Your SlideShare is downloading. ×
0
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Chap17 statistical applications on management
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Chap17 statistical applications on management

588

Published on

Modul Statistik Bisnis II

Modul Statistik Bisnis II

Published in: Technology, Business
0 Comments
2 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total Views
588
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
56
Comments
0
Likes
2
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Statistics for Managers Using Microsoft® Excel 4th Edition Chapter 17 Statistical Applications in Quality and Productivity Management Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-1
  • 2. Chapter Goals After completing this chapter, you should be able to:  Describe the concepts of Total Quality Management and Six Sigma® Management  Explain process variability and the theory of control charts  Construct and interpret p charts  Construct and interpret X and R charts  Obtain and explain measures of process capability Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-2
  • 3. Chapter Overview Quality Management and Tools for Improvement Philosophy of Quality Deming’s 14 Points Six Sigma® Management Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Tools for Quality Improvement Control Charts Process Capability p chart R chart X chart Chap 17-3
  • 4. Total Quality Management  Primary focus is on process improvement  Most variation in a process is due to the system, not the individual  Teamwork is integral to quality management  Customer satisfaction is a primary goal  Organization transformation is necessary  It is important to remove fear  StatisticsHigher quality costs less for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-4
  • 5. Deming’s 14 Points 1. Create a constancy of purpose toward improvement  become more competitive, stay in business, and provide jobs 2. Adopt the new philosophy  Better to improve now than to react to problems later 3. Stop depending on inspection to achieve quality -- build in quality from the start  Inspection to find defects at the end of production is too late 4. Stop awarding contracts on the basis of low bids Statistics for Managers Using Better Microsoft Excel, to build2004 purchaser/supplier relationships 4e © long-run Chap 17-5 Prentice-Hall, Inc. 
  • 6. Deming’s 14 Points (continued) 5. Improve the system continuously to improve quality and thus constantly reduce costs 6. Institute training on the job  Workers and managers must know the difference between common cause and special cause variation 7. Institute leadership  Know the difference between leadership and supervision 8. Drive out fear so that everyone may work effectively. 9. Break down barriers Statistics for Managers Using between departments so that people can work as a team. Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-6
  • 7. Deming’s 14 Points (continued)  10. Eliminate slogans and targets for the workforce      They can create adversarial relationships 11. Eliminate quotas and management by numerical goals 12. Remove barriers to pride of workmanship 13. Institute a vigorous program of education and self-improvement 14. Make the transformation everyone’s job Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-7
  • 8. The Shewhart-Deming Cycle Plan Act The Deming Cycle Statistics for Managers Using Study Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Do The key is a continuous cycle of improvement Chap 17-8
  • 9. Six Sigma® Management A method for breaking a process into a series of steps:  The goal is to reduce defects and produce near perfect results  The Six Sigma® approach allows for a shift of as much as 1.5 standard deviations, so is essentially a ±4.5 standard deviation goal  The mean of a normal distribution ±4.5 standard deviations Statistics for Managers Using includes all but 3.4 out of a million Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-9
  • 10. The Six Sigma® DMAIC Model DMAIC represents  Define -- define the problem to be solved; list costs, benefits, and impact to customer  Measure – need consistent measurements for each Critical-to-Quality characteristic  Analyze – find the root causes of defects  Improve – use experiments to determine importance of each Critical-to-Quality variable  Control – maintain Statistics for Managers Usinggains that have been made Microsoft Excel, 4e © 2004 Chap 17-10 Prentice-Hall, Inc.
  • 11. Theory of Control Charts  A process is a repeatable series of steps leading to a specific goal  Control Charts are used to monitor variation in a measured value from a process  Inherent variation refers to process variation that exists naturally. This variation can be reduced but not eliminated Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-11
  • 12. Theory of Control Charts (continued)  Control charts indicate when changes in data are due to:  Special or assignable causes     Fluctuations not inherent to a process Represents problems to be corrected Data outside control limits or trend Chance or common causes Inherent random variations  Consist of numerous small causes of random Statistics for Managers Using variability Microsoft Excel, 4e © 2004 Chap 17-12 Prentice-Hall, Inc. 
  • 13. Process Variation Total Process Common Cause Special Cause = + Variation Variation Variation Variation is natural; inherent in the world around us  No two products or service experiences are exactly the same  With a fine enough gauge, all things can be seen to differ Statistics for Managers Using Microsoft Excel, 4e © 2004 Chap 17-13 Prentice-Hall, Inc. 
  • 14. Total Process Variation Total Process Common Cause Special Cause = + Variation Variation Variation Variation is often due to differences in:  People  Machines  Materials  Methods  Measurement Statistics for Managers Using  Microsoft Excel,Environment 4e © 2004 Prentice-Hall, Inc. Chap 17-14
  • 15. Common Cause Variation Total Process Common Cause Special Cause = + Variation Variation Variation Common cause variation  naturally occurring and expected  the result of normal variation in materials, tools, machines, operators, and the environment Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-15
  • 16. Special Cause Variation Total Process Common Cause Special Cause = + Variation Variation Variation Special cause variation  abnormal or unexpected variation  has an assignable cause  variation beyond what is considered inherent to the process Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-16
  • 17. Control Limits Forming the Upper control limit (UCL) and the Lower control limit (LCL): UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations UCL +3σ Process Average - 3σ Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. LCL time Chap 17-17
  • 18. Control Chart Basics Special Cause Variation: Range of unexpected variability UCL Common Cause Variation: range of expected variability +3σ Process Average - 3σ LCL time UCL = Process Average + 3 Standard Deviations Statistics for Managers Using LCL = Process Average – 3 Standard Deviations Microsoft Excel, 4e © 2004 Chap 17-18 Prentice-Hall, Inc.
  • 19. Process Variability Special Cause of Variation: A measurement this far from the process average is very unlikely if only expected variation is present UCL ±3σ → 99.7% of process values should be in this range Process Average LCL time UCL = Process Average + 3 Standard Deviations Statistics for Managers Using LCL = Process Average – 3 Standard Deviations Microsoft Excel, 4e © 2004 Chap 17-19 Prentice-Hall, Inc.
  • 20. Using Control Charts  Control Charts are used to check for process control H0: The process is in control i.e., variation is only due to common causes H1: The process is out of control i.e., special cause variation exists If the process is found to be out of control, steps should be taken to find and eliminate the Statistics for Managers Using special causes of variation  Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-20
  • 21. In-control Process  A process is said to be in control when the control chart does not indicate any out-of-control condition  Contains only common causes of variation   If the common causes of variation is small, then control chart can be used to monitor the process If the common causes of variation is too large, you need to alter the process Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-21
  • 22. Process In Control  Process in control: points are randomly distributed around the center line and all points are within the control limits UCL Process Average LCL Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. time Chap 17-22
  • 23. Process Not in Control Out of control conditions:  One or more points outside control limits  8 or more points in a row on one side of the center line  8 or more points moving in the same direction Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-23
  • 24. Process Not in Control  One or more points outside control limits  Eight or more points in a row on one side of the center line UCL Process Average Process Average LCL  UCL LCL Eight or more points moving in the same direction UCL Process Average Statistics for ManagersLCL Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-24
  • 25. Out-of-control Processes  When the control chart indicates an out-ofcontrol condition (a point outside the control limits or exhibiting trend, for example)   Contains both common causes of variation and assignable causes of variation The assignable causes of variation must be identified   If detrimental to the quality, assignable causes of variation must be removed If increases quality, assignable causes must be incorporated into the process design Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-25
  • 26. Statistical Process Control Charts Statistical Process Control Charts p chart X chart and R chart Used for proportions (attribute data) Used for measured numeric data Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-26
  • 27. p Chart  Control chart for proportions   Is an attribute chart Shows proportion of nonconforming items  Example -- Computer chips: Count the number of defective chips and divide by total chips inspected  Chip is either defective or not defective Finding a defective chip can be classified a “success” Statistics for Managers Using Microsoft Excel, 4e © 2004 Chap 17-27 Prentice-Hall, Inc. 
  • 28. p Chart (continued)  Used with equal or unequal sample sizes (subgroups) over time    Unequal sizes should not differ by more than ±25% from average sample sizes Easier to develop with equal sample sizes Should have np > 5 and n(1 - p) > 5 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-28
  • 29. Creating a p Chart  Calculate subgroup proportions  Graph subgroup proportions  Compute average proportion  Compute the upper and lower control limits  Add centerline and control limits to graph Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-29
  • 30. p Chart Example Subgroup number Sample size Number of successes Sample Proportion, ps 1 2 3 … 150 150 150 15 12 17 … 10.00 8.00 11.33 … Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Average subgroup proportion = p Chap 17-30
  • 31. Average of Subgroup Proportions The average of subgroup proportions = p If equal sample sizes: If unequal sample sizes: k k p= ∑ pi i=1 k where: pi = sample proportion for subgroup i Statistics for Managers Using k = number of subgroups Microsoft size n 4e © 2004 of Excel, Prentice-Hall, Inc. p= ∑X i=1 k ∑n i =1 i i where: Xi = the number of nonconforming items in sample i Σni = total number of items sampled in k samples Chap 17-31
  • 32. Computing Control Limits  The upper and lower control limits for a p chart are UCL = Average Proportion + 3 Standard Deviations LCL = Average Proportion – 3 Standard Deviations  The standard deviation for the subgroup proportions is (p)(1 − p) n Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-32
  • 33. Computing Control Limits (continued)  The upper and lower control limits for the p chart are p(1 − p) UCL = p + 3 n p(1 − p) LCL = p − 3 n Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Proportions are never negative, so if the calculated lower control limit is negative, set LCL = 0 Chap 17-33
  • 34. p Chart Example You are the manager of a 500-room hotel. You want to achieve the highest level of service. For seven days, you collect data on the readiness of 200 rooms. Is the process in control? Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-34
  • 35. p Chart Example: Hotel Data Day 1 2 3 4 5 6 7 # Rooms 200 200 200 200 200 200 200 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. # Not Ready 16 7 21 17 25 19 16 Proportion 0.080 0.035 0.105 0.085 0.125 0.095 0.080 Chap 17-35
  • 36. p Chart Control Limits Solution k p= ∑X i=1 k ∑n i =1 i i 16 + 7 +  + 16 121 = = = .0864 200 + 200 +  + 200 1400 k n= ∑n i =1 k i 200 + 200 +  + 200 = = 200 7 p(1 − p) .0864(1 − .0864 ) UCL = p + 3 = .0864 + 3 = .1460 200 n p(1 − Using Statistics for Managers p) = .0864 − 3 .0864(1 − .0864 ) = .0268 LCL = p − 3 200 Microsoft Excel, 4e © n 2004 Chap 17-36 Prentice-Hall, Inc.
  • 37. p Chart Control Chart Solution P 0.15 UCL = .1460 _ p = .0864 0.10 0.05 0.00 LCL = .0268 1 2 3 4 5 Day 6 _ 7 Individual points are distributed around p without any pattern. Any improvement in the process must come from reduction of common-cause variation, Statistics for Managers Using which is the responsibility of management. Microsoft Excel, 4e © 2004 Chap 17-37 Prentice-Hall, Inc.
  • 38. Understanding Process Variability: Red Bead Experiment The experiment:  From a box with 20% red beads and 80% white beads, have “workers” scoop out 50 beads  Tell the workers their job is to get white beads  10 red beads out of 50 (20%) is the expected value. Scold workers who get more than 10, praise workers who get less than 10 Some workers will get better over time, some Statistics for Managers Using will get 4e © 2004 Microsoft Excel,worse  Prentice-Hall, Inc. Chap 17-38
  • 39. Morals of the Red Bead Experiment 2. 3. 4. Variation is an inherent part of any process. The system is primarily responsible for worker performance. Only management can change the system. Some workers will always be above average, and some will be below. proportion 1. Statistics for Managers Using Microsoft Excel, 4e © 2004 Subgroup number Prentice-Hall, Inc. UCL p LCL Chap 17-39
  • 40. R chart and X chart  Used for measured numeric data from a process  Start with at least 20 subgroups of observed values  Subgroups usually contain 3 to 6 observations each For the process to be in control, both the R Statisticschart and theUsing chart must be in control for Managers X-bar  Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-40
  • 41. Example: Subgroups  Process measurements: Subgroup measures Subgroup Individual measurements number (subgroup size = 4) 1 2 3 … 15 12 17 … 17 16 21 … 15 9 18 … Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. 11 15 20 … Mean, X Range, R 14.5 13.0 19.0 … 6 7 4 … Average subgroup mean = X Average subgroup range = R Chap 17-41
  • 42. The R Chart  Monitors variability in a process    The characteristic of interest is measured on a numerical scale Is a variables control chart Shows the sample range over time  Range = difference between smallest and largest values in the subgroup Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-42
  • 43. Steps to create an R chart  Find the mean of the subgroup ranges (the center line of the R chart)  Compute the upper and lower control limits for the R chart  Use lines to show the center and control limits on the R chart Plot the successive subgroup ranges as a Statisticsline Managers Using for chart  Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-43
  • 44. Average of Subgroup Ranges Average of subgroup ranges: ∑R R= i k where: Ri = ith subgroup range k = number of subgroups Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-44
  • 45. R Chart Control Limits  The upper and lower control limits for an R chart are UCL = D 4 ( R ) LCL = D3 ( R ) where: D4 and D3 are taken from the table Managers Using E.11) for subgroup size = n (Appendix Table Statistics for Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-45
  • 46. R Chart Example You are the manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the variation in the process in control? Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-46
  • 47. R Chart Example: Subgroup Data Day 1 2 3 4 5 6 7 Subgroup Subgroup Subgroup Size Average Range 5 5 5 5 5 5 5 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. 5.32 6.59 4.89 5.70 4.07 7.34 6.79 3.85 4.27 3.28 2.99 3.61 5.04 4.22 Chap 17-47
  • 48. R Chart Center and Control Limits ∑R R= k i 3.85 + 4.27 +  + 4.22 = = 3.894 7 UCL = D 4 ( R ) = (2.114 )(3.894 ) = 8.232 LCL = D3 ( R ) = (0)(3.894 ) = 0 D4 and D3 are from Statistics for Managers Using Table E.11 (n = 5) Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-48
  • 49. R Chart Control Chart Solution Minutes UCL = 8.232 8 6 4 2 0 _ R = 3.894 LCL = 0 1 2 3 4 Day 5 6 7 Conclusion: Variation is in control Statistics for Managers Using Microsoft Excel, 4e © 2004 Chap 17-49 Prentice-Hall, Inc.
  • 50. The X Chart  Shows the means of successive subgroups over time  Monitors process average  Must be preceded by examination of the R chart to make sure that the variation in the process is in control Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-50
  • 51. Steps to create an X chart  Compute the mean of the subgroup means (the center line of the X chart)  Compute the upper and lower control limits for the X chart  Graph the subgroup means  Add the center line and control limits to the graph Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-51
  • 52. Average of Subgroup Means Average of subgroup means: ∑X X= i k where: Xi = ith subgroup average k = number of subgroups Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-52
  • 53. Computing Control Limits  The upper and lower control limits for an X chart are generally defined as UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations  Use R d2 n to estimate the standard deviation of the process average, where d2 is from appendix Table E.11 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-53
  • 54. Computing Control Limits (continued)  The upper and lower control limits for an X chart are generally defined as UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations  so UCL = X + 3 LCL = X − 3 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. R d2 n R d2 n Chap 17-54
  • 55. Computing Control Limits (continued)  Simplify the control limit calculations by using UCL = X + A 2 ( R ) LCL = X − A 2 ( R ) where A2 = 3 d2 n Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-55
  • 56. X Chart Example You are the manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For seven days, you collect data on five deliveries per day. Is the process average in control? Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-56
  • 57. X Chart Example: Subgroup Data Day 1 2 3 4 5 6 7 Subgroup Subgroup Subgroup Size Average Range 5 5 5 5 5 5 5 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. 5.32 6.59 4.89 5.70 4.07 7.34 6.79 3.85 4.27 3.28 2.99 3.61 5.04 4.22 Chap 17-57
  • 58. X Chart Control Limits Solution ∑X X= i k ∑R R= k i 5.32 + 6.59 +  + 6.79 = = 5.813 7 3.85 + 4.27 +  + 4.22 = = 3.894 7 UCL = X + A 2 ( R ) = 5.813 + (0.577 )(3.894 ) = 8.060 LCL = X − A 2 ( R ) = 5.813 − (0.577 )(3.894 ) = 3.566 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. A2 is from Table E.11 (n = 5) Chap 17-58
  • 59. X Chart Control Chart Solution Minutes 8 6 4 2 0 1 UCL = 8.060 _ _ X = 5.813 LCL = 3.566 2 3 4 Day 5 6 7 Conclusion: Process average is in statistical control Statistics for Managers Using Microsoft Excel, 4e © 2004 Chap 17-59 Prentice-Hall, Inc.
  • 60. Control Charts in PHStat Use:  PHStat | control charts | p chart …  PHStat | control charts | R & XBar charts … Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-60
  • 61. Process Capability Process capability is the ability of a process to consistently meet specified customer-driven requirements  Specification limits are set by management in response to customers’ expectations  The upper specification limit (USL) is the largest value that can be obtained and still conform to customers’ expectations  The lower specification limit (LSL) is the smallest value that Statistics for Managers Using is still conforming  Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-61
  • 62. Estimating Process Capability  Must first have an in-control process  Estimate the percentage of product or service within specification  Assume the population of X values is approximately normally distributed with mean estimated by X and standard deviation estimated by R / d2 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-62
  • 63. Estimating Process Capability (continued)  For a characteristic with a LSL and a USL P(outcome will be within specifications)     USL − X   LSL − X = P(LSL < X < USL ) = P <Z<  R R    d  d2 2   Statistics for Managers Using  Where Z is a standardized normal random variable Microsoft Excel, 4e © 2004 Chap 17-63 Prentice-Hall, Inc.
  • 64. Estimating Process Capability (continued)  For a characteristic with only an USL P(outcome will be within specifications)     USL − X   = P( X < USL ) = P Z <  R     d2   Statistics for Managers Using  Where Z is a standardized normal random variable Microsoft Excel, 4e © 2004 Chap 17-64 Prentice-Hall, Inc.
  • 65. Estimating Process Capability (continued)  For a characteristic with only a LSL P(outcome will be within specifications)      LSL − X  = P(LSL < X) = P < Z R    d  2   Statistics for Managers Using  Where Z is a standardized normal random variable Microsoft Excel, 4e © 2004 Chap 17-65 Prentice-Hall, Inc.
  • 66. Process Capability Example You are the manager of a 500-room hotel. You have instituted a policy that 99% of all luggage deliveries must be completed within ten minutes or less. For seven days, you collect data on five deliveries per day. You know from prior analysis that the process is in control. Is the process capable? Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-66
  • 67. Process Capability: Hotel Data Day 1 2 3 4 5 6 7 Subgroup Subgroup Subgroup Size Average Range 5 5 5 5 5 5 5 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. 5.32 6.59 4.89 5.70 4.07 7.34 6.79 3.85 4.27 3.28 2.99 3.61 5.04 4.22 Chap 17-67
  • 68. Process Capability: Hotel Example Solution n=5 X = 5.813 R = 3.894 d2 = 2.326 P(outcome will be within specifications)    10 − 5.813   = P( X < 10) = P Z < 3.894     2.326   = P( Z < 2.50) = .9938 Therefore, we estimate that 99.38% of the luggage deliveries Statistics made within the ten minutes or less specification. The will be for Managers Using Microsoft Excel, 4e © of meeting the 99% goal. process is capable 2004 Chap 17-68 Prentice-Hall, Inc.
  • 69. Capability Indices  A process capability index is an aggregate measure of a process’s ability to meet specification limits  The larger the value, the more capable a process is of meeting requirements Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-69
  • 70. Cp Index  A measure of potential process performance is the Cp index USL − LSL specification spread Cp = = process spread 6(R / d2 ) Cp > 1 implies a process has the potential of having more than 99.73% of outcomes within specifications  C > 2 implies a process has the potential of p meeting the expectations set forth in six sigma Statistics for Managers Using management Microsoft Excel, 4e © 2004 Chap 17-70 Prentice-Hall, Inc. 
  • 71. CPL and CPU  To measure capability in terms of actual process performance: X − LSL CPL = 3(R / d2 ) CPU = USL − X 3(R / d2 ) CPL (CPU) > 1 implies that the process mean is more than 3 Using Statistics for Managers standard deviation away from the lower (upper) © 2004 Microsoft Excel, 4especification limit Chap 17-71 Prentice-Hall, Inc. 
  • 72. CPL and CPU (continued)  Used for one-sided specification limits  Use CPU when a characteristic only has a UCL  Use CPL when a characteristic only has an LCL Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-72
  • 73. Cpk Index   The most commonly used capability index is the Cpk index Measures actual process performance for characteristics with two-sided specification limits Cpk = min(CPL, CPU) Cpk = 1 indicates that the process average is 3 standard deviation away from the closest specification limit  Larger C indicates greater capability of meeting the pk Statistics for Managers Using > 2 indicates compliance with requirements, e.g., Cpk Microsoft Excel, 4e © 2004 six sigma management Chap 17-73 Prentice-Hall, Inc. 
  • 74. Process Capability Example You are the manager of a 500-room hotel. You have instituted a policy that all luggage deliveries must be completed within ten minutes or less. For seven days, you collect data on five deliveries per day. You know from prior analysis that the process is in control. Compute an appropriate capability index for the delivery process. Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 17-74
  • 75. Process Capability: Hotel Example Solution n=5 X = 5.813 R = 3.894 d2 = 2.326 USL − X 10 − 5.813 CPU = = = .833672 3(R / d2 ) 3(3.894 / 2.326 ) Since there is only the upper specification limit, we need to only compute CPU. The capability index for the luggage delivery process is .8337, which is less than 1. The upper specification limit is less than 3 standard deviation Using Statistics for Managers above the mean. Microsoft Excel, 4e © 2004 Chap 17-75 Prentice-Hall, Inc.
  • 76. Chapter Summary  Reviewed the philosophy of quality management   Deming’s 14 points Discussed Six Sigma® Management    Reduce defects to no more than 3.4 per million Uses DMAIC model for process improvement Discussed the theory of control charts  Common cause variation vs. special cause variation  Constructed and interpreted p charts  Constructed and interpreted X and R charts Obtained and interpreted process capability measures Statistics for Managers Using Microsoft Excel, 4e © 2004 Chap 17-76 Prentice-Hall, Inc. 

×