CH-11-12 Statistically Based Quality Improvement for Variables – Managing Quality: Integrating the Supply Chain : Book Guide

This Document Contains Chapters 11 to 12 Chapter 11: Statistically Based Quality Improvement for Variables Chapter Outline •Statistical Fundamentals •Process Control Charts •Some Control Chart Concepts for Variables •Process Capability for Variables •Other Statistical Techniques in Quality Management Overview The chapter begins on page 278 with a fascinating statement: … many people view the topic of statistics with fear, loathing, and trembling. This chapter unravels the seeming intricacies of statistical thought in a clear, process-oriented manner. The text presents a series of tools. Each tool is presented in a situation-based premise that illustrates not only the mechanics of the tool, but its use. The intent of the chapter is to present tools that are useable. Discussion Questions 1. Discuss the concept of control. Is control helpful? Isn’t being controlling a negative? Controlling is one of the managerial functions, like planning, organizing, staffing and directing. It is an important function because it helps to check for errors and take corrective action so that deviation from standards are minimized and stated goals of the organization are achieved in a desired manner. According to modern concepts, control is a foreseeing action, whereas earlier concepts of control were used only when errors were detected. Control in management means setting standards, measuring actual performance, and taking corrective action. Thus, control comprises these three main activities. Characteristics of control: •Control is a continuous process. •Control is a management process. •Control is embedded in each level of organizational hierarchy. •Control is forward looking. •Control is closely linked with planning. •Control is a tool for achieving organizational activities. •Control is an end process. 2. The concept of statistical thinking is an important theme in this chapter. What are some examples of statistical thinking? On page 279, the author defines statistical thinking as being based on three concepts: • All work occurs in a system of interconnected processes. • All processes have variation; the amount of variation tends to be underestimated. • Understanding and reducing variation are important keys to success. This concentration on the concept of variation is the focal point. Statistics allows you to use that variation as your entry into the effectiveness of the process. Examining a measurable quantity on each product, or more like a sample of products, allows you to maintain a continuing quality control. The quantity being measured can vary from the amount of breakfast cereal being loaded into a box to measuring the diameter of a sample of ball bearings to determine whether they are within specifications. 3. Sometimes you do well on exams. Sometimes you have bad days. What are the assignable causes when you do poorly? Assignable causes are those situations that can be linked directly to a quality issue. Poor performance on an exam might be linked to a variety of causes, such as lack of preparation, lack of sleep, illness, or distractions in one’s personal life. 4. What is the relationship between statistical quality improvement and Deming’s 14 points? The relationship is subtle, but present. Deming is instrumental to the philosophy of continuing improvement. He talks about improved planning and stresses an environment in which the employee feels empowered. Point 3 presents a lessened dependence on inspections to reduce variation. Statistical analysis is a powerful tool for this purpose. However, Chapter 9 makes the point that: Some critics of the technique believe that the assumption in acceptance sampling that a percentage will be defective or less than perfect (called acceptable quality level, or AQL) is counter to Deming’s concepts of continual improvement. However, there is still need for acceptance sampling in many different circumstances This apparent disagreement is, as stated previously, quite subtle. This topic should be resolved via a classroom discussion. 5. What are some applications of process charts in services? Could demerits (points off for mistakes) be charted? How? Process charts, as defined in the chapter, are tools for measuring quantifiable data. A process chart could be used to measure a quantifiable property of a service environment. This would include items that are time-based or measurable, such as response time, time spent to deliver a service, or number of complaints. A demerit could be tracked if there were a predictable and standardized manner of assigning the demerits. This technique might contradict the approach to continued improvement. This is a good discussion topic for your class. 6. What is random variation? Is it always uncontrollable? Random variation is that variation in a process that can be measured and analyzed. If it is controlled, then by definition it is not random. A point that needs be made: the word “random” has a very specific meaning in statistics. Random variables are those values that are all members of the same set of variables and have an equal probability of occurring. Figure 11-1 demonstrates this property. 7. When would you choose an np chart over a p chart? An X chart over an x ¯ chart? An s chart over an R chart? Charts are tools for portraying statistical information in an easy-to-comprehend manner. A p chart presents the proportion of defective parts whereas an np chart presents the number of non-conforming items. A p chart could be used to compare different items to observe the difference in the processes. An X chart is used to evaluate a population. An x ¯ (x-bar) chart presents the same information for a sample. The cost and ease of getting an x ¯ chart obviously make them preferable. An R chart presents the range of values; this is simply the high-value minus the low value. An s chart presents the range of standard deviations. The standard deviation presents the average variance that the sample points are from the mean or average value. An s chart shows much more detailed information whereas an R chart shows an overview of the situation. 8. Design a control chart to monitor the gas mileage in your car. Collect the data over time. What did you find? Figure 11-4 presents a simplified control chart. This will display the gas mileage over the specified period of time. This might be a factor in a term paper. 9. What does “out-of-control” mean? Is it the same as a “bad hair day?” How often do you have a “bad hair day?” How do you document or evaluate a “bad hair day?” This is a situation in which we are quantifying non-quantifiable data. “Out-of-control” specifically addresses a situation in which you have set up control limits to define the bounds of a process. “Out-of-control” indicates a data point that lies outside of these control limits. “Out-of-control” refers to a situation or process that deviates significantly from expected standards or norms, often requiring intervention to correct. It is not the same as a “bad hair day,” which typically refers to a minor, personal inconvenience related to appearance. In quality management, “out-of-control” indicates a need for corrective actions due to deviations from desired performance levels, while a “bad hair day” is a more casual, everyday problem. 10. Design a control chart to monitor the amounts of the most recently charged 50 debits from your debit card. What did you find? A debit is a highly quantifiable and measurable quantity. This data is ideal for statistical analysis. A simple x ¯ chart might look like this: This might be used for a number of observations. Trends can be analyzed by debit amounts, by days of the week, or days of the month. As in question 8, this might be a good component for a term paper. Case 11-1: Ore-Ida Fries Take the data provided and use control charts to determine whether the measurements are consistent. Report your results to management. To develop this chart, do the following: 1. Load the data to Excel. 2. Compute the average for each sample. 3. Create a line chart to display the data points plotted against the sample number. The results show a definite trend in the values. Suggested Answers to End of Chapter Problems 1. Return to the chart in Figure 11-8. Is this process stable? No. The x-bar chart shows out-of-control points for samples 3 and 8. Assignable causes of variation should be investigated. 2. Return to the data in Figure 11-8. Is this process capable? Compute both Cpk and Ppk. Hint: Use the calculation work sheet to compute the population standard deviation and for Ppk, treat each observation as a population value. No. The process is not capable. For Ppk, standard deviation is 4.92 (see partial Excel printout below), Ppu = .457 Ppl = .356 Ppk = .356 Process is not in control. 3. For the following product characteristics, choose where to inspect first: Choose the lowest ratio to inspect first. Therefore, inspect characteristic D first. 4. For the following product characteristics, chose where to inspect first: Choose the lowest ratio to inspect first. Therefore, inspect characteristic B first. 5. Interpret the charts in the text to determine if the processes are stable. a. 5 points in a row above the mean. Investigate. b. 2 pts. near the lower limit. Investigate. c. Stable. d. 7 points, all decreasing. Investigate. e. Process is erratic. Investigate. f. Process is stable. However, variation is less than expected. Investigate to see if process has changed and the control limits need recalculation. 6. Interpret the charts in the text to determine if the processes are stable. a. Stable. b. Two out of control points. First five points all above the mean. Investigate. c. Runs. Five points above and below the mean. Investigate for the cause. d. Drift. 7 points decreasing. Investigate for cause. e. Process is erratic and successive points near the upper and lower limits. f. Erratic. 7. Tolerances for a new assembly call for weights between 32 and 33 pounds. The assembly is made using a process that has a mean of 32.6 pounds with a population standard deviation of .22 pounds. The process population is normally distributed. a. Is the process capable? b. If not, what proportion will meet tolerances? .49683 + .46562 = .96245 or only 96.2% will meet specifications. c. Within what values will 99.5% of sample means of this process fall if the sample size is constant at 10 and the process is stable? 99.5% of sample means will fall between 32.4 and 32.8.
8. Specifications for a part are 62” +/- .01”. The part is constructed from a process with a mean of 62.01” and a population standard deviation of .033”. The process is normally distributed. a. Is the process capable? b. What proportion will meet specifications? About 23% will meet specifications. c. Within what values will 95% of sample means of the process fall if the sample size is constant at 5 and the process is stable? 62.01 +/- 1.65(.033/SQRT5) = 62.03 (upper limit), 61.99 (lower limit) 95% of the sample means will fall between 62.03 and 61.99. 9. Tolerances for a bicycle derailleur are 6 cm +/- .001 cm. The current process produces derailleurs with a mean of 6.0001 with a population standard deviation of .0004. The process population is normally distributed. a. Is the process capable? b. If not, what proportion will meet specifications? About 98.5% will meet specifications. c. Within what values will 75% of sample means of this process fall if the sample size is constant at 6 and the process is stable? 6.0001 +/- 1.15(.0004/SQRT6) = 6.000263 (upper limit), 5.999937 (lower limit) 75% of the sample means will fall between 6.000263 and 5.999937. 10. A services process is monitored using x-bar and R charts. Eight samples of n = 10 observations have been gathered with the following results: a. Using the data in the table, compute the centerline, the upper control limit, and the lower control limits for the x-bar and R charts. b. Is the process in control? Please interpret the charts. c. If the next sample results in the following values (2.5, 5.5, 4.6, 3.2, 4.6, 3.2, 4.0, 4.0, 3.6, 4.2), will the process be in control? (a) Grand mean = 3.9125 R-bar = .40375 A2 = 1.03 CL = 3.9125+/-1.03(4.0375) = {4.33 (upper); 3.50 (lower) (b) (c) mean = 3.94. This point is in control. The process is unstable and erratic. 11. A production process for the JMF Semicon is monitored using x-bar and R charts. 10 samples of n=15 observations have been gathered with the following results: a. Develop a control chart and plot the means. b. Is the process in control? Explain. The process is not in control. 12. Experiment: Randomly select the heights of at least 15 of the students in your class. a. Develop a control chart and plot the heights on the chart. b. Which chart should you use? c. Is this process in control? Results will vary. Experiment: Control Chart for Heights a. Develop a Control Chart 1. Data Collection: • Randomly select heights of at least 15 students. 2. Calculate Key Metrics: • Mean (X̄): Average height. • Range (R): Difference between the highest and lowest heights. • Standard Deviation (σ): Measure of dispersion. 3. Control Limits: • Upper Control Limit (UCL): Mean + (3 × Standard Deviation). • Lower Control Limit (LCL): Mean• (3 × Standard Deviation). 4. Plot Data: • Create a control chart with the X-axis representing student samples and the Y-axis representing heights. • Plot the individual heights, mean line, UCL, and LCL. b. Which Chart to Use? For this type of data, a X-bar chart (for the mean of a sample) is suitable if you are monitoring the average height over time or multiple samples. If you are monitoring individual measurements and looking at variation within a sample, an Individual/moving range chart might be used. c. Is This Process in Control? To determine if the process is in control: • Check for Points Outside Control Limits: Any data points outside the UCL or LCL indicate that the process may be out of control. • Look for Patterns: Check for trends, cycles, or runs that suggest the process is not stable. If all data points fall within the control limits and there are no non-random patterns, the process is considered in control. Otherwise, further investigation is needed to identify any sources of variation. 13. A finishing process packages assemblies into boxes. You have noticed variability in the boxes and desire to improve the process to fix the problem because some products fit too tightly into the boxes and others fit too loosely. Following are width measurements for the boxes. Sample 68.63479 = X-bar, bar 0.4 = R Using x-bar and R charts, plot and interpret the process. x-bar and R chart computations: There are two out of control points from samples 7 and 8. Investigate. 14. For the data in problem 13, if the mean specification is 68.5 +/- .25 and the estimated process standard deviation is .10, is the process capable? Compute Cpu, Cpl, and Cpk. No, the process is not capable. 15. For the data in problem 13, treat the data as if it were population data, and find the limits for an x-bar chart. Is the process in control? Compare your answer with the answers to Problem 14. Hint: Use the formula CLx = x-bar  (3/d2)R-bar (Figure 11-8) No. Looking at the chart, for all but 4 samples in the first 33 observations, the process is off centered. Several of these are in a successive pattern. There is also a significant shift starting at observation 37. Points 37 through 45 are in a five successive point pattern. Need to investigate cause factors. Our observation that the process is off center corresponding to the low Cpu of .40 from Problem 14. 16. A Rochester, NY firm produces grommets that have to fit into a slot in an assembly. Following are dimensions of grommets (in millimeters): a. Use x-bar and R charts to determine if the process is in control. The process is in control. 17. Using the data from Problem 13, compute the limits for x-bar and s charts. Is the process still in control? Point 6 Is above the upper limit. 18. Using the data from Problem 16, compute the limits for x-bar and s charts. Is the process still in control? The process is in control. We confirm the results of the prior analysis using x-bar charts. 19. Use a median chart to determine if this process is centered. See the Excel spreadsheet below. Data from the textbook has been entered. The process is not in control. The limits are: UCL = 8.43; LCL = 7.77. 20. Use an x-bar chart to determine if the data in Problem 19 are in control. Do you get the same answer? The process is reasonably centered, however, the process is out of control with observations 4, 7, and 10 outside the control limits. The control limits are shown in the above spreadsheet. 21. The following data are for a component used in the space shuttle. Since the process dispersion is closely monitored, use an x-bar and s chart to see if the process is in control. Yes, the process is in control. 22. Develop an R-chart for the data in Problem 21. Do you get the same answer? Yes, the process is in control. 23. Using the data from Problem 21, compute limits for a median chart. Is the process in control? Yes, the process is in control. 24. Design a control plan for exam scores for your quality management class. Describe how you would gather data, what type of chart is needed, how to gather data, how to interpret the data, how to identify causes, and remedial action to be taken when out-of-control situations occur. Answers will vary. Control Plan for Exam Scores 1. Data Gathering • Sample: Collect all students' exam scores after each exam. • Frequency: After each major test (midterms, finals). • Method: Store in a spreadsheet/database with student ID, date, and score. 2. Control Chart • Use an Individuals (I) Control Chart to track individual exam scores. • Include an X-bar chart for average exam scores and an R chart for score range. 3. Data Interpretation • Set Upper Control Limit (UCL) and Lower Control Limit (LCL) at ±3 standard deviations. • Scores outside these limits indicate an out-of-control situation. 4. Identifying Causes • Common Causes: Normal variations (study habits, question difficulty). • Special Causes: Unclear exam content, grading errors, external factors. 5. Remedial Actions • Investigate and correct special causes (e.g., ambiguous questions). • Provide review sessions or re-assessments. • Continuously update control limits based on performance trends. This plan ensures monitoring and addressing any issues in exam performance systematically. 25. For the sampling plan from Problem 24, how would you measure process capability? The respondent should use the Cpk to measure capability. Scoring guidelines can be used as the tolerances (e.g: USL = 100; LSL = 60). 26. For the data in Problem 16, if the process target is 50.25 with spec limits +/-5, describe statistically the problems that would occur if you used your spec limits on a control chart where n=5. Discuss type I and type II error. Mean = 50.28 USL = 55.25 LSL = 45.25 Using Excel I computed the standard deviation of the means as 4.85 and will use that Number in this analysis. Zupper = (55.25-50.28)/4.85 = 1.03 ~ p = .3485 Zlower = (45.25-50.28)/4.85 = –1.04 ~ p = .35083 About 70% of the sample means will fall within the specification limits. This means that about 29.5% of the good product will be rejected erroneously. This is a type I error. However, it should be noted that this process is highly incapable, as we would expect the control limits to be inside the tolerances. Chapter 12: Statistically Based Quality Improvement for Attributes Chapter Outline •Generic Processes for Developing Structure Charts •Understanding Attributes Charts •Choosing the Right Attributes Chart •Reliability Models Overview An attribute is a physical property; it is something that either exists or does not exist. There are five attribute types in the continuous quality improvement process. This chapter provides tools for dealing with these attributes. Table 12-1 on page 315 presents a list of the types of attributes:
Discussion Questions 1. What are key attributes for a high-quality university? The key to this question is the phrase “high-quality.” The question might be taken to mean: What are the attributes that differentiate between a university and a high-quality university. The list might include: •Quality teachers •Up-to-date technology •Degree program content •Internship placement potential •Suitable launch for advanced degrees •Job placement An analysis will define which of these attributes are needed and how they might be qualified. 2. What are some attributes that you can identify for an automobile tire? As the chapter brings out, the key attributes depend on the customer. For instance, a young person or a teenager might be looking for a specific set of attributes such as raised white letters, a low profile, or a mud tread. A family man or woman might be looking for tread design in terms of safety, stopping distance, and puncture repair. An over-the-road trucker might look for a set of attributes that relate to use in business. All of these are valid. The attributes are dependent on the intended use of the product. 3. What are some attributes for a university financial aid process? Chapter 11 addressed constructing control charts. The generic process for developing control charts is revisited here: 1. Identify critical operations in the process where inspection might be needed. 2. Identify critical product characteristics. 3. Determine whether the critical product characteristic is a variable or an attribute. 4. Select the appropriate process chart. 5. Establish the control limits and use the chart to continually monitor and improve. 6. Update the limits when changes have been made to the process. These rules could be adapted to this question quite easily. The resulting list might include such items as ease of access, friendly consultants, and ease of understanding. 4. What are some personal attributes that you could monitor using control charts? Which control chart would you use? One begins by asking: “What do you want to accomplish by monitoring personal attributes?” Make a list to help identify the personal attributes to be monitored. Once this is done, a methodology for tracking and charting the use of these attributes can be constructed. As a class exercise, the professor can divide the class into teams and ask each team to construct a list. The professor then compares the lists. For instance, a student could monitor how often he or she makes reinforcing comments to other people. It could be set up as a daily count using a C chart or as a reinforcing comment per person contacted using a P chart. 5. What are examples of structural attributes? On page 315, structural attributes are defined: Structural attributes have to do with physical characteristics of a particular product or service. For example, an automobile might have electric windows. Services have structural attributes as well, such as a balcony in a hotel room. If one were to revisit Question 2, the answer would be a list of structural attributes. For a computer, we might have a list containing the monitor, keyboard, and mouse. (Structural attributes can be touched.) 6. What are some examples of sensory attributes? On page 315, sensory attributes are defined: Sensory attributes relate to senses of touch, smell, taste, and sound. For products, these attributes relate to form design or packaging design to create products that are pleasing to customers. In services such as restaurants and hotels, atmosphere is very important to the customer experience. A new car smell immediately comes to mind. There is something ethereal about the smell, glow, and feel of a new car. If you go to a supermarket, check where the breakfast foods are located. Traditionally, the breakfast foods that appeal to children are on the lowest shelf so that a child will be “assaulted” by the colors and pictures on the packages, all of which are sensory attributes. One of the old proverbs in the advertising industry is “sell the sizzle, not the steak.” People react to sensory attributes psychologically. This is a very powerful motivator. 7. What are some examples of performance attributes? On page 316, we find the definition for performance attributes: Performance attributes relate to whether or not a particular product or service performs as it is supposed to. For example, does the lawn mower engine start? Does the stereo system meet a certain threshold for low distortion? Performance attributes are heavily based upon requirements. For instance, what is the required mean time to failure (MTTF) as opposed to the MTTF specified in the requirements? We are measuring an instance that can relate directly to customer satisfaction. One example of a performance attribute is a car’s fuel efficiency. When a car is purchased, a certain range of fuel efficiency is expected – if the car is rated as 25-mpg city and 40-mpg highway, those numbers should be approximately valid when driving the new car. If in fact the mileage is 30% to 50% lower, the purchaser could be dissatisfied in the car’s performance. 8. What are some examples of temporal attributes? Page 316 defines temporal attributes: Temporal attributes relate to time. Were delivery schedules met? This often has to do with the reliability of delivery. Example: You and your spouse go down to the local big-box store and buy a new dishwasher. Excitedly, your spouse stays home from work to allow delivery and installation on the planned day. When the delivery does not happen on time and there has been no communication, the excitement of the new appliance quickly fades. This will directly affect where you go shopping for the new stove that you also want. The more directly an attribute affects you, the more important it is. 9. What are some examples of ethical attributes? Ethical attributes are discussed on page 316: Ethical attributes are important to firms. Do they report properly? Is their accounting transparent? Is the service provider empathetic? Is the teacher kind or not? Some years ago, a prominent car salesman in Denver was indicted and convicted for rolling back odometers on used cars. At the time, he had a large business with several car lots. His “empire” has since disappeared. After the recent Enron scandals, major accounting firms have also ceased to exist. People are watching businesses and expecting ethical performances from them. An organization that has questionable ethics will find that its prospective customers will be curious about its other attributes. Fortunes have been lost over questionable ethics. 10. What ethical attributes might you use to determine where you should go to work after graduation? Where do you work? What do you do? A person will field these questions regularly. For many of us, what we do is who we are. This is a personal question that relates directly to an individual’s self-image. A job candidate might list his or her personal ethical attributes and note the potential company’s ethical attributes. Do they correspond? Are there any major differences? When considering where to work after graduation, key ethical attributes to evaluate include: 1. Company Values and Mission: Align with organizations whose mission and core values reflect your own ethical beliefs, such as integrity, respect, and social responsibility. 2. Corporate Social Responsibility (CSR): Assess the company’s commitment to social and environmental responsibility, including sustainability practices and community engagement. 3. Diversity and Inclusion: Look for workplaces that promote diversity, equity, and inclusion, ensuring fair treatment and equal opportunities for all employees. 4. Transparency and Accountability: Evaluate how transparent the company is about its operations, decision-making processes, and financial practices, ensuring accountability for its actions. 5. Workplace Ethics: Consider the company’s policies on ethical conduct, such as anti-corruption measures, fair labor practices, and employee treatment. 6. Leadership Integrity: Assess the ethical leadership in the company, ensuring leaders model ethical behavior and promote an ethical work culture. Choosing a company that aligns with these attributes ensures you work in an environment that prioritizes ethical behavior and positive societal impact. Case 12-1: Decision Sciences Institute National Conference Take the raw data provided and develop research questions. Next, using the statistical tools from this chapter, analyze the data. Finally, put the data into a form that will be useful for decision makers. A lot of data is presented. Some ideas come immediately. Comparisons of these items are easily extracted from an excel spreadsheet. Specifically, one can compute the percentage of submitted against the percentage of each of the various levels. The data is all attribute data. A variety of hypothesis can be constructed. For instance, a simplistic example might be: Ho: Most of the time the reviewers agree H1: Most of the time the reviewers do not agree Two sets of data are presented. The individual reviewers can be compared to each other. The results of the decisions can be plotted in a variety of ways. For instance, given a subset of the table, we might have the following results: A simple line chart can be constructed. Perhaps a pie chart or two might also be constructed. All of the charts and graphs that are shown in the chapter can be presented. Again, the question is asked: What is the purpose of the analysis? Suggested Answers to End of Chapter Problems 1. Suppose you want to inspect a lot of 10,000 products to see whether or not they meet requirements. Design a sampling plan used to test these products. Answers will vary, but students should start with the six steps in the generic process for developing attributes charts (see text page 316): identifying critical operations, identifying product characteristics, determining whether those characteristics are variables or attributes, selecting the appropriate process chart, establishing the control limits, and updating those limits when changes have been made to the process. The step of selecting the right chart is further developed in Figure 12-8’s flow chart. Sampling Plan for Inspecting 10,000 Products 1. Lot Size: 10,000 products. 2. Sample Size: Use the AQL (Acceptable Quality Level) method. For example, if AQL is 1%, select n = 200 products as the sample. 3. Sampling Method: Random sampling. Select 200 products at random from the lot to ensure an unbiased selection. 4. Acceptance Criteria: Set a maximum number of defects allowed in the sample. For instance, if the AQL is 1%, allow a maximum of 2 defects. 5. Decision Rule: • Accept the Lot: If the number of defective products in the sample is ≤ 2. • Reject the Lot: If more than 2 defective products are found. This plan ensures a balance between inspection effort and product quality assurance. 2. Suppose a product is made of 100 components, each with a 97% reliability. What is the overall reliability for the product? R = .97100 = .0476 3. Suppose a product is made of 1,000 components, each with .999 reliability. What is the unreliability of this product? Is this acceptable? Why or why not? Q = 1 – R = 1 – .9991,000 = 1 – .3677 = .6323. This means that the product has a 63% chance of failing within the reliability period. This might be acceptable if the product is not critical in use, such as a light bulb. 4. A product consists of 45 components. Each component has an average reliability of .97. What is the overall reliability for this product? R = .9745 = .2539 5. A radio is made up of 125 components. What would have to be the average reliability for each component for the radio to have a reliability of 98% over its useful life? R = P125 = .98 P = .981/125 = .9999 6. List five products with low reliability. List five that have high reliability. What are the elemental design differences between these products? In other words, what are the factors that make some products reliable and others unreliable? Following are some examples of products with low reliability and high reliability. Low reliability: •Light bulbs •Chandeliers High reliability: •Cell phones •Pens Low reliability products tend to be made of fragile materials and have many components. In contrast, high reliability products tend to be mass-produced in highly automated processes with rigorous testing protocols. 7. An assembly consists of 240 components. Your customer has stated that your overall reliability must be at least 99%. What needs to be the average reliability factor for each component? R = P240 = .99 P = .991/240 = .99996 8. A product is made up of six components. They are wired in series with reliabilities of .95, .98, .94, .96, .98, and .97. What is the overall reliability for this product? .95 x .98 x .94 x .96 x .98 x .97 = .7986 9. Suppose that redundant components are introduced for the two components in Problem 8 with the lowest reliability. What is now the overall reliability for the product? (1 – .052) x .98 x (1 – .062) x .96 x .98 x .97 = .8989 10. Suppose that redundant components are introduced for all of the components in Problem 8. What is now the overall reliability for the product? (1 – .052) x (1 – .022) x (1 – .062) x (1 – .042) x (1 – .022) x (1 – .032) = .9906 11. A product is made up of components A, B, C, and D. These components are wired in series. Their reliability factors are .98, .999, .97, and .989 respectively. Compute the overall reliability for this product. .939 = .98 x .999 x .97 x .989 12. A product is made up of components A, B, C, D, E, F, G, H, I, and J. Components A, B, C, and F have a 1/10,000 chance of failure during useful life. D, E, G, and H have a 3/10,000 chance of failure. Component I and J and a 5/10,000 chance of failure. What is the overall reliability of the product? .99994 x .99974 x .99952 = .9974 13. For the product in Problem 12, if parallel components are provided for components I and J, what is the overall reliability for the product? 99994 x .99974 x (1.-00052)2 = .9984 14. A product is made up of 20 components in a series. Ten of the components have a 1/10,000 chance of failure. Five have a 3/10,000 chance for failure. Four have a 4/10,000 chance for failure. One component has a 1/100 chance for failure. What is the overall reliability of the product? .999910 x .99975 x .99964 x .99 = .9859 15. For the product in Problem 14, if parallel components are used for any component with worse than a 1/1,000 chance for failure, what is the overall reliability? How many components will the new design have? What will be the average component reliability for the redesigned product? .999910 x .99975 x .99964 x (1-.012) = .9958 16. An inspector visually inspects 200 sheets of paper for aesthetics. Using trained judgment, the inspector will either accept or reject sheets based on whether they are flawless. Following are the results of recent inspections: a. Given these results, using a p chart, determine if the process is stable. CL = .064 LCL = .0118 UCL = .1152 The process is out of control at sample 5. b. What would need to be done to improve the process? Investigate causes in Sample 5 and eliminate. Also investigate how the product was produced differently in Sample 6 (with significantly lower defects) and incorporate it into the process. 17. Using the data in Problem 16, compute the limits for an np chart. Control Limits = 200(.064)  3[SQRT 200(.064)(.936)] = 2.41 and 23.19. 18. Suppose a company makes the following product with the following (see text) number of defects. Construct a p chart to see if the process is in control. n = 100 CL = .417, LCL = .2689, UCL = .5647 The process is not in control. 19. Using the data from Example 12.3, evaluate the Demis using a u chart and evaluate the Streakless using a c chart. Assume that the Demis are twice the size as the Streakless on average. Demis: CL = 6, LCL = .804, UCL = 11.196 Streakless: CL = 5.833, LCL = –1.412 (use zero), UCL = 13.079 The Demis are out of control, the Streakless are not. 20. Politicians closely monitor their popularity based on approval ratings. For the previous 16 weeks, Governor Johnny’s approval ratings have been (in percentages): a. Prepare a report for the governor outlining the results of your analysis. Use control charts to analyze the data (n = 200). b. What action would you propose to the governor based on your analysis. Note p chart was constructed with disapproval (“defect”) rating: CL = .4056 LCL = .301, UCL = .510 Although not out of control, the governor’s disapproval rating rose during weeks 8 through 12. He should investigate and address any issues or activities in the news media during that period that might have contributed to this rising disapproval. If the p chart is constructed on the approval rating percentages, Governor Johnny’s approval would be decreasing during weeks 8 through 12. 21. Construct and interpret a c chart using the following (see text) data: CL = 5.433, LCL = –1.56 (use zero), UCL = 12.426 The process is in control, but Sample 20 with no defects should be investigated for improved methods and Sample 21 should be investigated for poor of sloppy methods. 22. Construct and interpret a u chart using the following (see text) data. Note that the average size is two times the original product. CL = .4963, LCL = .237, UCL = 9.689 The process is in control, but the last samples indicate a decrease in the defects. Investigate and incorporate into the process. 23. Dellana Company tested 50 products for 75 hours each. In this time, they experienced 4 breakdowns. Compute the number of failures per hour. What is the mean time between failures? Failure/hour = 4/(50 X 75) = .0011 MTBF = 1/.0011 = 909.09 24. The Collier Company tested 200 products for 100 hours each. In this time, they experienced 12 breakdowns. Compute the number of failures per hour. What is the mean time between failures? Failure/hour = 12/(200 x 100) = .0006 MTBF = 1/ .0006 = 1666.7 hours 25. Crager company tested 100 products for 50 hours each. During the test, 3 breakdowns occurred. Compute the number of failures per hour and MTBF. Failure/hour = 3/(50 x 100) = .0006 MTBF = 1/ .0006 = 1666.7 hours 26. Suppose a product is designed to function for 10,000 hours with a 3% chance of failure. Find the average number of failures per hour and the MTTF. .97 = e-(10,000) ln .97 = -10,000  = -(ln .97)/10,000  = .0000030 = average failures/hr. MTTF = 1/ = 33,333.33 hrs. 27. Suppose a product is designed to function for 100,000 hours with a 1% chance of failure. Suppose that there are six of these in use at a facility. Find the average number of failures per hour and the MTTF. First, determine overall reliability: .996 = .9415, then use R to determine MTTF. .9415 = e-(100,000) ln .9415 = -100,000  = -(ln .9415)/100,000  = .0000006 = average failures/hr. MTTF = 1/ = 1,666,666.67 hrs. 28. Suppose that there are 42 pumps used in a refinery. These pumps are continuously being used with a 2% chance of failure over 50,000 hours. If repair time is 10 hours to install a new rebuilt pump, how many pumps should be kept on hand to keep the chance of a plant shutdown to less than 1%. (Hint: Treat this problem as a traditional safety stock problem and use a z table.) .98 = e-(50000) ln .98 = -50,000  = (-ln .98)/50,000  = .000000404 = average failures/hr. MTTF = 1/ = 2,474,915 hours for one unit to fail. (1-.000000404)42 = .999989 reliability for 42 units, which exceeds the 99% reliability. No safety stock is needed at this time. However, a good preventive maintenance program would be helpful. 29. Suppose that a product is designed to work for 1000 hours with a 2% chance of failure. Find the average number of failures per hour and the MTTF. .98 = e-(1000) ln .98 = -1000  = -(ln .98)/1000  = .0000202027 = average failures/hr. MTTF = 1/ = 49,998.3 hrs. 30.A product has been used for 5000 hours with 1 failure. Find the mean time between failures (MTBF) and λ. MTBF = 5000/1 = 5000 hours between failures λ = 1/5000 = .0002 failures/hour 31. You are to decide between 3 potential suppliers for an assembly for a product you are designing. After performing life testing on several assemblies, you find the following. See Calculated SA column above. Choose supplier A. 32. You are to choose a supplier of a copier based on reliability and service. After gathering data about the alternatives, here is what you found. What do you recommend? Recommend Supplier 2. Solution Manual for Managing Quality: Integrating the Supply Chain Thomas S. Foster 9780133798258