Statistics for Managers Using Microsoft Excel 3rd Edition Chapter 15 Statistical Applications in Quality and Productivity Management © 2002 Prentice-Hall, Inc.

Chapter Topics Total quality management (TQM) Theory of process management (Deming’s fourteen points) The theory of control charts Common cause variation vs. Special cause variation Control charts for the proportion of nonconforming items © 2002 Prentice-Hall, Inc.

Chapter Topics Process variability The c chart (continued) Process variability The c chart Control charts for the mean and the range Process capability © 2002 Prentice-Hall, Inc.

Themes of Quality Management Primary focus is on process improvement Most variations in process are due to systems Teamwork is integral to quality management Customer satisfaction is a primary goal Organization transformation is necessary It is important to remove fear Higher quality costs less © 2002 Prentice-Hall, Inc.

Deming’s 14 Points: Point 1 Point 1. Create Constancy of Purpose Plan Act Do Study The Shewhart-Deming Cycle Focuses on Constant Improvement © 2002 Prentice-Hall, Inc.

Deming’s 14 Points: Points 2 and 3 Point 2. Adopt a New Philosophy Better to be proactive and change before crisis occurs. Point 3. Cease Dependence on mass inspection achieve quality. Any inspection the purpose of which is to improve quality is too late. © 2002 Prentice-Hall, Inc.

Deming’s 14 Points: Points 4 and 5 Point 4. End the practice of awarding business on the basis of price tag alone Develop a long-term relationship between purchaser and supplier. Point 5. Improve constantly and forever Reinforce the importance of the Shewhart-Deming cycle. © 2002 Prentice-Hall, Inc.

Deming’s 14 Points: Points 6 and 7 Point 6. Institute Training Especially important for managers to understand the difference between special causes and common causes. Point 7. Adopt and Institute Leadership Differentiate between leadership and supervision. Leadership is to improve the system and achieve greater consistency of performance. © 2002 Prentice-Hall, Inc.

Deming’s 14 Points: Points 8 to 12 8. Drive out fear 9. Break down barriers between staff areas 10. Eliminate slogans 11. Eliminate numerical quotas for workforce and numerical goals for management 12. Remove barriers to pride of workmanship © 2002 Prentice-Hall, Inc.

Deming’s 14 Points: Points 13 and 14 Point 13. Encourage education and self improvement for everyone. Improved knowledge of people will improve assets of organization. Point 14. Take action to accomplish transformation. Continually strive toward improvement. © 2002 Prentice-Hall, Inc.

Control Charts Monitors variation in data Exhibits trend -- make correction before process is out of control A process -- A repeatable series of steps leading to a specific goal © 2002 Prentice-Hall, Inc.

Control Charts Show when changes in data are due to: (continued) Show 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 variability © 2002 Prentice-Hall, Inc.

Process Control Chart Graph of sample data plotted over time Special Cause Variation Process Average  UCL Mean LCL Common Cause Variation © 2002 Prentice-Hall, Inc.

Control Limits UCL = Process Average + 3 Standard Deviations LCL = Process Average - 3 Standard Deviations X UCL + 3 Process Average - 3 LCL TIME © 2002 Prentice-Hall, Inc.

Types of Error First Type: Second Type: Belief that observed value represents special cause when in fact it is due to common cause Second Type: Treating special cause variation as if it is common cause variation © 2002 Prentice-Hall, Inc.

Comparing Control Chart Patterns X X X Common Cause Variation: No Points Outside Control Limits Special Cause Variation: 2 Points Outside Control Limits Downward Pattern: No Points Outside Control Limits but Trend Exists © 2002 Prentice-Hall, Inc.

When to Take Corrective Action Take corrective action when you observe points outside the control limits or when a trend has been detected Eight consecutive points above the center line (or eight below) Eight consecutive points that are increasing (decreasing) © 2002 Prentice-Hall, Inc.

Out-of-control Processes When the control chart indicates an out-of-control condition (a point outside the control limits or exhibiting trend) 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 © 2002 Prentice-Hall, Inc.

In-control Process When the control chart does not indicate any out-of-control condition Contains only common causes of variation Sometimes said to be in a state of statistical control 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 © 2002 Prentice-Hall, Inc.

p Chart Control chart for proportions Is an attribute chart Shows proportion of nonconforming (success) items e.g.: Count the number defective chairs and divide by total chairs inspected Chair is either defective or not defective Used with equal or unequal sample sizes over time Unequal sizes should not differ by more than ±25% from average sample size © 2002 Prentice-Hall, Inc.

p Chart Control Limits Average Proportion of Nonconforming Items Average Group Size # Defective Items in Sample i # of Samples Size of Sample i © 2002 Prentice-Hall, Inc.

p Chart Example You’re 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? © 2002 Prentice-Hall, Inc.

p Chart Hotel Data # Not Day # Rooms Ready Proportion 1 200 16 0.080 2 200 7 0.035 3 200 21 0.105 4 200 17 0.085 5 200 25 0.125 6 200 19 0.095 7 200 16 0.080 © 2002 Prentice-Hall, Inc.

p Chart Control Limits Solution 16 + 7 +...+ 16 © 2002 Prentice-Hall, Inc.

p Chart Control Chart Solution 0.15 UCL 0.10 Mean 0.05 LCL 0.00 1 2 3 4 5 6 7 Day Individual points are distributed around without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management. © 2002 Prentice-Hall, Inc.

p Chart in PHStat PHStat | control charts | p chart … Excel spreadsheet for the hotel room example © 2002 Prentice-Hall, Inc.

Understanding Process Variability: Red Bead Example Four Workers (A, B, C, D) spent three days to collect beads, at 50 beads per day. The expected number of red bead to be collected per day per worker is 10 or 20%. Worker Day 1 Day 2 Day 3 All Days A 9 (18%) 11 (12%) 6 (12%) 26 (17.33%) B 12 (24%) 12 (24%) 8 (16%) 32 (21.33%) C 13 (26%) 6 (12%) 12 (24%) 31(20.67%) D 7 (14%) 9 (18%) 8 (16%) 24 (16.0%) Totals 41 38 34 113 © 2002 Prentice-Hall, Inc.

Understanding Process Variability: Example Calculations Average Day 1 Day 2 Day 3 All Days X 10.25 9.5 8.5 9.42 p 20.5% 19% 17% 18.83% _ © 2002 Prentice-Hall, Inc.

Understanding Process Variability: Example Control Chart UCL .30 .20 .10 _ p LCL 0 A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3 © 2002 Prentice-Hall, Inc.

Morals of the Example 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. © 2002 Prentice-Hall, Inc.

The c Chart Control chart for number of nonconformities (occurrences) in a unit (an area of opportunity) Is an attribute chart Shows total number of nonconforming items in a unit e.g.: Count number of defective chairs manufactured per day Assume that the size of each subgroup unit remains constant © 2002 Prentice-Hall, Inc.

c Chart Control Limits Average Number of Occurrences # of occurrences in sample i # of Samples © 2002 Prentice-Hall, Inc.

c Chart: Example You’re 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? © 2002 Prentice-Hall, Inc.

c Chart: Hotel Data # Not Day # Rooms Ready 1 200 16 2 200 7 3 200 21 4 200 17 5 200 25 6 200 19 7 200 16 © 2002 Prentice-Hall, Inc.

c Chart: Control Limits Solution © 2002 Prentice-Hall, Inc.

c Chart: Control Chart Solution 30 UCL 20 10 LCL 1 2 3 4 5 6 7 Day Individual points are distributed around without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management. © 2002 Prentice-Hall, Inc.

Variable Control Charts: R Chart Monitors variability in process Characteristic of interest is measured on numerical scale Is a variables control chart Shows sample range over time Difference between smallest and largest values in inspection sample e.g.: Amount of time required for luggage to be delivered to hotel room © 2002 Prentice-Hall, Inc.

R Chart Control Limits From Table Sample Range at Time i or subgroup i # Samples © 2002 Prentice-Hall, Inc.

R Chart Example You’re 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 process in control? © 2002 Prentice-Hall, Inc.

R Chart and Mean Chart Hotel Data Sample Sample Day Average Range 1 5.32 3.85 2 6.59 4.27 3 4.88 3.28 4 5.70 2.99 5 4.07 3.61 6 7.34 5.04 7 6.79 4.22 © 2002 Prentice-Hall, Inc.

R Chart Control Limits Solution From Table E.11 (n = 5) © 2002 Prentice-Hall, Inc.

R Chart Control Chart Solution Minutes UCL 8 6 _ 4 R 2 LCL 1 2 3 4 5 6 7 Day © 2002 Prentice-Hall, Inc.

Variables Control Charts: Mean Chart (The Chart) Shows sample mean over time Compute mean of inspection sample over time e.g.: Average luggage delivery time in hotel Monitors process average Must be preceded by examination of the R chart to make sure that the process is in-control © 2002 Prentice-Hall, Inc.

Mean Chart Computed From Table Sample Mean at Time i Sample Range at Time i # Samples © 2002 Prentice-Hall, Inc.

Mean Chart Example You’re 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 in control? © 2002 Prentice-Hall, Inc.

R Chart and Mean Chart Hotel Data Sample Sample Day Average Range 1 5.32 3.85 2 6.59 4.27 3 4.88 3.28 4 5.70 2.99 5 4.07 3.61 6 7.34 5.04 7 6.79 4.22 © 2002 Prentice-Hall, Inc.

Mean Chart Control Limits Solution From Table E.9 (n = 5) © 2002 Prentice-Hall, Inc.

Mean Chart Control Chart Solution Minutes UCL 8 _ _ 6 X 4 2 LCL 1 2 3 4 5 6 7 Day © 2002 Prentice-Hall, Inc.

R Chart and Mean Chart in PHStat PHStat | control charts | R & Xbar charts … Excel spreadsheet for the hotel room example © 2002 Prentice-Hall, Inc.

Process Capability Process capability is the ability of a process to consistently meet specified customer-driven requirement 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 is still conforming © 2002 Prentice-Hall, Inc.

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 and standard deviation estimated by © 2002 Prentice-Hall, Inc.

Estimating Process Capability (continued) For a characteristic with an LSL and a USL Where Z is a standardized normal random variable © 2002 Prentice-Hall, Inc.

Estimating Process Capability (continued) For a characteristic with only a LSL Where Z is a standardized normal random variable © 2002 Prentice-Hall, Inc.

Estimating Process Capability (continued) For a characteristic with only a USL Where Z is a standardized normal random variable © 2002 Prentice-Hall, Inc.

Process Capability Example You’re 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. Is the process capable? © 2002 Prentice-Hall, Inc.

Process Capability: Hotel Data Sample Sample Day Average Range 1 5.32 3.85 2 6.59 4.27 3 4.88 3.28 4 5.70 2.99 5 4.07 3.61 6 7.34 5.04 7 6.79 4.22 © 2002 Prentice-Hall, Inc.

Process Capability: Hotel Example Solution Therefore, we estimate that 99.38% of the luggage deliveries will be made within the ten minutes or less specification. The process is capable of meeting the 99% goal. © 2002 Prentice-Hall, Inc.

Capability Indices Aggregate measures of a process’s ability to meet specification limits. The larger (>1) the values, the more capable a process is of meeting requirements Measure of process potential performance Cp>1 implies a process has the potential of having more than 99.73% of outcomes within specifications © 2002 Prentice-Hall, Inc.

Capability Indices Measures of actual process performance (continued) Measures of actual process performance For one-sided specification limits CPL (CPU) >1 implies that the process mean is more than 3 standard deviation away from the lower (upper) specification limit © 2002 Prentice-Hall, Inc.

Capability Indices For two-sided specification limits (continued) For two-sided specification limits Cpk = 1 indicates that the process average is 3 standard deviation away from the closest specification limit. Larger Cpk indicates larger capability of meeting the requirements © 2002 Prentice-Hall, Inc.

Process Capability Example You’re 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. Compute an appropriate capability index for the delivery process. © 2002 Prentice-Hall, Inc.

Process Capability: Hotel Data Sample Sample Day Average Range 1 5.32 3.85 2 6.59 4.27 3 4.88 3.28 4 5.70 2.99 5 4.07 3.61 6 7.34 5.04 7 6.79 4.22 © 2002 Prentice-Hall, Inc.

Process Capability: Hotel Example Solution 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 above the mean. © 2002 Prentice-Hall, Inc.

Chapter Summary Described total quality management (TQM) Addressed the theory of process management Deming’s fourteen points Discussed the theory of control charts Common cause variation vs. special cause variation © 2002 Prentice-Hall, Inc.

Chapter Summary (continued) Computed control charts for the proportion of nonconforming items Described process variability Described c chart Computed control charts for the mean and the range Discussed process capability © 2002 Prentice-Hall, Inc.