Group: Amira- Meera -Noura 1- Introduction 2- Literature a. Definition of operation management b. Definition of operation strategy and why it is important c. Components of operations strategy 3- Case study a. b. Overviews of corporate strategy of GASCO Discussion of operation strategy of GASCO b1. Overviews of OS of GASCO b2. Comparison with competitors' OS 4- Conclusion GOOD LUCK Quality and Performance Chapter 5 Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 01 What is Quality? Quality A term used by customers to describe their general satisfaction with a service or product. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 02 Costs of Quality Prevention Costs Appraisal Costs Internal Failure Costs External Failure Costs Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 03 Ethics and Quality Balancing the traditional measures of quality performance and the overall benefits to society. Identifying deceptive business practices. Developing a culture around ethics. Training employees to understand how ethics interfaces with their jobs. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 -04 Total Quality Management TQM A philosophy that stresses principles for achieving high levels of process performance and quality. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 05 Customer Satisfaction Conformance to Specifications Value Fitness for Use Support Psychological Impressions Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 06 Employee Involvement Cultural Change Teams - Employee Empowerment - Problem-solving teams - Special-purpose teams - Self-managed teams Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 07 Continuous Improvement Kaizen Problem-solving tools PDSA Cycle Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 08 What is Six Sigma? Six Sigma A comprehensive and flexible system for achieving, sustaining, and maximizing business success by minimizing defects and variability in processes. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 09 Six Sigma Approach Process average OK; too much variation Process variability OK; process off target X X X X X XX X X X X X X Process on target with low variability X X X X X Reduce spread Center process X XX X X X XX Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 10 Six Sigma Improvement Model Six Sigma Certification Master Black Belts Black Belts Green Belts Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 11 Acceptance Sampling Acceptance Sampling - The application of statistical techniques to determine if a quantity of material from a supplier should be accepted or rejected based on the inspection or test of one or more samples. Acceptable Quality Level - A statement of the proportion of defective items that the buyer will accept in a shipment. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 12 Acceptance Sampling Interface Buyer Manufactures furnaces Fan mot o Motor inspection Yes Accept motors? Firm A uses TQM or Six Sigma to achieve internal process performance rs Firm A Manufacturers furnace fan motors TARGET: Buyer's specs Fan bla des No Blade inspection Yes Accept blades? Supplier uses TQM or Six Sigma to achieve internal process performance Supplier Manufactures fan blades TARGET: Firm A's specs No Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 13 Statistical Process Control (SPC) SPC The application of statistical techniques to determine whether a process is delivering what the customer wants. Performance Measurements - Variables - Characteristics that can be measured. - Attributes - Characteristics that can be counted. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 14 Sampling Sampling Plan - Size of the sample - Time between successive samples - Decision rules that determine when action should be taken Complete Inspection - Inspect each product at each stage Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 15 Sampling Statistics Sample Mean Sample Range Sum of the observations divided by the total observations n Difference between the largest and smallest observation in a sample x i where x i 1 n xi = observation of a quality characteristic (such as time) n = total number of observations x = mean Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 16 Sampling Statistics Standard deviation- The square root of the variance of a distribution. An estimate of the process standard deviation based on a sample is given by: x i x n 1 2 or xi2 x 2 i n n 1 where = standard deviation of a sample xi = observation of a quality characteristic (such as time) n = total number of observations x = mean Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 17 Sampling Statistics 1. The sample mean is the sum of the observations divided by the total number of observations. n x i x i 1 n where xi = observation of a quality characteristic (such as time) n = total number of observations x = mean Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 18 Sampling Statistics 2. The range is the difference between the largest observation in a sample and the smallest. The standard deviation is the square root of the variance of a distribution. An estimate of the process standard deviation based on a sample is given by x x i n 1 2 or 2 i x x 2 i n n 1 where = standard deviation of a sample Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 19 Sampling Distribution Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 20 Types of Variation Common cause - Variation that is random, unidentifiable and unavoidable Assignable cause - Variation that can be identified and eliminated Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 21 Effects of Assignable Cause Variation on the Process Distribution Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 22 Control Charts Time-ordered diagram used to determine whether observed variations are abnormal - Mean - Upper control limit - Lower control limit Steps for a control chart 1. 2. 3. 4. Random sample Plot statistics Eliminate the cause, incorporate improvements Repeat the procedure Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 23 Control Limits and Sampling Distribution UCL Nominal LCL Assignable causes likely 1 2 3 Samples Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 24 Control Charts Variations UCL Nominal LCL Sample number (a) Normal - No action Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 25 Control Charts Variations UCL Nominal LCL Sample number (b) Run - Take action Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 26 Control Charts Variations UCL Nominal LCL Sample number (c) Sudden change - Monitor Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 27 Control Charts Variations UCL Nominal LCL Sample number (d) Exceeds control limits - Take action Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 28 Control Chart Errors Type I error - Concluding that a process is out of control when it is in control Type II error - Concluding that a process is in control when it is out of control Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 29 Control Chart Types Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 30 Variable Control Charts R-Chart UCLR = D4R and LCLR = D3R Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 31 Variable Control Charts UCLx = x + A2R and LCLx = x - A2R Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 32 Calculating Control Chart Factors Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 33 Steps for x- and R-Charts 1. Collect data. 2. Compute the range. 3. Use Table 5.1 to determine R-chart control limits. 4. Plot the sample ranges. If all are in control, proceed to step 5. Otherwise, find the assignable causes, correct them, and return to step 1. 5. Calculate x for each sample. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 34 Steps for x- and R-Charts 6. Use Table 5.1 to determine x-chart control limits 7. Plot the sample means. If all are in control, the process is in statistical control. Continue to take samples and monitor the process. If any are out of control, find the assignable causes, correct them, and return to step 1. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 35 Example 5.1 The management of West Allis Industries is concerned about the production of a special metal screw used by several of the company's largest customers. The diameter of the screw is critical to the customers. Data from five samples appear in the accompanying table. The sample size is 4. Is the process in statistical control? Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 36 Example 5.1 Compute the range for each sample and the control limits UCLR = D4R = 2.282(0.0021) = 0.00479 in. LCLR = D3R = 0(0.0021) = 0 in. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 37 Example 5.1 Process variability is in statistical control. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 38 Example 5.1 Compute the mean for each sample and the control limits. 0.5027 + 0.729(0.0021) = 0.5042 in. 0.5027 - 0.729(0.0021) = 0.5012 in. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 39 Example 5.1 Process average is NOT in statistical control. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 40 An Alternate Form If the standard deviation of the process distribution is known, another form of the xchart may be used: Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 41 Example 5.2 For Sunny Dale Bank the time required to serve customers at the drive-by window is an important quality factor in competing with other banks in the city. After several weeks of sampling, two successive samples came in at 3.70 and 3.68 minutes, respectively. Is the customer service process in statistical control? Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 42 Example 5.2 For Sunny Dale Bank the time required to serve customers at the drive-by window is an important quality factor in competing with other banks in the city. After several weeks of sampling, two successive samples came in at 3.70 and 3.68 minutes, respectively. Is the customer service process in statistical control? Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 43 Example 5.2 x n z = 5 minutes = 1.5 minutes = 6 customers = 1.96 The process variability is in statistical control, so we proceed directly to the x-chart. The control limits are UCLx = x + z/n = 5.0 + 1.96(1.5)/6 = 6.20 minutes LCLx = x - z/n = 5.0 - 1.96(1.5)/6 = 3.80 minutes The new process is an improvement. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 44 Application 5.1 Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped. Webster is concerned whether the filling process for tubes of caulking is in statistical control. The process should be centered on 8 ounces per tube. Several samples of eight tubes are taken and each tube is weighed in ounces. Tube Number Sample 1 2 3 4 5 6 7 8 Avg Range 1 7.98 8.34 8.02 7.94 8.44 7.68 7.81 8.11 8.040 0.76 2 8.23 8.12 7.98 8.41 8.31 8.18 7.99 8.06 8.160 0.43 3 7.89 7.77 7.91 8.04 8.00 7.89 7.93 8.09 7.940 0.32 4 8.24 8.18 7.83 8.05 7.90 8.16 7.97 8.07 8.050 0.41 5 7.87 8.13 7.92 7.99 8.10 7.81 8.14 7.88 7.980 0.33 6 8.13 8.14 8.11 8.13 8.14 8.12 8.13 8.14 8.130 0.03 Avgs 8.050 0.38 Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 45 Application 5.1 Assuming that taking only 6 samples is sufficient, is the process in statistical control? 1.864(0.38) = 0.708 0.136(0.38) = 0.052 The range chart is out of control since sample 1 falls outside the UCL and sample 6 falls outside the LCL. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 46 Application 5.1 Consider dropping sample 6 because of an inoperative scale, causing inaccurate measures. Tube Number Sample 1 2 3 4 5 6 7 8 Avg Range 1 7.98 8.34 8.02 7.94 8.44 7.68 7.81 8.11 8.040 0.76 2 8.23 8.12 7.98 8.41 8.31 8.18 7.99 8.06 8.160 0.43 3 7.89 7.77 7.91 8.04 8.00 7.89 7.93 8.09 7.940 0.32 4 8.24 8.18 7.83 8.05 7.90 8.16 7.97 8.07 8.050 0.41 5 7.87 8.13 7.92 7.99 8.10 7.81 8.14 7.88 7.980 0.33 Avgs 8.034 0.45 What is the conclusion on process variability and process average? Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 47 Application 5.1 1.864(0.45) = 0.839 0.136(0.45) = 0.061 8.034 + 0.373(0.45) = 8.202 8.034 - 0.373(0.45) = 7.866 The resulting control charts indicate that the process is actually in control. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 48 Control Charts for Attributes p-charts are used to control the proportion defective Sampling involves yes/no decisions so the underlying distribution is the binomial distribution The standard deviation is p p 1 p / n p = the center line on the chart and Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 49 Example 5.3 Hometown Bank is concerned about the number of wrong customer account numbers recorded. Each week a random sample of 2,500 deposits is taken and the number of incorrect account numbers is recorded Using three-sigma control limits, which will provide a Type I error of 0.26 percent, is the booking process out of statistical control? Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 50 Example 5.3 Sample Number Wrong Account Numbers Sample Number Wrong Account Numbers 1 15 7 24 2 12 8 7 3 19 9 10 4 2 10 17 5 19 11 15 6 4 12 3 Total Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 147 05 - 51 Example 5.3 Total defectives 147 = = 0.0049 p= Total number of observations 12(2,500) p = p(1 - p)/n = 0.0049(1 - 0.0049)/2,500 = 0.0014 UCLp = p + zp = 0.0049 + 3(0.0014) = 0.0091 LCLp = p - zp = 0.0049 - 3(0.0014) = 0.0007 Calculate the sample proportion defective and plot each sample proportion defective on the chart. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 52 Example 5.3 .0091 Fraction Defective X X .0049 X UCL X X X X Mean X .0007 X | | | 1 2 3 X X | | 4 5 | | | | | | 6 7 Sample 8 9 10 11 X | LCL 12 The process is NOT in statistical control. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 53 Application 5.2 A sticky scale brings Webster's attention to whether caulking tubes are being properly capped. If a significant proportion of the tubes aren't being sealed, Webster is placing their customers in a messy situation. Tubes are packaged in large boxes of 144. Several boxes are inspected and the following numbers of leaking tubes are found: Sample Tubes 1 3 2 Tubes Sample Tubes 8 6 15 5 5 9 4 16 0 3 3 10 9 17 2 4 4 11 2 18 6 5 2 12 6 19 2 Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 4 13 5 20 1 6 Sample 05- 54 Application 5.2 Calculate the p-chart three-sigma control limits to assess whether the capping process is in statistical control. p Total number of leaky tubes 72 0.025 Total number of tubes 20 144 p 0.025 1 0.025 p 1 p 0.01301 144 n UCL p p z p 0.025 3 0.01301 0.06403 LCL p p z p 0.025 3 0.01301 0.01403 0 The process is in control as the p values for the samples all fall within the control limits. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 55 Control Charts for Attributes c-charts count the number of defects per unit of service encounter The underlying distribution is the Poisson distribution UCLc = c + zc and LCLc = c - zc Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 56 Example 5.4 The Woodland Paper Company produces paper for the newspaper industry. As a final step in the process, the paper passes through a machine that measures various product quality characteristics. When the paper production process is in control, it averages 20 defects per roll. Set up a control chart for the number of defects per roll. For this example, use two-sigma control limits. b. Five rolls had the following number of defects: 16, 21, 17, 22, and 24, respectively. The sixth roll, using pulp from a different supplier, had 5 defects. Is the paper production process in control? a. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 57 Example 5.4 a. The average number of defects per roll is 20. Therefore = 20 + 2(20) = 28.94 LCLc = c - zc = 20 - 2(20) = 11.06 Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 58 Example 5.4 b. The process is technically out of control due to Sample 6. However, Sample 6 shows that the new supplier is a good one. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 59 Application 5.3 At Webster Chemical, lumps in the caulking compound could cause difficulties in dispensing a smooth bead from the tube. Even when the process is in control, there will still be an average of 4 lumps per tube of caulk. Testing for the presence of lumps destroys the product, so Webster takes random samples. The following are results of the study: Tube # Lumps Tube # Lumps Tube # Lumps 1 6 5 6 9 5 2 5 6 4 10 0 3 0 7 1 11 9 4 4 8 6 12 2 Determine the c-chart two-sigma upper and lower control limits for this process. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 60 Application Problem 5.3 c 6 5 0 4 6 4 1 6 5 0 9 2 4 12 c 4 2 UCL c c z c 4 2 2 8 LCL c c z c 4 2 2 0 Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 61 Process Capability Process Capability - The ability of the process to meet the design specification for a service or product - Nominal Value - Tolerance Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 62 Process Capability Nominal value Lower specification 20 Process distribution Upper specification 25 30 Minutes (a) Process is capable Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 63 Process Capability Nominal value Upper specification Lower specification 20 Process distribution 25 30 Minutes (b) Process is not capable Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 64 Process Capability Nominal value Six sigma Four sigma Two sigma Upper specification Lower specification Mean Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 65 Process Capability Index Measures how well a process is centered and whether the variability is acceptable Cpk = Minimum of x - Lower specification Upper specification - x , 3 3 where = standard deviation of the process distribution Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 66 Process Capability Ratio A test to see if the process variability is capable of producing output within a product's specifications. Upper specification - Lower specification Cp = 6 Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 67 Example 5.5 The intensive care unit lab process has an average turnaround time of 26.2 minutes and a standard deviation of 1.35 minutes. The nominal value for this service is 25 minutes + 5 minutes. Is the lab process capable of four sigma-level performance? Upper specification = 30 minutes Lower specification 20 minutes Average service 26.2 minutes = 1.35 minutes Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 68 Example 5.5 Cpk = Minimum of , Cpk = Minimum of 26.2 - 20 , 30 - 26.2 3 ( 1.53) 3( 1.53) Cpk = Minimum of 1.53, 0.94 Cpk = 0.94 Process does not meets 4-sigma level of 1.33 Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 69 Example 5.5 Cp = Upper Specification - Lower Specification 6 Cp = 30 - 20 = 1.23 6 (1.35) Process did not meet 4-sigma level of 1.33 Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 70 Example 5.5 New Data is collected: Upper specification = 30 minutes Lower specification 20 minutes Average service 26.1 minutes = 1.20 minutes Cp = Upper - Lower 6 Cp = 30 - 20 = 1.39 6 (1.20) Process meets 4-sigma level of 1.33 for variability Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 71 Example 5.5 Cpk = Minimum of x - Lower specification ,Upper specification - x 3 3 Cpk = Minimum of 26.1 - 20 , 30 - 26.1 3 ( 1.20) 3 ( 1.20) Cp = 1.08 Process does not meets 4-sigma level of 1.33 Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 72 Application 5.4 Webster Chemical's nominal weight for filling tubes of caulk is 8.00 ounces 0.60 ounces. The target process capability ratio is 1.33, signifying that management wants 4-sigma performance. The current distribution of the filling process is centered on 8.054 ounces with a standard deviation of 0.192 ounces. Compute the process capability index and process capability ratio to assess whether the filling process is capable and set properly. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 73 Application 5.4 a. Process capability index: Cpk = Minimum of = Minimum of x - Lower specification Upper specification - x , 3 3 8.600 - 8.054 8.054 - 7.400 = 1.135, = 0.948 3(0.192) 3(0.192) The value of 0.948 is far below the target of 1.33. Therefore, we can conclude that the process is not capable. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 74 Application 5.4 b. Process capability ratio: Upper specification - Lower specification 8.60 - 7.40 Cp = = = 1.0417 6 6(0.192) The value of Cp is less than the target for four-sigma quality. Therefore we conclude that the process variability must be addressed first, and then the process should be retested. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 75 Loss (dollars) Quality Loss Function Lower specification Nominal value Upper specification Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05- 76 International Quality Documentation Standards ISO 9001:2008 - Quality Standards ISO 14000:2004 - Environmental Management Standards ISO 26000:2010 - Social Responsibility Guidelines Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 77 Baldridge Performance Excellence Program Leadership Strategic Planning Customer Focus Measurement, Analysis, and Knowledge Management Workforce Focus Operations Focus Results Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 78 Solved Problem 1 The Watson Electric Company produces incandescent light bulbs. The following data on the number of lumens for 40-watt light bulbs were collected when the process was in control. Observation Sample 1 2 3 4 1 604 612 588 600 2 597 601 607 603 3 581 570 585 592 4 620 605 595 588 5 590 614 608 604 Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 79 Solved Problem 1 x= 604 + 612 + 588 + 600 4 R = 612 - 588 = 24 Sample = 601 R 1 601 24 2 602 10 3 582 22 4 602 32 5 604 24 2,991 x = 598.2 112 R = 22.4 Total Average Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 80 Solved Problem 1 The R-chart control limits are 2.282(22.4) = 51.12 0(22.4) = 0 The x-chart control limits are 598.2 + 0.729(22.4) = 614.53 598.2 - 0.729(22.4) = 581.87 b. First check to see whether the variability is still in control based on the new data. The range is 53 (or 623 - 570), which is outside the UCL for the R-chart. Since the process variability is out of control, it is meaningless to test for the process average using the current estimate for R. A search for assignable causes inducing excessive variability must be conducted. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 81 Solved Problem 2 The data processing department of the Arizona Bank has five data entry clerks. Each working day their supervisor verifies the accuracy of a random sample of 250 records. A record containing one or more errors is considered defective and must be redone. The results of the last 30 samples are shown in the table. All were checked to make sure that none was out of control. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 82 Solved Problem 2 Sample Number of Defective Records Sample Number of Defective Records 1 7 16 8 2 5 17 12 3 19 18 4 4 10 19 6 5 11 20 11 6 8 21 17 7 12 22 12 8 9 23 6 9 6 24 7 10 13 25 13 11 18 26 Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 10 05 - 83 Solved Problem 2 a. Based on these historical data, set up a p-chart using z = 3. b. Samples for the next four days showed the following: Sample Number of Defective Records Tues 17 Wed 15 Thurs 22 Fri 21 What is the supervisor's assessment of the dataentry process likely to be? Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 84 Solved Problem 2 SOLUTION a. From the table, the supervisor knows that the total number of defective records is 300 out of a total sample of 7,500 [or 30(250)]. Therefore, the central line of the chart is 300 p= = 0.04 7,500 The control limits are UCL p p z p1 p 0.04(0.96) 0.04 3 0.077 n 250 p 1 p 0.04 3 0.04(0.96) 0.003 LCL p p z 250 n Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 85 Solved Problem 2 b. Samples for the next four days showed the following: Number of Defective Records Proportion Tues 17 0.068 Wed 15 0.060 Thurs 22 0.088 Fri 21 0.084 Sample Samples for Thursday and Friday are out of control. The supervisor should look for the problem and, upon identifying it, take corrective action. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 86 Solved Problem 3 The Minnow County Highway Safety Department monitors accidents at the intersection of Routes 123 and 14. Accidents at the intersection have averaged three per month. Which type of control chart should be used? Construct a control chart with three sigma control limits. b. Last month, seven accidents occurred at the intersection. Is this sufficient evidence to justify a claim that something has changed at the intersection? a. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 87 Solved Problem 3 SOLUTION a. The safety department cannot determine the number of accidents that did not occur, so it has no way to compute a proportion defective at the intersection. Therefore, the administrators must use a c-chart for which UCLc = c + z LCLc = c - z c = 3 + 3 3 = 8.20 c = 3 - 3 3 = -2.196 There cannot be a negative number of accidents, so the LCL in this case is adjusted to zero. b. The number of accidents last month falls within the UCL and LCL of the chart. We conclude that no assignable causes are present and that the increase in accidents was due to chance. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 88 Solved Problem 4 Pioneer Chicken advertises \"lite\" chicken with 30 percent fewer calories. (The pieces are 33 percent smaller.) The process average distribution for \"lite\" chicken breasts is 420 calories, with a standard deviation of the population of 25 calories. Pioneer randomly takes samples of six chicken breasts to measure calorie content. a. Design an x-chart using the process standard deviation. b. The product design calls for the average chicken breast to contain 400 100 calories. Calculate the process capability index (target = 1.33) and the process capability ratio. Interpret the results. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 89 Solved Problem 4 SOLUTION a. For the process standard deviation of 25 calories, the standard deviation of the sample mean is x n 25 10.2 calories 6 420 + 3(10.2) = 450.6 calories 420 - 3(10.2) = 389.4 calories Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 90 Solved Problem 4 b. The process capability index is Cpk = Minimum of = Minimum of 420 - 300 = 1.60, 3(25) , 500 - 420 = 1.07 3(25) The process capability ratio is Cp = Upper specification - Lower specification 6 = 500 - 300 = 1.33 6(25) Because the process capability ratio is 1.33, the process should be able to produce the product reliably within specifications. However, the process capability index is 1.07, so the current process is not centered properly for four-sigma performance. The mean of the process distribution is too close to the upper specification. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 91 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall. 05 - 92