Six Sigma DMAIC Case Study


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Application of Six Sigma on the Cricket Field.

This is a sample case study to demonstrate the application of Six Sigma methodology and tools for process improvement.

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Six Sigma DMAIC Case Study

  1. 1. Business Case 18 58 Mike’s Batting Average (runs scored per completed innings) Matches Lost Matches Won Mike is the best batsman in the team and the probability of winning a match is higher when he bats well Improving Mike’s consistency with the bat will help the team win more matches.
  2. 2. The average number of runs scored per innings by Mike was 32.5 for the last 50 matches (Jan to Dec 2011) against a benchmark of 40 runs per innings. This has had a negative impact on the match results as the team has won only 36% of the matches played (Jan to Dec 2011).
  3. 3. LSL Mike’s Average 40 32.5 The objective of the project is to improve Mike’s batting average and consistency
  4. 4. Process Capability Mean 32.52 Median 15 Standard Deviation 39.47 Count 50 Defect 36 DPMO 720000 Sigma (Zst) 0.92 Project CTQ Number of runs scored by Mike in each completed innings Defect Definition Any complete innings with a score of less than 40 runs would be a defect
  5. 5. What should be the desired outcome? Mike scoring 40 runs or more in half the matches played will be a significant improvement (p-value: 0.001)
  6. 6. What are the causes affecting Mike’s batting performance?
  7. 7. Let’s look at the defective innings (Innings where Mike got out for less than 40 runs)  In 30 out of 36 defective innings (83%), Mike was dismissed for less than 20 runs  Once Mike crosses 20 runs, the probability of playing a long innings is high (only 6 dismissals between 20 & 40 out of 50 completed innings)  Why is Mike getting out so often before scoring 20 runs?
  8. 8. How is Mike getting dismissed? Pareto Charts of dismissal types: Innings Score < 20 runs Innings Score > 20 runs  “Caught Behind” is the major cause for dismissal when Mike scores less than 20 runs: 50% compared to 10% when he scores more than 20 runs  Why is Mike getting caught by the keeper & the slip fielders so often at the start of his innings?  Team statistician Dave was asked to provide Mike’s shot selection data
  9. 9. Why is Mike getting “Caught Behind”? Analysis based on Mike’s shot selection data provided by Dave Pareto Chart of Type of Stroke Pareto Chart of Attacking Shot Played  67% caught behind dismissals at the start of his innings were while playing attacking strokes  Attacking shots contributing to most Caught Behind dismissals are Hook, Pull and Upper Cut
  10. 10. Hook, Pull & Upper Cut played by Mike Box Plot of Strike Rate (p-value: 0.000) 2-proportion test Statistics 0-25 Balls 25+ Balls Totals shots played 28 117 Number of dismissals 10 4 % Defective 35.71% 3.42% 90% CI (20.82, 53.00) (1.18, 7.65) P-value 0.000 Balls per dismissal 2.80 29.25  On an average, Mike plays 25 balls to score 20 runs  We tested the success of Hook, Pull & Upper Cuts during the first 25 balls played by Mike in comparison to shots played after 25 balls  The Strike Rate for 25+ balls is almost double compared to first 25 balls (strike rate is number of runs scored per ball)  Compared to 10 dismissals out of 28 attempts in the first 25 balls, Mike got out just 4 times in 117 attempts after playing 25 balls Mike needs to avoid playing the high risk shots (hook, pull & upper cut) in the initial stages of his innings
  11. 11. What are the other causes affecting Mike’s batting performance?
  12. 12. Cause & Effect Diagram Mike’s Batting Performance
  13. 13. Potential Causes (Xs) Critical Not Critical Causes shortlisted as critical in brainstorming session with project team and chief batting coach
  14. 14. Impact of Batting Innings & Pitch Conditions on Mike’s Performance
  15. 15.  There is no difference in Mike’s performance while batting first or chasing a target  Mike performs better on flat pitches compared to Green pitches  What can he do to score more runs while batting on Green pitches? Pitch Conditions Flat Green Number of Innings 24 26 Number of defectives 14 22 % Defective 58.33 84.62 95% CI (36.64, 77.89) (65.13, 95.64) P-value 0.059 Batting Innings First Second Number of Innings 23 27 Number of defectives 16 20 % Defective 69.57 74.07 95% CI (47.08, 86.79) (53.72, 88.89) P-value 0.761 Impact of Batting Innings & Pitch Conditions
  16. 16. What is affecting Mike’s batting on Green pitches? P-value: 0.031  While batting on Green pitches, Mike bats better when he is not required to open the batting and face the new ball bowlers (p-value: 0.03)  His average at 4th position is 52.5 compared to 12.1 while opening the batting on Green pitches
  17. 17. Impact of Bowling Style on Mike’s Batting Chi-Square % Defective Test for Bowling Style  “Number Tested” is no. of balls played  “Defectives” are no. of false or risky shots that did or could lead to a dismissal  There are differences among the % defectives at the 0.05 level of significance (p-value: 0.000)  Mike plays more risky / false shots while playing Left Arm Seam Bowlers (21.48%)
  18. 18. How can Mike improve his batting against left arm seam bowlers?
  19. 19. We asked the Chief Batting Coach and the Chairman of the Cricket Academy to analyze his batting video footage against Left Arm Seam Bowlers  Mike plays Left Arm Seam with a Closed Stance (Figure 1.1)  The orthodox stance blocks him before he begins playing a shot & he ends up playing around the front pad  Mike also keeps his backswing too straight & thus he plays across the line & ends up too chest on Figure 1.1  Mike needs to play Left Arm Seam with an Open Stance (Figure 1.2) & Wider Back-lift  With an open stance, he can align himself up to the angle that the ball is arriving at  For a wider back-lift, he needs to pick the bat up over the off stump or 1st slip area rather than over the middle stumpFigure 1.2 Analysis Suggestions
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  21. 21. Conclusions & Action Plan Root Cause Description Improvement Plan Responsibility Batting Style Hook, Pull and Upper Cut are shots contributing to maximum dismissals at the start of Mike's innings Mike needs to avoid playing these high risk shots in the initial stages of his innings (first 20-25 balls) Mike, Batting Coach, Team Captain Pitch Conditions Mike’s batting average on Green Pitches is significantly lower compared to his performance on Flat pitches. The problem is facing the new ball at the start of his innings on Green pitches that suit seam bowling. He does well batting lower down the order on Green pitches (average: 52.5) Suggestion: Mike should be sent at 4th position in matches played on Green pitches Action Plan: Continuously changing the batting order based on pitch conditions would negatively impact other players. As his batting is consistent at all positions on Flat pitches, Mike would bat at number 4 in all matches irrespective of pitch conditions Team Captain, Batting Coach Bowling Style Mike tends to play more false / risky shots while facing left arm seam bowlers Mike needs to play Left Arm Seam bowling with an open stance & wider back-lift. Mandatory inclusion of left arm net bowlers for team practice sessions Mike, Batting Coach, Team Manager
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  23. 23. Results LSL: 40 Mean: 32.52 Median: 15.00 LSL: 40 Mean: 49.32 Median: 46.50
  24. 24. Improvement Metric Measure Improve Mean 32.52 49.32 Median 15.00 46.50 Standard Deviation 39.47 42.51 Innings Played 50 28 Defective Innings 36 12 DPMO 72000 428571 Sigma (Zst) 0.92 1.68 % Innings < 40 Runs (LSL)
  25. 25. Benefits % Matches Won by the Team