Basic Business Statistics(9th Edition)Chapter 18Statistical Applications in Quality and Productivity ManagementChap 18-1

Chapter TopicsTotal Quality Management (TQM)Theory of Management (Demings Fourteen Points)Six Sigma Management ApproachThe Theory of Control ChartsCommon-cause variation versus special-cause variationControl Charts for the Proportion of Nonconforming Items

Chapter TopicsProcess VariabilityThe c ChartControl Charts for the Mean and the RangeProcess Capability(continued)

Themes of Quality Management1. Primary Focus on Process Improvement2. Most Variation in Process Due to System3. Teamwork is Integral to Quality Management4. Customer Satisfaction is a Primary Goal5. Organizational Transformation Necessary6. Remove Fear7. Higher Quality Costs Less

Demings 14 Points: Point 1:PlanDoStudyActPoint 1. Create Constancy of PurposeThe Shewhart-Deming Cycle Focuses on Constant Improvement

Demings 14 Points: Points 2 and 3Point 2. Adopt New PhilosophyBetter to be proactive and change before crisis occurs.Point 3. Cease Dependence on Mass Inspection to Achieve QualityAny inspection whose purpose is to improve quality is too late.

Demings 14 Points: Points 4 and 5Point 4. End the Practice of Awarding Business on the Basis of Price Tag AloneDevelop long term relationship between purchaser and supplier.Point 5. Improve Constantly and ForeverReinforce the importance of the Shewhart-Deming cycle.

Demings 14 Points: Points 6 and 7Point 6. Institute TrainingEspecially important for managers to understand the difference between special causes and common causes.Point 7. Adopt and Institute LeadershipDifferentiate between leadership and supervision. Leadership is to improve the system and achieve greater consistency of performance.

Demings 14 Points: Points 8 to 128. Drive Out Fear9. Break Down Barriers between Staff Areas10. Eliminate Slogans11. Eliminate Numerical Quotas for Workforce and Numerical Goals for Management12. Remove Barriers to Pride of Workmanship300

Demings 14 Points: Points 13 and 14Point 13. Encourage Education and Self-Improvement for Everyone Improved knowledge of people will improve the assets of the organization.

Point 14. Take Action to Accomplish Transformation Continually strive toward improvement.Quality is important

Six Sigma ManagementA Managerial Approach Designed to Create Processes that Result in No More Than 3.4 Defects Per MillionA Method for Breaking Processes into a Series of Steps in Order to Eliminate Defects and Produce Near Perfect Results(1) Define: Define the problem along with costs, benefits and the impact on customers(2) Measure: Develop operational definitions for each Critical-to-Quality characteristic and verify measurement procedure to achieve consistency over repeated measurements

Six Sigma Management(3) Analyze: Use control charts to monitor defects and determine the root causes of defects(4) Improve: Study the importance of each process variable on the Critical-to-Quality characteristic to determine and maintain the best level for each variable in the long term(5) Control: Avoid potential problems that occur when a process is changed and maintain the gains that have been made in the long term(continued)

Control ChartsMonitor Variation in DataExhibit trend - make correction before process is out of controlA Process - A Repeatable Series of Steps Leading to a Specific Goal

Control ChartsShow When Changes in Data are Due to:Special or assignable causesFluctuations not inherent to a processRepresent problems to be correctedData outside control limits or trendChance or common causesInherent random variationsConsist of numerous small causes of random variability(continued)

Process Control Chart Graph of sample data plotted over timeSpecial Cause VariationCommon Cause VariationProcess Average MeanUCLLCL

Control LimitsUCL = Process Average + 3 Standard DeviationsLCL = Process Average - 3 Standard DeviationsProcess AverageUCLLCLX+ 3- 3 TIME

Types of ErrorFirst Type: Belief that observed value represents special cause when, in fact, it is due to common causeSecond Type: Treating special cause variation as if it is common cause variation

Comparing Control Chart PatternsXXXCommon Cause Variation: No Points Outside Control LimitsSpecial Cause Variation: 2 Points Outside Control LimitsDownward Pattern: No Points Outside Control Limits but Trend Exists

When to Take Corrective ActionCorrective Action Should Be Taken When Observing Points Outside the Control Limits or when a Trend Has Been DetectedEight consecutive points above the center line (or eight below)Eight consecutive points that are increasing (decreasing)

Out-of-Control ProcessesIf 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 variationThe assignable causes of variation must be identifiedIf detrimental to quality, assignable causes of variation must be removedIf increases quality, assignable causes must be incorporated into the process design

In-Control ProcessIf the Control Chart is Not Indicating Any Out-of-Control Condition, thenOnly common causes of variation existIt is sometimes said to be in a state of statistical controlIf the common-cause variation is small, then control chart can be used to monitor the processIf the common-cause variation is too large, the process needs to be altered

p ChartControl Chart for ProportionsIs an attribute chartShows Proportion of Nonconforming ItemsE.g., Count # of nonconforming chairs & divide by total chairs inspectedChair is either conforming or nonconformingUsed with Equal or Unequal Sample Sizes Over TimeUnequal sizes should not differ by more than 25% from average sample size

p Chart Control LimitsAverage Group SizeAverage Proportion of Nonconforming Items# Defective Items in Sample iSize of Sample i# of Samples

p Chart ExampleYoure manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control?

p Chart Hotel Data# Not Day# RoomsReadyProportion1200160.080 2200 70.035 3200210.105 4200170.085 5200250.125 6200190.095 7200160.080

p Chart Control Limits Solution16 + 7 +...+ 16

p Chart Control Chart SolutionMean UCLLCL0.000.050.100.151234567PDayIndividual 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.

p Chart in PHStatPHStat | Control Charts | p Chart

Excel Spreadsheet for the Hotel Room Example

pChart

0.080.0268203480.08642857140.1460367949

0.0350.0268203480.08642857140.1460367949

0.1050.0268203480.08642857140.1460367949

0.0850.0268203480.08642857140.1460367949

0.1250.0268203480.08642857140.1460367949

0.0950.0268203480.08642857140.1460367949

0.080.0268203480.08642857140.1460367949

p

LCL

Center

UCL

X

Proportion

p Chart

LCL

pBar

UCL

ForPChart

Number# Not ReadypLCLCenterUCL

1200160.080.0268203480.08642857140.1460367949

220070.0350.0268203480.08642857140.1460367949

3200210.1050.0268203480.08642857140.1460367949

4200170.0850.0268203480.08642857140.1460367949

5200250.1250.0268203480.08642857140.1460367949

6200190.0950.0268203480.08642857140.1460367949

7200160.080.0268203480.08642857140.1460367949

Calculations

p Chart

Sum of Subgroup Sizes1400

Number of Subgroups Taken7

Average Subgroup Size200

Average Proportion of Nonconforming Items0.0864285714

p Chart Values

Lower Control Limit0.026820348

Center0.0864285714

Upper Control Limit0.1460367949

&A

Page &P

data

Day# Room# Not ReadyProportion

1200160.08

220070.035

3200210.105

4200170.085

5200250.125

6200190.095

7200160.08

Understanding Process Variability:Red Bead ExampleWorkerDay 1 Day 2 Day 3All 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 113Four workers (A, B, C, D) spend 3 days to collect beads, at 50 beads per day. The expected number of red beads to be collected per day per worker is 10 or 20%.

Understanding Process Variability:Example CalculationsAverageDay 1Day 2Day 3All Days X10.259.58.5 9.42 p20.5%19%17% 18.83%_

Understanding Process Variability:Example Control Chart0 A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3 .30

.20

.10

pUCLLCL_

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.

The c ChartControl Chart for Number of Nonconformities (Occurrences) in a Unit (an Area of Opportunity)Is an attribute chartShows Total Number of Nonconforming Items in a UnitE.g., Count # of defective chairs manufactured per dayAssume that the Size of Each Subgroup Unit Remains Constant

c Chart Control LimitsAverage Number of Occurrences# of Samples# of Occurrences in Sample i

c Chart: ExampleYoure manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control?

c Chart: Hotel Data# Not Day# RoomsReady120016 2200 7 320021 420017 520025 620019 720016

c Chart: Control Limits Solution

c Chart: Control Chart SolutionUCLLCL01020301234567cDayIndividual 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.

Variables Control Charts: R ChartMonitors Variability in ProcessCharacteristic of interest is measured on numerical scaleIs a variables control chartShows Sample Range Over TimeDifference between smallest & largest values in inspection sampleE.g., Amount of time required for luggage to be delivered to hotel room

R Chart Control LimitsSample Range at Time i or Sample i# SamplesFrom Table

R Chart ExampleYoure 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?

R Chart and Mean Chart Hotel DataSampleSample DayAverageRange15.323.85 26.594.27 34.883.28 45.702.99 54.073.61 67.345.04 76.794.22

R Chart Control Limits SolutionFrom Table (n = 5)

R Chart Control Chart SolutionUCL024681234567MinutesDayLCLR_

Variables Control Charts: Mean Chart (The Chart)Shows Sample Means Over TimeCompute mean of inspection sample over timeE.g., Average luggage delivery time in hotelMonitors Process AverageMust be preceded by examination of the R chart to make sure that the process is in control

Mean ChartSample Range at Time i# SamplesSample Mean at Time iComputed From Table

Mean Chart ExampleYoure 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?

R Chart and Mean Chart Hotel DataSampleSample DayAverageRange15.323.85 26.594.27 34.883.28 45.702.99 54.073.61 67.345.04 76.794.22

Mean Chart Control Limits SolutionFrom Table E.9 (n = 5)

Mean Chart Control Chart SolutionUCLLCL024681234567MinutesDayX__

R Chart and Mean Chartin PHStatPHStat | Control Charts | R & Xbar Charts

Excel Spreadsheet for the Hotel Room Example

XBar Chart

5.323.56585428575.81285714298.05986

6.593.56585428575.81285714298.05986

4.883.56585428575.81285714298.05986

5.73.56585428575.81285714298.05986

4.073.56585428575.81285714298.05986

7.343.56585428575.81285714298.05986

6.793.56585428575.81285714298.05986

XBar

LCL-X

Center-X

UCL-X

XBar Chart

LCL

XBar

UCL

RChart

3.8503.89428571438.23252

4.2703.89428571438.23252

3.2803.89428571438.23252

2.9903.89428571438.23252

3.6103.89428571438.23252

5.0403.89428571438.23252

4.2203.89428571438.23252

Range

LCL-R

Center-R

UCL-R

R Chart

LCL

RBar

UCL

ForCharts

NumberXBarRangeLCL-RCenter-RUCL-RLCL-XCenter-XUCL-X

15.323.8503.89428571438.232523.56585428575.81285714298.05986

26.594.2703.89428571438.232523.56585428575.81285714298.05986

34.883.2803.89428571438.232523.56585428575.81285714298.05986

45.72.9903.89428571438.232523.56585428575.81285714298.05986

54.073.6103.89428571438.232523.56585428575.81285714298.05986

67.345.0403.89428571438.232523.56585428575.81285714298.05986

76.794.2203.89428571438.232523.56585428575.81285714298.05986

Calculations2

Control Chart

Control Chart Factors Table.

Sample/Subgroup Size5Subgroup sizeD3D4A2

RBar3.8942857143203.2671.880

R Chart302.5751.023

D3 Factor0402.2820.729

D4 Factor2.114502.1140.577

Lower Control Limit0602.0040.483

Center3.894285714370.0761.9240.419

Upper Control Limit8.2325280.1361.8640.373

90.1841.8160.337

XBar Chart100.2231.7770.308

Average of Subgroup Averages5.8128571429110.2561.7440.285

A2 Factor0.577120.2831.7170.266

Lower Control Limit3.5658542857130.3071.6930.249

Center5.8128571429140.3281.6720.235

Upper Control Limit8.05986150.3471.6530.223

160.3631.6370.212

170.3781.6220.203

180.3911.6090.194

190.4041.5960.187

200.4151.5850.180

210.4251.5750.173

220.4351.5650.167

230.4431.5570.162

240.4521.5480.157

250.4591.5410.153

26Value not available from table. Possible error in number of observations in sample.Value not available from table. Possible error in number of observations in sample.Value not available from table. Possible error in number of observations in sample.

Value not available from table. Possible error in number of observations in sample.

pChart

0.080.0268203480.08642857140.1460367949

0.0350.0268203480.08642857140.1460367949

0.1050.0268203480.08642857140.1460367949

0.0850.0268203480.08642857140.1460367949

0.1250.0268203480.08642857140.1460367949

0.0950.0268203480.08642857140.1460367949

0.080.0268203480.08642857140.1460367949

p

LCL

Center

UCL

X

Proportion

p Chart

LCL

pBar

UCL

ForPChart

Number# Not ReadypLCLCenterUCL

1200160.080.0268203480.08642857140.1460367949

220070.0350.0268203480.08642857140.1460367949

3200210.1050.0268203480.08642857140.1460367949

4200170.0850.0268203480.08642857140.1460367949

5200250.1250.0268203480.08642857140.1460367949

6200190.0950.0268203480.08642857140.1460367949

7200160.080.0268203480.08642857140.1460367949

Calculations

p Chart

Sum of Subgroup Sizes1400

Number of Subgroups Taken7

Average Subgroup Size200

Average Proportion of Nonconforming Items0.0864285714

p Chart Values

Lower Control Limit0.026820348

Center0.0864285714

Upper Control Limit0.1460367949

&A

Page &P

data

Day# DeliverySample AverageSample Range

155.323.85

256.594.27

354.883.28

455.72.99

554.073.61

657.345.04

756.794.22

Process CapabilityProcess Capability is the Ability of a Process to Consistently Meet Specified Customer-Driven RequirementsSpecification Limits are Set by Management in Response to Customers ExpectationsThe Upper Specification Limit (USL) is the Largest Value that Can Be Obtained and Still Conform to Customers ExpectationThe Lower Specification Limit (LSL) is the Smallest Value that is Still Conforming

Estimating Process CapabilityMust Have an In-Control Process FirstEstimate the Percentage of Product or Service Within SpecificationAssume the Population of X Values is Approximately Normally Distributed with Mean Estimated by and Standard Deviation Estimated by

Estimating Process CapabilityFor a Characteristic with an LSL and a USL

where Z is a standardized normal random variable(continued)

Estimating Process CapabilityFor a Characteristic with Only a LSL

where Z is a standardized normal random variable (continued)

Estimating Process CapabilityFor a Characteristic with Only a USL

where Z is a standardized normal random variable (continued)

Process Capability ExampleYoure manager of a 500-room hotel. You have instituted a policy that 99% of all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect data on 5 deliveries per day. Is the process capable?

Process Capability:Hotel DataSampleSample DayAverageRange15.323.85 26.594.27 34.883.28 45.702.99 54.073.61 67.345.04 76.794.22

Process Capability:Hotel Example SolutionTherefore, we estimate that 99.38% of the luggage deliveries will be made within the 10 minutes or less specification. The process is capable of meeting the 99% goal.

Capability IndicesAggregate Measures of a Process Ability to Meet Specification LimitsThe larger (>1) the values, the more capable a process is of meeting requirementsMeasure of Process Potential Performance

Cp>1 implies that a process has the potential of having more than 99.73% of outcomes within specifications

Capability IndicesMeasures of Actual Process PerformanceFor one-sided specification limits

CPL (CPU) >1 implies that the process mean is more than 3 standard deviations away from the lower (upper) specification limit(continued)

Capability Indices For two-sided specification limits Cpk = 1 indicates that the process average is 3 standard deviations away from the closest specification limitLarger Cpk indicates larger capability of meeting the requirements(continued)

Process Capability ExampleYoure manager of a 500-room hotel. You have instituted a policy that all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect data on 5 deliveries per day. Compute an appropriate capability index for the delivery process.

Process Capability:Hotel DataSampleSample DayAverageRange15.323.85 26.594.27 34.883.28 45.702.99 54.073.61 67.345.04 76.794.22

Process Capability:Hotel Example SolutionSince 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 deviations above the mean.

Chapter SummaryDescribed Total Quality Management (TQM)Addressed the Theory of Management Demings 14 PointsDescribed the Six Sigma Management ApproachDiscussed the Theory of Control ChartsCommon-cause variation versus special-cause variation

Chapter SummaryComputed Control Charts for the Proportion of Nonconforming ItemsDescribed Process VariabilityDescribed c ChartComputed Control Charts for the Mean and the RangeDiscussed Process Capability(continued)