6 Managing Quality PowerPoint presentation to accompany Heizer and Render Operations Management, 10e Principles of Operations Management, 8e PowerPoint slides by Jeff Heyl 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Outline Defining Quality Total Quality Management 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 ) 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Learning Objectives Define quality and TQM Explain Six Sigma Explain the use of a control chart Build 𝒙 -charts and R-charts Build p-charts Explain process capability and compute Cp and Cpk 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Two Ways Quality Improves Profitability Improved response Flexible pricing Improved reputation Sales Gains via Improved Quality Increased Profits Increased productivity Lower rework and scrap costs Lower warranty costs Reduced Costs via Figure 6.1 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Defining Quality Different Views User-based Manufacturing-based 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 User-based: better performance, more features Manufacturing-based: conformance to standards, making it right the first time Product-based: specific and measurable attributes of the product Implications of Quality Company reputation Perception of new products Employment practices Supplier relations Product liability Reduce risk Global implications Improved ability to compete 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Key Dimensions of Quality Performance Features Reliability Conformance Durability Serviceability Aesthetics Perceived quality Value 07: Ch6S - Quality and SPC (MGMT3102:Fall13) 7

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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Deming’s Fourteen Points Create consistency of purpose Lead to promote change Build quality into the product; stop depending on inspections Build long-term relationships based on performance instead of awarding business on price Continuously improve product, quality, and service Start training Emphasize leadership Table 6.2 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Deming’s Fourteen Points Drive out fear Break down barriers between departments Stop haranguing workers Support, help, and improve Remove barriers to pride in work Institute education and self-improvement Put everyone to work on the transformation Table 6.2 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Continuous Improvement Represents continual improvement of all processes Involves all operations and work centers including suppliers and customers People, Equipment, Materials, Procedures 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

6 Six Sigma Program 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) Mean Lower limits Upper limits 3.4 defects/million ±6 2,700 defects/million ±3 Figure 6.4 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Six Sigma Define critical outputs and identify gaps for improvement Measure the work and collect process data Analyze the data Improve the process Control the new process to make sure new performance is maintained DMAIC Approach 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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 - Statistical process control measures the performance of a process, it does not help to identify a particular specimen produced as being “good” or “bad,” in or out of tolerance. - Statistical process control requires the collection and analysis of data - therefore it is not helpful when total production consists of a small number of units - While statistical process control can not help identify a “good” or “bad” unit, it can enable one to decide whether or not to accept an entire production lot. If a sample of a production lot contains more than a specified number of defective items, statistical process control can give us a basis for rejecting the entire lot. The issue of rejecting a lot which was actually good can be raised here, but is probably better left to later. 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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” 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Types of Data Variables Attributes Characteristics that can take any real value May be in whole or in fractional numbers Continuous random variables Defect-related characteristics Classify products as either good or bad or count defects Categorical or discrete random variables Once the categories are outlined, students may be asked to provide examples of items for which variable or attribute inspection might be appropriate. They might also be asked to provide examples of products for which both characteristics might be important at different stages of the production process. 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Setting Chart Limits For x-Charts when we know s Upper control limit (UCL) = x + zsx Lower control limit (LCL) = x - zsx where x = mean of the sample means or a target value set for the process z = number of normal standard deviations sx = standard deviation of the sample means = s/ n s = population standard deviation n = sample size 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Setting Control Limits Hour 1 Sample Weight of Number Oat Flakes 1 17 2 13 3 16 4 18 5 17 6 16 7 15 8 17 9 16 Mean 16.1 s = 1 Hour Mean Hour Mean 1 16.1 7 15.2 2 16.8 8 16.4 3 15.5 9 16.3 4 16.5 10 14.8 5 16.5 11 14.2 6 16.4 12 17.3 n = 9 For 99.73% control limits, z = 3 UCLx = x + zsx = 16 + 3(1/3) = 17 ozs LCLx = x - zsx = 16 - 3(1/3) = 15 ozs 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Setting Control Limits Control Chart for sample of 9 boxes Variation due to assignable causes Out of control Sample number | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 17 = UCL 15 = LCL 16 = Mean Variation due to natural causes Out of control 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Setting Chart Limits For x-Charts when we don’t know s 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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Control Chart Factors Sample Size Mean Factor Upper Range Lower Range n A2 D4 D3 2 1.880 3.268 0 3 1.023 2.574 0 4 .729 2.282 0 5 .577 2.115 0 6 .483 2.004 0 7 .419 1.924 0.076 8 .373 1.864 0.136 9 .337 1.816 0.184 10 .308 1.777 0.223 12 .266 1.716 0.284 Table S6.1 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Setting Control Limits Process average x = 12 ounces Average range R = .25 Sample size n = 5 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Setting Control Limits Process average x = 12 ounces Average range R = .25 Sample size n = 5 UCL = 12.144 Mean = 12 LCL = 11.857 UCLx = x + A2R = 12 + (.577)(.25) = 12 + .144 = 12.144 ounces LCLx = x - A2R = 12 - .144 = 11.857 ounces 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Restaurant Control Limits For salmon filets at Darden Restaurants Sample Mean x Bar Chart UCL = 11.524 x – 10.959 LCL – 10.394 | | | | | | | | | 1 3 5 7 9 11 13 15 17 11.5 – 11.0 – 10.5 – Sample Range Range Chart UCL = 0.6943 R = 0.2125 LCL = 0 | | | | | | | | | 1 3 5 7 9 11 13 15 17 0.8 – 0.4 – 0.0 – 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Setting Control Limits Average range R = 5.3 pounds Sample size n = 5 From Table S6.1 D4 = 2.115, D3 = 0 UCL = 11.2 Mean = 5.3 LCL = 0 UCLR = D4R = (2.115)(5.3) = 11.2 pounds LCLR = D3R = (0)(5.3) = 0 pounds 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Mean and Range Charts (a) These sampling distributions result in the charts below (Sampling mean is shifting upward but range is consistent) x-chart (x-chart detects shift in central tendency) UCL LCL R-chart (R-chart does not detect change in mean) UCL LCL Figure S6.5 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Mean and Range Charts (b) These sampling distributions result in the charts below (Sampling mean is constant but dispersion is increasing) x-chart (x-chart does not detect the increase in dispersion) UCL LCL R-chart (R-chart detects increase in dispersion) UCL LCL Figure S6.5 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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) 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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 + zsp ^ p(1 - p) n sp = ^ LCLp = p - zsp ^ Instructors may wish to point out the calculation of the standard deviation reflects the binomial distribution of the population where p = mean fraction defective in the sample z = number of standard deviations sp = standard deviation of the sampling distribution n = sample size ^ 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

p-Chart for Data Entry p = = .04 sp = = .02 1 6 .06 11 6 .06 Sample Number Fraction Sample Number Fraction Number of Errors Defective Number of Errors Defective 1 6 .06 11 6 .06 2 5 .05 12 1 .01 3 0 .00 13 8 .08 4 1 .01 14 7 .07 5 4 .04 15 5 .05 6 2 .02 16 4 .04 7 5 .05 17 11 .11 8 3 .03 18 3 .03 9 3 .03 19 0 .00 10 2 .02 20 4 .04 Total = 80 p = = .04 80 (100)(20) (.04)(1 - .04) 100 sp = = .02 ^ 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

p-Chart for Data Entry UCLp = p + zsp = .04 + 3(.02) = .10 ^ LCLp = p - zsp = .04 - 3(.02) = 0 ^ .11 – .10 – .09 – .08 – .07 – .06 – .05 – .04 – .03 – .02 – .01 – .00 – Sample number Fraction defective | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 UCLp = 0.10 LCLp = 0.00 p = 0.04 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Possible assignable causes present p-Chart for Data Entry UCLp = p + zsp = .04 + 3(.02) = .10 ^ Possible assignable causes present LCLp = p - zsp = .04 - 3(.02) = 0 ^ .11 – .10 – .09 – .08 – .07 – .06 – .05 – .04 – .03 – .02 – .01 – .00 – Sample number Fraction defective | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 UCLp = 0.10 LCLp = 0.00 p = 0.04 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Which Control Chart to Use Variables Data Using an x-Chart and R-Chart Observations are variables 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 R-chart Track samples of n observations each. Table S6.3 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Which Control Chart to Use Attribute Data Using the p-Chart Observations are attributes that can be categorized as good or bad (or pass–fail, or functional–broken), that is, in two states. We deal with fraction, proportion, or percent defectives. There are several samples, with many observations in each. For example, 20 samples of n = 100 observations in each. Table S6.3 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Patterns in Control Charts Normal behavior. Process is “in control.” UCL Target LCL UCL Target LCL One plot out above (or below). Process is “out of control.” UCL Target LCL Trends in either direction, 5 plots. Progressive change. Ask the students to imagine a product, and consider what problem might cause each of the graph configurations illustrated. UCL Target LCL Two plots very near lower (or upper) control. UCL Target LCL Run of 5 above (or below) central line. UCL Target LCL Erratic behavior. 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Process Capability Ratio Cp = Upper Specification - Lower Specification 6s 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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process standard deviation s = .516 minutes Design specification = 210 ± 3 minutes Cp = Upper Specification - Lower Specification 6s 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process standard deviation s = .516 minutes Design specification = 210 ± 3 minutes Cp = Upper Specification - Lower Specification 6s = = 1.938 213 - 207 6(.516) 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process standard deviation s = .516 minutes Design specification = 210 ± 3 minutes Cp = Upper Specification - Lower Specification 6s = = 1.938 213 - 207 6(.516) Process is capable 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Process Capability Index Cpk = minimum of , Upper Specification - x Limit 3s Lower x - Specification Limit 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 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Process Capability Index New Cutting Machine New process mean x = .250 inches Process standard deviation s = .0005 inches Upper Specification Limit = .251 inches Lower Specification Limit = .249 inches 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Process Capability Index New Cutting Machine New process mean x = .250 inches Process standard deviation s = .0005 inches Upper Specification Limit = .251 inches Lower Specification Limit = .249 inches Cpk = minimum of , (.251) - .250 (3).0005 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Process Capability Index New Cutting Machine New process mean x = .250 inches Process standard deviation s = .0005 inches Upper Specification Limit = .251 inches Lower Specification Limit = .249 inches Cpk = minimum of , (.251) - .250 (3).0005 .250 - (.249) Both calculations result in New machine is NOT capable Cpk = = 0.67 .001 .0015 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

Interpreting Cpk Cpk = negative number Cpk = zero Cpk = between 0 and 1 Cpk = 1 Cpk > 1 Figure S6.8 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

SPC and Process Variability Lower specification limit Upper specification limit Process mean, m (a) Acceptance sampling (Some bad units accepted) (b) Statistical process control (Keep the process in control) This may be a good time to stress that an overall goal of statistical process control is to “do it better,” i.e., improve over time. (c) Cpk >1 (Design a process that is in control) Figure S6.10 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

In-Class Problems from the Lecture Guide Practice Problems 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 . Problem 1 Solution: 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

In-Class Problems from the Lecture Guide Practice Problems 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. A2 = 0.373 from Table S6.1 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

In-Class Problems from the Lecture Guide Practice Problems 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. From Table S6.1, D4 = 1.78 and D3 = 0.22 𝑈𝐶𝐿 𝑅 = 𝐷 4 𝑅 = 1.78 10 =17.8 𝑙𝑏𝑠 𝐿𝐶𝐿 𝑅 = 𝐷 3 𝑅 = 0.22 10 =2.2 𝑙𝑏𝑠 07: Ch6S - Quality and SPC (MGMT3102:Fall13)

In-Class Problems from the Lecture Guide Practice Problems 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. 07: Ch6S - Quality and SPC (MGMT3102:Fall13)