Effects of Reducing Variability on Process Capability Nominal value Six sigma Four sigma Two sigma Lower specification © 2007 Pearson Education Upper specification Mean
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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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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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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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Lean Six Sigma – What is it? • Lean Six Sigma is a comprehensive and flexible system for achieving, sustaining and maximizing organizational success. • The Lean Six Sigma approach is driven by: Improve Processes Process Flow Teamwork Variation & Defects Speed • To insure an organizational transformation, Lean Six Sigma also focuses on the culture of an organization. Delight Customers Quality – Closely understanding customer needs – Disciplined use of facts, data & statistical analysis – Diligent attention to managing, improving & reinventing organizational processes Lean Six Sigma Data and Facts Source: What Is Lean Six Sigma, George, Rowlands & Kastle 2
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References • • • • • • • David N. Card, “Sorting out Six Sigma and the CMM”, IEEE Software, May June 2000, pp. 11-13 Jack Horgan, “Six Sigma and CMM”, September 13 - 17, 2004, http://www10.edacafe.com/nbc/articles/view_weekly.php?articleid=2 09200 M. Murugappan and G. Keeni, “Blending CMM and Six Sigma to Meet Business Goals”, IEEE Software, March/April 2003 “IT Perspective: Balancing Six Sigma and the Capability Maturity Model (CMM ®/CMMI SM )”, http://www.gartner.com/4_decision_tools/measurement/measure_it_art icles/2002_10/six_sig.jsp SEI Website, http://www.sei.cmm.edu/ Six Sigma, http://www.isixsigma.com/ Thomas Pyzdek, "DMAIC and DMADV", Pyzdek Consulting, Inc. Six Sigma Handbook, http://www.pyzdek.com/DMAICDMADV.htm
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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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TEAMS WHITE OPAL Alpha Sigma Alpha Sigma Phi Epsilon SILVER QUARTZ Sigma Sigma Sigma Delta Chi Phi Lambda Phi Cardinal Key PURPLE AMETHYST Alpha Phi Omega Phi Kappa Tau Prim Roses EMERALD GREEN AMBER ORANGE Delta Zeta Tau Lambda Sigma Lambda Chi Alpha Alpha Gamma Rho MAP Phi Delta RUBY RED YELLOW TOPAZ Delta Phi Epsilon Sigma Kappa Tau Kappa Epsilon Phi Sigma Kappa Delta Sigma Pi Sigma Tau Gamma BLUE SAPPHIRE BLACK ONYX Alpha Gamma Delta Alpha Sigma Gamma Pi Kappa Phi ABC Beta Theta Pi Alpha Kappa Lambda
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