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Managing Controlling and Improving Quality 1st edition Douglas C. Montgomery, Cheryl L. Jennings, Michele E. Pfund - Solutions

The weights of nominal 1-kg containers of a concentrated chemical ingredient are shown in Table 5E.14. Prepare a normal probability plot of the data and estimate process capability.
Consider the package weight data in Exercise 5.45. Suppose there is a lower specification at 0.985 kg. Calculate an appropriate process capability ratio for this material. What percentage of the packages produced by this process is estimated to be below the specification limit?In exercise
The height of the disk used in a computer disk drive assembly is a critical quality characteristic. Table 5E.15 gives the heights (in mm) of 25 disks randomly selected from the manufacturing process. Prepare a normal probability plot of the disk height data and estimate process capability.
The length of time required to reimburse employee expense claims is a characteristic that can be used to describe the performance of the process. Table 5E.16 gives the cycle times (in days) of 30 randomly selected employee expense claims. Estimate the capability of this process.
An electric utility tracks the response time to customer reported outages. The data in Table 5E.17are a random sample of 40 of the response times (in minutes) for one operating division of this utility during a single month.a. Estimate the capability of the utility€™s process for responding to
If a process is in a state of statistical control, does it necessarily follow that all or nearly all of the units of product produced will be within the specification limits? Discuss.
The failure time in hours of 10 memory devices follows: 1210, 1275, 1400, 1695, 1900, 2105, 2230, 2250, 2500, and 2625. Plot the data on normal probability paper and, if appropriate, estimate the process capability. Is it safe to estimate the proportion of circuits that fail below 1200 h?
Discuss the logic underlying the use of three-sigma limits on Shewhart control charts. How will the chart respond if narrower limits are chosen? How will it respond if wider limits are chosen? Discuss.
Discuss the rational subgroup concept. What part does it play in control chart analysis?
When taking samples of subgroups from a process, do you want assignable causes occurring within the subgroups or between them? Fully explain your answer.
A molding process uses a five-cavity mold for a part used in an automotive assembly. The wall thickness of the part is the critical quality characteristic. It has been suggested to use and R charts to monitor this process, and to use as the subgroup or sample all five parts that result from a
The data in Table 6E.1 give the number of nonconforming bearing and seal assemblies in samples of size 100. Construct a fraction nonconforming control chart for these data. If any points plot out of control, assume that assignable causes can be found and determine the revised control limits.
Why is the np chart not appropriate with variable sample sizes?
A process that produces bearing housings is controlled with a fraction nonconforming control chart, using sample size and a center line.a. Find the three-sigma limits for this chart. b. Analyze the ten new samples shown in Table 6E.8 for statistical control. What
Consider the fraction nonconforming control chart in Exercise 6.4. Find the equivalent np chart.In exercise
Consider the fraction nonconforming control chart in Exercise 6.5. Find the equivalent npchart. $Consider the fraction nonconforming control chart in Exercise 6.5. Find$
Surface defects have been counted on 25 rectangular steel plates, and the data are shown in Table 6E.9. Set up a control chart for nonconformities using these data. Does the process producing the plates appear to be in statistical control?
A paper mill uses a control chart to monitor the imperfection in finished rolls of paper. Production output is inspected for 20 days, and the resulting data are shown in Table 6E.10. Use these data to set up a control chart for nonconformities per roll of paper. Does the process appear to be in
Consider the papermaking process in Exercise 6.15. Set up a u chart based on an average sample size to control this process.In exercise
The number of nonconformities found on final inspection of a tape deck is shown in Table 6E.11. Can you conclude that the process is in statistical control? What center line and control limits would you recommend for controlling future production?
The data in Table 6E.12 represent the number of nonconformities per 1,000 meters of telephone cable. From an analysis of these data, would you conclude that the process is in statistical control? What control limits would you recommend for future production?
Consider the data in Exercise 6.17. Suppose we wish to define a new inspection unit of four tape decks.In exercisea. What are the center line and control limits for a control chart for monitoring future production based on the total number of defects in the new inspection unit?b. What are the
The number of nonconforming switches in samples of size 150 is shown in Table 6E.2. Construct a fraction nonconforming control chart for these data. Does the process appear to be in control? If not, assume that assignable cause can be found for all points outside the control limits, and calculate
Consider the data in Exercise 6.18. Suppose a new inspection unit is defined as 2,500 meters of wire.In exercisea. What are the center line and control limits for a control chart for monitoring future production based on the total number of nonconformities in the new inspection unit?b. What are the
An automobile manufacturer wishes to control the number of nonconformities in a subassembly area producing manual transmissions. The inspection unit is defined as four transmissions, and data from 16 samples (each of size 4) are shown in Table 6E.13.a. Set up a control chart for nonconformities per
The number of workmanship nonconformities observed in the final inspection of disk-drive assemblies has been tabulated as shown in Table 6E.14. Does the process appear to be in control?
The manufacturer wishes to set up a control chart at the final inspection station for a gas water heater. Defects in workmanship and visual quality features are checked in this inspection. For the past 22 working days, 176 water heaters were inspected and a total of 924 nonconformities reported. a.
Assembled portable television sets are subjected to a final inspection for surface defects. A total procedure is established based on the requirement that the average number of nonconformities per unit be 4.0 units. What is the appropriate type of control chart?
A control chart for nonconformities is to be established in conjunction with the final inspection of a radio. The inspection unit is to be a group of ten radios. The average number of nonconformities per radio has, in the past, been 0.5. Find three-sigma control limits for a c chart based on this
A production line assembles electric clocks. The average number of nonconformities per clock is estimated to be 0.75. The quality engineer wishes to establish a c chart for this operation using an inspection unit of six clocks. Find the three-sigma limits for this chart.
Kittlitz (1999) presents data on homicides in Waco, Texas, for the years 1980-1989 (data taken from the Waco Tribune-Herald, December 29, 1989). There were 29 homicides in 1989. Table 6E.15 gives the dates of the 1989 homicides and the number of days between each homicide. The asterisks refer to
Suggest at least two nonmanufacturing scenarios in which attributes control charts could be useful for process monitoring.
The data in Table 6E.3 represent the results of inspecting all units of a personal computer produced for the past 10 days. Does the process appear to be in control?
A paper by R. N. Rodriguez (“Health Care Applications of Statistical Process Control: Examples Using the SAS® System,” SAS Users Group International: Proceedings of the 21st Annual Conference,1996) illustrated several informative applications of control charts to the health care environment.
A paper by R. N. Rodriguez (“Health Care Applications of Statistical Process Control: Examples Using the SAS® System,”, SAS Users Group International: Proceedings of the 21st Annual Conference, 1996) illustrated several informative applications of control charts to the health care environment.
The data in Table 6E.18 are the number of information errors found in customer records in a marketing company database. Five records were sampled each day. Set up a c chart for the total number of errors. Is the process in control?
Kaminski et al. (1992) present data on the number of orders per truck at a distribution center. Some of this data is shown in Table 6E.19. Set up a c chart for the number of orders per truck. Is the process in control?
A process that produces titanium forgings for automobile turbocharger wheels is to be controlled through the use of a fraction nonconforming chart. Initially, one sample of size 150 is taken each day for 20 days, and the results shown in Table 6E.4 are observed.a. Establish a control chart to
A process produces rubber belts in lots of size 2,500. Inspection records on the last 20 lots reveal the data in Table 6E.5.a. Compute trial control limits for a fraction nonconforming control chart.b. If you wanted to set up a control chart for controlling future production, how would you use
Based on the data in Table 6E.6 if an np chart is to be established, what would you recommend as the center line and control limits? Assume that n = 500.
A company purchases a small metal bracket in containers of 5,000 each. Ten containers have arrived at the unloading facility, and 250 brackets are selected at random from each container. The fraction nonconforming in each sample are 0, 0, 0, 0.004, 0.008, 0.02, 0.004, 0, 0, and 0.008. Do the data
A control chart for the fraction nonconforming is to be established using a center line of . What sample size is required if we wish to detect a shift in the process fraction nonconforming to 0.20 with probability 0.50?
A maintenance group improves the effectiveness of its repair work by monitoring the number of maintenance requests that require a second call to complete the repair. Twenty weeks of data are shown in Table 6E.7.a. Find trial control limits for this process.b. Design a control chart for controlling
Draw the type-B OC curve for the single sampling plan n = 50, c = 1.
Suppose that a single-sampling plan with and is being used for receiving inspection where the supplier ships the product in lots of size .a. Draw the OC curve for this plan.b. Draw the AOQ curve and find the AOQL.c. Draw the ATI curve for this plan.
Suppose that a supplier ships components in lots of size 5,000. A single-sampling plan with and is being used for receiving inspection. Rejected lots are screened, and all defective items are reworked and returned to the lot. a. Draw the OC curve for this plan.b. Find the
Draw the primary and supplementary OC curves for a double-sampling plan with . If the incoming lots have fraction nonconforming , what is the probability of acceptance on the first sample? What is the probability of final acceptance? Calculate the probability of rejection on the first sample.
a. Derive an item-by-item sequential-sampling plan for which p1 = 0.01, α = 0.05, p2 = 0.10 and β = 0.10.b. Draw the OC curve for this plan.
a. Derive an item-by-item sequential-sampling plan for which p1 = 0.02, α = 0.05, p2 = 0.15 and β = 0.10. b. Draw the OC curve for this plan.
Consider rectifying inspection for single sampling. Develop an AOQ equation assuming that all defective items are removed but not replaced with good ones.
A supplier ships a component in lots of size . The AQL has been established for this product at 1%. Find the normal, tightened, and reduced single-sampling plans for this situation from MIL STD 105E, assuming that general inspection level II is appropriate.
Repeat Exercise 7.16, using general inspection level I. Discuss the differences in the various sampling plans.In exercise 7.16A supplier ships a component in lots of size N = 3000. The AQL has been established for this product at 1%. Find the normal, tightened, and reduced single-sampling
A product is supplied in lots of size . The AQL has been specified at 0.10%. Find the normal, tightened, and reduced single-sampling plans from MIL STD 105E, assuming general inspection level II.
MIL STD 105E is being used to inspect incoming lots of size . Single-sampling, general inspection level II, and an of 0.65% are being used. a. Find the normal, tightened, and reduced inspection plans.a. Draw the OC curves of the normal, tightened, and reduced inspection plans
Draw the type-B OC curve for the single-sampling plan n = 100, c = 2.
A product is shipped in lots of size . Find a Dodge-Romig single-sampling plan for which the LTPD = 1%, assuming that the process average is 0.25% defective. Draw the OC curve and the ATI curve for this plan. What is the AOQL for this sampling plan?
We wish to find a single-sampling plan for a situation where lots are shipped from a supplier. The supplier’s process operates at a fallout level of 0.50% defective. We want the from the inspection activity to be 3%.a. Find the appropriate Dodge–Romig plan.b. Draw the curve and the
A supplier ships a product in lots of size . We wish to have an AOQL of 3%, and we are going to use single-sampling. We do not know the supplier’s process fallout but suspect that it is at most 1% defective.a. Find the appropriate Dodge-Romig plan.b. Find the ATI for this plan, assuming that
An inspector wants to use a variables sampling plan with an AQL of 1.5%. Lots are of size 7,000 and the standard deviation is unknown. Find a sampling plan using Procedure 1 from MIL STD 414.
How does the sample size found in Exercise 7.23 compare with what would have been used under?In exercise An inspector wants to use a variables sampling plan with an AQL of 1.5%. Lots are of size 7,000 and the standard deviation is unknown. Find a sampling plan using Procedure 1 from MIL STD
A lot of 500 items is submitted for inspection. Suppose that we wish to find a plan from MIL STD 414, using inspection level II. If the AQL is 4%, find the Procedure 1 sampling plan from the standard.
A soft-drink bottler purchases nonreturnable glass bottles from a supplier. The lower specification on the bursting strength of the bottles is 225 psi. The bottler wishes to use variables sampling to sentence the lots and has decided to use an of 1%. Find an appropriate set of normal and
A chemical ingredient is packed in metal containers. A large shipment of these containers has been delivered to a manufacturing facility. The mean bulk density of this ingredient should not be less than 0.15g/cm3. Suppose that lots of this quality are to have a 0.95 probability of acceptance. If
A standard of 0.3 ppm has been established for formaldehyde emission levels in wood products. Suppose that the standard deviation of emissions in an individual board is. Any lot that contains 1% of its items above 0.3 ppm is considered acceptable. Any lot that has 8% or more of its items above
Consider a single-sampling plan with Draw the OC curve for this plan. Now consider chain-sampling plans with Sketch the OC curves for these chain-sampling plans on the same axis. Discuss the behavior of chain sampling in this situation compared to the conventional single-sampling plan with .
Suppose that a product is shipped in lots of size . The receiving inspection procedure used is single-sampling with and . a. Draw the type-A OC curve for the plan.b. Draw the type-B OC curve for this plan and compare it to the type-A OC curve found in part (a).c. Which
An electronics manufacturer buys memory devices in lots of 30,000 from a supplier. The supplier has a long record of good quality performance, with an average fraction defective of approximately 0.10%. The quality engineering department has suggested using a conventional acceptance-sampling plan
Suppose that a manufacturing process operates in continuous production, such that continuous sampling plans could be applied. Determine three different CSP-1 sampling plans that could be used for an AOQL of 0.198%.
For the sampling plans developed in Exercise 7.31, compare the plans’ performance in terms of average fraction inspected, given that the process is in control at an average fallout level of 0.15%. Compare the plans in terms of their operating-characteristic curves.In exercise Suppose that a
Suppose that CSP-1 is used for a manufacturing process where it is desired to maintain an AOQL of 1.90%. Specify two CSP-1 plans that would meet this AOQL target.
Compare the plans developed in Exercise 7.33 in terms of average fraction inspected and their operating-characteristic curves. Which plan would you prefer if?Exercise 7.33Suppose that CSP-1 is used for a manufacturing process where it is desired to maintain an AOQL of 1.90%. Specify two CSP-1 plans
A company uses the following acceptance-sampling procedure. A sample equal to 10% of the lot is taken. If 2% or less of the items in the sample are defective, the lot is accepted; otherwise, it is rejected. If submitted lots vary in size from 5,000 to 10,000 units, what can you say about the
A company uses a sample size equal to the square root of the lot size. If 1% or less of the items in the sample are defective, the lot is accepted; otherwise, it is rejected. Submitted lots vary in size from 1,000 to 5,000 units. Comment on the effectiveness of this procedure.
Consider the single-sampling plan found in Exercise 7.4. Suppose that lots of are submitted. Draw the curve for this plan. Draw the curve and find the.In exercise 7.4Find a single sample-sampling plan for which and .
An article in Industrial Quality Control (1956, pp. 5€“8) describes an experiment to investigate the effect of glass type and phosphor type on the brightness of a television tube. The response measured is the current necessary (in microamps) to obtain a specified brightness level. The data are
R. D. Snee (“Experimenting with a Large Number of Variables,” in Experiments in Industry: Design, Analysis and Interpretation of Results, by R. D. Snee, L. B. Hare, and J. B. Trout, editors, ASQC, 1985) describes an experiment in which a 25-1 design with was used to investigate the
a. Verify that the design generators used were I=ACE and I = BDE.b. Write down the complete defining relation and the aliases from this design.c. Estimate the main effects.
A 24 factorial design has been run in a pilot plant to investigate the effect of four factors on the molecular weight of a polymer. The data from this experiment are as follows (values are coded by dividing by 10).a. Construct a normal probability plot of the effects. Which effects are active?b.
Reconsider the data in Exercise 8.12. Suppose that four center points were added to this experiment. The molecular weights at the center point are 90, 87, 86, and 93.In exercisea. Analyze the data as you did in Exercise 8.12, but include a test for curvature.b. If curvature is significant in an
An engineer has performed an experiment to study the effect of four factors on the surface roughness of a machined part. The factors (and their levels) are A = tool angle (12, 15), B = cutting fluid viscosity (300, 400), C = feed rate (10, 15 in/min), and D = cutting fluid cooler used (no, yes).
An experiment was run to study the effect of two factors, time and temperature, on the inorganic impurity levels in paper pulp. The results of this experiment are shown in Table 8E.5:a. What type of experimental design has been used in this study?b. Fit a quadratic model to the response, using
An article in Rubber Chemistry and Technology (Vol. 47, 1974, pp. 825–836) describes an experiment that studies the relationship of the Mooney viscosity of rubber to several variables, including silica filler (parts per hundred) and oil filler (parts per hundred). Some of the data from this
In their book Empirical Model Building and Response Surfaces (John Wiley, 1987), G. E. P. Box and N. R. Draper describe an experiment with three factors. The data shown in Table 8E.7 are a variation of the original experiment on p. 247 of their book. Suppose that these data were collected in a
The data shown in the Table 8E.8 were collected in an experiment to optimize crystal growth as a function of three variables . Large values of y (yield in grams) are desirable. Fit a second-order model and analyze the fitted surface. Under what set up conditions is maximum growth achieved?
Reconsider the crystal growth experiment from Exercise 8.18. Suppose that is now a noise variable, and that the modified experimental design shown in Table 8E.9 has been conducted. The experimenters want the growth rate to be as large as possible, but they also want the variability transmitted
A process engineer is trying to improve the life of a cutting tool. He has run a 23 experiment using cutting speed (A), metal hardness (B), and cutting angle (C) as the factors. The data from two replicates are shown in Table 8E.2.a. Do any of the three factors affect tool life?b. What combination
Find the residuals from the tool life experiment in Exercise 8.2. Construct a normal probability plot of the residuals. Plot the residuals versus the predicted values. Comment on the plots.
Four factors are thought to possibly influence the taste of a soft-drink beverage: type of sweetener (A), ratio of syrup to water (B), carbonation level (C), and temperature (D). Each factor can be run at two levels, producing a 24 design. At each run in the design, samples of the beverage are
Consider the experiment in Exercise 8.4. Plot the residuals against the levels of factors A, B, C, and D. Also construct a normal probability plot of the residuals. Comment on these plots.In exercise
Find the standard error of the effects for the experiment in Exercise 8.4. Using the standard errors as a guide, what factors appear significant?In exercise
Suppose that only the data from replicate I in Exercise 8.4 were available. Analyze the data and draw appropriate conclusions.
Suppose that only one replicate of the 24 design in exercise 8.4 could be run, and that we could only conduct eight tests each day. Set up a design that would block out the day effect. Show specifically which runs would be made on each day.
Show how a 25 experiment could be set up in two blocks of 16 runs each. Specifically, which runs would be made in each block?
An electronic component in a dental x-ray system has an exponential time to failure distribution with. What are the mean and variance of the time to failure? What is the reliability at 30,000 hours?
A component has a Weibull time-to-failure distribution. The value of the scale parameter is Calculate the reliability at 250 hours for the following values of the shape parameter: . For the fixed value of the scale parameter, what impact does changing the shape parameter have on the reliability?
A component has a Weibull time-to-failure distribution. The value of the scale parameter is . Suppose that the shape parameter is . Find the mean and variance of the time to failure. What is the reliability at 600 hours?
Continuation of Exercise 9.11. If a Weibull distribution has a shape parameter of , it can be reasonably well approximated by a normal distribution with the same mean and variance. For the situation of Exercise 9.11, calculate the reliability at 600 hours using the normal distribution. How close is
Suppose that a unit had a Weibull time-to-failure distribution. The value of the scale parameter is . Graph the hazard function for the following values of the shape parameter: . For the fixed values of the scale parameter, what impact does changing the shape parameter have on the hazard function?
Suppose that you have 15 observations on the number of hours to failure of a unit. The observations are 442, 381, 960, 571, 1861, 162, 334, 825, 2562, 324, 312, 368, 367, 968, and 15. Is the exponential distribution a reasonable choice for the time to failure distribution? Estimate MTTF.
Suppose that you have 15 observations on the number of hours to failure of a unit. The observations are 259, 53, 536, 1320, 341, 667, 538, 1713, 428, 152, 29, 445, 677, 637, 696, 540, 1392, 192, 1871, and 2469. Is the exponential distribution a reasonable choice for the time to failure

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