopy; for (int k = 0; k < n; k++) Lcopy[k] = L[k]; order(Lcopy, L, 0, n - 1); } void order(list source, list dest, int lower, int upper) { int middle; if (lower != upper) { middle = (lower + upper) / 2; order(dest, source, lower, middle); order(dest, source, middle + 1, upper); merge(source, dest, lower, middle, upper); } } CS 240 void merge(list source, list dest, int lower, int middle, int upper) { int s1 = lower; int s2 = middle + 1; int d = lower; do { if (source[s1] < source[s2]) { dest[d] = source[s1]; s1++; } else { dest[d] = source[s2]; s2++; } d++; } while ((s1 <= middle) && (s2 <= upper)); if (s1 > middle) do { dest[d] = source[s2]; s2++; d++; } while (s2 <= upper); else do { dest[d] = source[s1]; s1++; d++; } while (s1 <= middle); } 57
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Intensive Care Lab Assessing Process Capability Example 6.5 Cpk = Minimum of Cpk = Cpk = Upper specification = 30 minutes Lower specification = 20 minutes Average service = 26.2 minutes  = 1.35 minutes x= – Lower specification Minimum of 3 26.2 – 20.0 3(1.35) Minimum of © 2007 Pearson Education , 1.53, 0.94 Upper specification – x= 3 , 30.0 – 26.2 3(1.35) = 0.94 Process Capability Index
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Excel Methods to Create Frequency Distribution • COUNTIFS Excel function with two criteria • Count between the lower and upper limit • Because you have control over the comparative operators, you can create any type of Upper and Lower Limit. • This is different than with the PivotTable Grouping feature and the FREQUENCY Array Function. • PivotTables and the Grouping feature • When Grouping in a PivotTable: • Integer data yields unambiguous labels • Decimal data yields ambiguous labels • Remember: when you are counting between an upper and lower limit, the Upper Limit is NOT included and the Lower Limit IS included; unlike formulas we do not have control over how the upper and lower limits work when grouping. • FREQUENCY Array Function: • Next slide has full details about this function • One note here: For FRQUENCY Array Formula when you are counting between an upper and lower limit, the Upper Limit IS included and the Lower Limit is NOT included; unlike formulas we do not have control over how the upper and lower limits work when grouping. • FREQUENCY Array Function and Data Analysis Tools, Histogram yield the same answer. • Data Analysis Tools, Histogram • You must add this feature in: File tab, Options, Add-ins, Manage: Excel Ass-ins, Click Go, Check box for Analysis Toolpak, Click OK • This feature will create the Frequency Table (just like the FREQUENCY Array Function), a Histogram and a Cumulative Distribution. If Gap Width in Chart is not zero, you must change it!! • FREQUENCY Array Function and Data Analysis Tools, Histogram yield the same answer. 33
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Jagged arrays  Implemented as arrays of arrays , 4 index type index lower bound index upper bound address address , 3 , 3 index type index type index lower bound index lower bound index upper bound index upper bound address address , 7 , 7 index type index type index lower bound index lower bound index upper bound index upper bound address address , 4 , 4 index type index type index lower bound index lower bound index upper bound index upper bound address address , 5 , 5 index type index type index lower bound index lower bound index upper bound index upper bound address address 24
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Merge Sort Recursively sort both halves of the list, and then quickly merge the two sorted halves to form the entire sorted list.int s1 = lower; int s2 = middle + 1; int d = lower; do { if (source[s1] < source[s2]) { dest[d] = source[s1]; s1++; } else { dest[d] = source[s2]; s2++; } d++; } while ((s1 <= middle) && (s2 <= upper)); template void mergeSort(Etype A[], const int n) { Etype Acopy[n+1]; int size; for (int k = 1; k <= n; k++) Acopy[k] = A[k]; order(Acopy, A, 1, size); } template void order(Etype source[], Etype dest[], int lower, int upper) { int middle; if (lower != upper) { middle = (lower + upper) / 2; order(dest, source, lower, middle); order(dest, source, middle + 1, upper); merge(source, dest, lower, middle, upper); } } template void merge(Etype source[], Etype dest[], int lower, int middle, int upper) { CS 340 } if (s1 > middle) do { dest[d] = source[s2]; s2++; d++; } while (s2 <= upper); else do { dest[d] = source[s1]; s1++; d++; } while (s1 <= middle); Page 14
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Process Capability Nominal value Process distribution Upper specification Lower specification 20 25 30 Process is not capable © 2007 Pearson Education Minutes
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Process Capability Nominal value Process distribution Upper specification Lower specification 20 25 Process is capable © 2007 Pearson Education 30 Minutes
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Short-Term Recommendations ● Pilot: Reduce the scheduled time from 60 minutes  45 minutes ○ Head/Neck Average Length: 36.17 minutes ○ Prostate Average Length: 30.35 minutes ○ Lung (No SDX) Average Length: 28.09 minutes ○ Spine Average Length: 26.50 minutes ○ Pelvis Average Length: 31.67 minutes ● Pilot: Reduce the scheduled time from 90 minutes  75 minutes ○ Liver Average Length: 66.09 minutes ○ Abdomen Average Length: 43.40 minutes 25
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Readback of Error Count CDL Readback of ERROR_COUNT Block: RCA 0x1000, FC 5 COUNT DESCRIPTION LIMIT 0 No Known cause 1 Temperature Greater than Upper Limit Error. > 50.0 C. 2 28V Voltage Lower Limit Error. < 27.0 V. 3 28V Voltage Upper Limit Error. > 29.0 V. 4 Rectifier High Voltage Error. 5 Rectifier Low Voltage Error. 6 1.8V Voltage Upper Limit Error. > 2.2 V. 7 3.3V Voltage Upper Limit Error. > 3.6 V. 8 5.0V Voltage Upper Limit Error. > 5.5 V. 9 Rectifier Over Temperature Alert. 10 1.8V Current Upper Limit Error. > 60.0 A. 11 9UBPS 3.3V Current Upper Limit Error. > 50.0 A. 12 5.0V Current Upper Limit Error. > 3.0 A. 13 QCC V1.8 Lower Limit Error. < 1.6 V. 14 QCC V3.3 Lower Limit Error. < 3.0 V. 15 QCC V5.0 Lower Limit Error. < 4.5 V. 16 QCC V1.8 Upper Limit Error. > 2.2 V. 17 QCC V3.3 Upper Limit Error. > 3.6 V. ALMA Correlator Workshop, May 2016 11
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Effects of Money Market and Output Market Changes on the Long-Run Nominal Dollar/Euro Exchange Rate, E$/€ Change Effect on the long-run nominal $/€ exchange rate, E$/€ Money Market 1. Increase in U.S. money supply level Proportional increase (nominal depreciation of $) 2. Increase in European money supply level Proportional decrease(nominal depreciation of €) 3. Increase in U.S. money supply growth rate Increase (nominal depreciation of $) 4. Increase in European money supply growth rate Decrease (nominal depreciation of €) Output Market 1. Increase in demand for U.S. output Decrease (nominal appreciation of $) 2. Increase in demand for European output Increase (nominal appreciation of €) 3. Output supply increase in the U.S. Ambiguous 4. Output supply increase in the Europe Ambiguous
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QC - Perpendicularity 25 20 20 15 10 5 Point I After Tack Weld H Pe rpendicularity (Actual - Nominal) (in) Point L After Tack W eld Per p en d icu la r ity (A ctu a l - N o m in al ) (in ) Perpendicula rity (Actual - Nom ina l) (in) I 12 10 J 20 15 16 14 12 10 8 6 4 2 0 K 25 0 Perpendicularity (Actual - Nominal) (in) 2 12 30 5 0 4 0 Frequency 5 6 P o int K A ft e r T a c k W e ld F req u en cy 10 8 B F re quency 10 40 35 25 G Perpendicularity (Actual - Nominal) (in) Perpe ndicularit y (Act ual - Nominal) ( in) Point J After Tack Weld 15 5 Point H After T ack Weld 16 14 12 10 8 6 4 2 0 Perpendicularity (Actual - Nominal) (in) 20 10 Pe rpendicularity (Ac tual - Nominal) (in) Freq uency 14 12 10 8 6 4 2 0 15 0 0 Point G After Tack Weld Freque nc y Frequency 25 Perpe ndicularity (Actual - Nominal) (in) Frequency Point F After Tack Weld Point E After Tack Weld Fre quenc y Freque ncy Point D After Tack Weld 16 14 12 10 8 6 4 2 0 Pe rpendicula rity ( Ac tual - Nom ina l) ( in) Pe rpendicularity (Actua l - Nom inal) (in) 12 Perpendicularity (Actual - Nominal) (in) F 0 • QC Sheet 12 4 2 0 C 6 A 5 8 14 12 10 8 6 4 2 0 L 10 10 Frequency Freq uency 15 E 12 20 Frequency Point C After Tack Weld D Point B After Tack Weld Point A After Tack Weld
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