Transcript Chapter 6S
6 Managing Quality PowerPoint presentation to accompany Heizer and Render Operations Management, 10e Principles of Operations Management, 8e PowerPoint slides by Jeff Heyl 1 Outline Defining Quality Implications of Quality Ethics and Quality Management Total Quality Management Continuous Improvement Six Sigma Employee Empowerment TQM in Services Statistical Process Control (SPC) Control Charts for Variables Control Charts for Attributes Process Capability Process Capability Ratio (Cp) Process Capability Index (Cpk ) 2 Learning Objectives 1. Define quality and TQM 2. Explain Six Sigma 3. Explain the use of a control chart 4. Build 𝒙-charts and R-charts 5. Build p-charts 6. Explain process capability and compute Cp and Cpk 3 Two Ways Quality Improves Profitability Sales Gains via Improved response Flexible pricing Improved Quality Improved reputation Reduced Costs via Increased Profits Increased productivity Lower rework and scrap costs Lower warranty costs Figure 6.1 4 Defining Quality The totality of features and characteristics of a product or service that bears on its ability to satisfy stated or implied needs American Society for Quality Different Views User-based Manufacturing-based Product-based 5 Key Dimensions of Quality Performance Durability Features Serviceability Reliability Aesthetics Conformance Perceived quality Value 6 Ethics and Quality Management Operations managers must deliver healthy, safe, quality products and services Poor quality risks injuries, lawsuits, recalls, and regulation Organizations are judged by how they respond to problems All stakeholders much be considered 7 Deming’s Fourteen Points 1. Create consistency of purpose 2. Lead to promote change 3. Build quality into the product; stop depending on inspections 4. Build long-term relationships based on performance instead of awarding business on price 5. Continuously improve product, quality, and service 6. Start training 7. Emphasize leadership Table 6.2 8 Deming’s Fourteen Points 6. Drive out fear 7. Break down barriers between departments 8. Stop haranguing workers 9. Support, help, and improve 12. Remove barriers to pride in work 13. Institute education and self-improvement 14. Put everyone to work on the transformation Table 6.2 9 Continuous Improvement Represents continual improvement of all processes Involves all operations and work centers including suppliers and customers People, Equipment, Materials, Procedures 10 Six Sigma Program 6 A highly structured program developed by Motorola A discipline – DMAIC Also, Statistical definition of a process that is 99.9997% capable, 3.4 defects per million opportunities (DPMO) Lower limits Upper limits 2,700 defects/million 3.4 defects/million Mean ±3 ±6 Figure 6.4 11 Six Sigma 1. Define critical outputs and identify gaps for improvement DMAIC Approach 2. Measure the work and collect process data 3. Analyze the data 4. Improve the process 5. Control the new process to make sure new performance is maintained 12 Employee Empowerment Getting employees involved in product and process improvements 85% of quality problems are due to process and material Techniques Build communication networks that include employees Develop open, supportive supervisors Move responsibility to employees Build a high-morale organization Create formal team structures 13 TQM In Services Service quality is more difficult to measure than the quality of goods Service quality perceptions depend on Intangible differences between products Intangible expectations customers have of those products 14 Statistical Process Control (SPC) Variability is inherent in every process Natural or common causes Special or assignable causes Provides a statistical signal when assignable causes are present Detect and eliminate assignable causes of variation 15 Natural Variations Also called common causes Affect virtually all production processes Expected amount of variation Output measures follow a probability distribution For any distribution there is a measure of central tendency and dispersion If the distribution of outputs falls within acceptable limits, the process is said to be “in control” 16 Assignable Variations Also called special causes of variation Generally this is some change in the process Variations that can be traced to a specific reason The objective is to discover when assignable causes are present Eliminate the bad causes Incorporate the good causes 17 Types of Data Variables Characteristics that can take any real value May be in whole or in fractional numbers Continuous random variables Attributes Defect-related characteristics Classify products as either good or bad or count defects Categorical or discrete random variables 18 Control Charts for Variables For variables that have continuous dimensions Weight, speed, length, strength, etc. x-charts are to control the central tendency of the process R-charts are to control the dispersion of the process These two charts must be used together 19 Setting Chart Limits For x-Charts when we know Upper control limit (UCL) = x + zx Lower control limit (LCL) = x - zx where x = mean of the sample means or a target value set for the process z = number of normal standard deviations x = standard deviation of the sample means = / n = population standard deviation n = sample size 20 Setting Control Limits Hour 1 Sample Weight of Number Oat Flakes 1 17 2 13 3 16 4 18 n=9 5 17 6 16 7 15 8 17 9 16 Mean 16.1 = 1 Hour 1 2 3 4 5 6 Mean 16.1 16.8 15.5 16.5 16.5 16.4 Hour 7 8 9 10 11 12 Mean 15.2 16.4 16.3 14.8 14.2 17.3 For 99.73% control limits, z = 3 UCLx = x + zx = 16 + 3(1/3) = 17 ozs LCLx = x - zx = 16 - 3(1/3) = 15 ozs 21 Setting Control Limits Control Chart for sample of 9 boxes Variation due to assignable causes Out of control 17 = UCL Variation due to natural causes 16 = Mean 15 = LCL | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 Sample number Out of control Variation due to assignable causes 22 Setting Chart Limits For x-Charts when we don’t know Upper control limit (UCL) = x + A2R Lower control limit (LCL) = x - A2R where R = average range of the samples A2 = control chart factor found in Table S6.1 x = mean of the sample means 23 Control Chart Factors Sample Size n Mean Factor A2 Upper Range D4 Lower Range D3 2 3 4 5 6 7 8 9 10 12 1.880 1.023 .729 .577 .483 .419 .373 .337 .308 .266 3.268 2.574 2.282 2.115 2.004 1.924 1.864 1.816 1.777 1.716 0 0 0 0 0 0.076 0.136 0.184 0.223 0.284 Table S6.1 24 Setting Control Limits Process average x = 12 ounces Average range R = .25 Sample size n = 5 25 Setting Control Limits Process average x = 12 ounces Average range R = .25 Sample size n = 5 UCLx = x + A2R = 12 + (.577)(.25) = 12 + .144 = 12.144 ounces From Table S6.1 26 Setting Control Limits Process average x = 12 ounces Average range R = .25 Sample size n = 5 UCLx LCLx = x + A2R = 12 + (.577)(.25) = 12 + .144 = 12.144 ounces UCL = 12.144 = x - A2R = 12 - .144 = 11.857 ounces LCL = 11.857 Mean = 12 27 Restaurant Control Limits Sample Mean For salmon filets at Darden Restaurants x Bar Chart 11.5 – UCL = 11.524 11.0 – x – 10.959 10.5 – | | | | | | | | | 1 3 5 7 9 11 13 15 17 LCL – 10.394 Sample Range Range Chart 0.8 – UCL = 0.6943 0.4 – R = 0.2125 0.0 – | 1 | | | | | | | | 3 5 7 9 11 13 15 17 LCL = 0 28 R – Chart Type of variables control chart Shows sample ranges over time Difference between smallest and largest values in sample Monitors process variability Independent from process mean 29 Setting Chart Limits For R-Charts Upper control limit (UCLR) = D4R Lower control limit (LCLR) = D3R where R = average range of the samples D3 and D4 = control chart factors from Table S6.1 30 Setting Control Limits Average range R = 5.3 pounds Sample size n = 5 From Table S6.1 D4 = 2.115, D3 = 0 UCLR = D4R = (2.115)(5.3) = 11.2 pounds UCL = 11.2 LCLR LCL = 0 = D3R = (0)(5.3) = 0 pounds Mean = 5.3 31 Mean and Range Charts (a) (Sampling mean is shifting upward but range is consistent) These sampling distributions result in the charts below UCL (x-chart detects shift in central tendency) x-chart LCL UCL (R-chart does not detect change in mean) R-chart LCL Figure S6.5 32 Mean and Range Charts (b) These sampling distributions result in the charts below (Sampling mean is constant but dispersion is increasing) UCL (x-chart does not detect the increase in dispersion) x-chart LCL UCL (R-chart detects increase in dispersion) R-chart LCL Figure S6.5 33 Control Charts for Attributes For variables that are categorical Good/bad, yes/no, acceptable/unacceptable Measurement is typically counting defectives Charts may measure Percent defective (p-chart) Number of defects (c-chart) 34 Control Limits for p-Charts Population will be a binomial distribution, but applying the Central Limit Theorem allows us to assume a normal distribution for the sample statistics UCLp = p + zp^ p = ^ LCLp = p - zp^ where p z p^ n = = = = p(1 - p) n mean fraction defective in the sample number of standard deviations standard deviation of the sampling distribution sample size 35 p-Chart for Data Entry Sample Number 1 2 3 4 5 6 7 8 9 10 Number of Errors Fraction Defective 6 5 0 1 4 2 5 3 3 2 .06 .05 .00 .01 .04 .02 .05 .03 .03 .02 80 p = (100)(20) = .04 Sample Number Number of Errors 11 6 12 1 13 8 14 7 15 5 16 4 17 11 18 3 19 0 20 4 Total = 80 p^ = Fraction Defective .06 .01 .08 .07 .05 .04 .11 .03 .00 .04 (.04)(1 - .04) = .02 100 36 p-Chart for Data Entry UCLp = p + zp^ = .04 + 3(.02) = .10 Fraction defective LCLp = p - zp^ = .04 - 3(.02) = 0 .11 .10 .09 .08 .07 .06 .05 .04 .03 .02 .01 .00 – – – – – – – – – – – – UCLp = 0.10 p = 0.04 | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 LCLp = 0.00 Sample number 37 p-Chart for Data Entry UCLp = p + zp^ = .04 + 3(.02) = .10 Fraction defective Possible LCLp = p - zp^ = .04 - 3(.02) = 0 assignable causes present .11 .10 .09 .08 .07 .06 .05 .04 .03 .02 .01 .00 – – – – – – – – – – – – UCLp = 0.10 p = 0.04 | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 LCLp = 0.00 Sample number 38 Which Control Chart to Use Variables Data Using an x-Chart and R-Chart 1. Observations are variables 2. Collect 20 - 25 samples of n = 4, or n = 5, or more, each from a stable process and compute the mean for the x-chart and range for the Rchart 3. Track samples of n observations each. Table S6.3 39 Which Control Chart to Use Attribute Data Using the p-Chart 1. Observations are attributes that can be categorized as good or bad (or pass–fail, or functional–broken), that is, in two states. 2. We deal with fraction, proportion, or percent defectives. 3. There are several samples, with many observations in each. For example, 20 samples of n = 100 observations in each. Table S6.3 40 Patterns in Control Charts UCL Target LCL Normal behavior. Process is “in control.” UCL UCL Target LCL One plot out above (or below). Process is “out of control.” UCL UCL Target LCL Trends in either direction, 5 plots. Progressive change. UCL Target Target Target LCL LCL LCL Two plots very near lower (or upper) control. Run of 5 above (or below) central line. Erratic behavior. 41 Process Capability The natural variation of a process should be small enough to produce products that meet the standards required A process in statistical control does not necessarily meet the design specifications Process capability is a measure of the relationship between the natural variation of the process and the design specifications 42 Process Capability Ratio Upper Specification - Lower Specification Cp = 6 A capable process must have a Cp of at least 1.0 Does not look at how well the process is centered in the specification range Often a target value of Cp = 1.33 is used to allow for off-center processes Six Sigma quality requires a Cp = 2.0 43 Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process standard deviation = .516 minutes Design specification = 210 ± 3 minutes Upper Specification - Lower Specification Cp = 6 44 Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process standard deviation = .516 minutes Design specification = 210 ± 3 minutes Upper Specification - Lower Specification Cp = 6 213 - 207 = = 1.938 6(.516) 45 Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process standard deviation = .516 minutes Design specification = 210 ± 3 minutes Upper Specification - Lower Specification Cp = 6 213 - 207 = = 1.938 6(.516) Process is capable 46 Process Capability Index Upper Lower Cpk = minimum of Specification - x , x - Specification Limit Limit 3 3 A capable process must have a Cpk of at least 1.0 A capable process is not necessarily in the center of the specification, but it falls within the specification limit at both extremes 47 Process Capability Index New Cutting Machine New process mean x = .250 inches Process standard deviation = .0005 inches Upper Specification Limit = .251 inches Lower Specification Limit = .249 inches 48 Process Capability Index New Cutting Machine New process mean x = .250 inches Process standard deviation = .0005 inches Upper Specification Limit = .251 inches Lower Specification Limit = .249 inches (.251) - .250 Cpk = minimum of , (3).0005 49 Process Capability Index New Cutting Machine New process mean x = .250 inches Process standard deviation = .0005 inches Upper Specification Limit = .251 inches Lower Specification Limit = .249 inches (.251) - .250 .250 - (.249) Cpk = minimum of , (3).0005 (3).0005 Both calculations result in .001 Cpk = = 0.67 .0015 New machine is NOT capable 50 Interpreting Cpk Cpk = negative number Cpk = zero Cpk = between 0 and 1 Cpk = 1 Cpk > 1 Figure S6.8 51 SPC and Process Variability Lower specification limit Upper specification limit (a) Acceptance sampling (Some bad units accepted) (b) Statistical process control (Keep the process in control) (c) Cpk >1 (Design a process that is in control) Process mean, m Figure S6.10 52 In-Class Problems from the Lecture Guide Practice Problems Problem 1: Twenty-five engine mounts are sampled each day and found to have an average width of 2 inches, with a standard deviation of 0.1 inches. What are the control limits that include 99.73% of the sample means 𝑋 . 53 In-Class Problems from the Lecture Guide Practice Problems Problem 2: Several samples of size have been taken from today’s production of fence posts. The average post was 3 yards in length and the average sample range was 0.015 yard. Find the 99.73% upper and lower control limits. 54 In-Class Problems from the Lecture Guide Practice Problems Problem 3: The average range of a process is 10 lbs. The sample size is 10. Use Table S6.1 to develop upper and lower control limits on the range. 55 In-Class Problems from the Lecture Guide Practice Problems Problem 4: Based on samples of 20 IRS auditors, each handling 100 files, we find that the total number of mistakes in handling files is 220. Find the 95.45% upper and lower control limits. 56