Finance

Q: A car mechanic is thinking of guaranteeing customers that an oil change will take no more than 15 minutes with a 99.73% confidence level. He takes a few samples of size 5 and finds the process mean to be 13 minutes with a standard deviation of .2 minutes and average sample range of 1.2 minutes. Find the A2, D4, and D3 values and use them to compute the upper and lower limits for an x-bar chart. Use the upper limit to determine if the mechanic can offer a 15 minute guarantee. Assume the mechanic plots the samples on the x-bar control chart and finds the process is in control, is there anything else the mechanic is missing to ensure the process is in control?

Q: A consultant has been brought in to a manufacturing plant to help apply six sigma principles. Her first task is to work on the production of rubber balls. The upper and lower spec limits are 21 and 19 cm respectively. The consultant takes ten samples of size five and computes the sample standard deviation to be .7 cm and the sample mean to be 19.89 cm. Compute Cp and Cpk for the process. Give the consultant advice on what to do with the process based on your findings.

Q: A city police chief decides to do an annual review of the police department by checking the number of monthly complaints. If the total number of complaints in each of the 12 months were 15, 18, 13, 12, 16, 20, 5, 10, 9, 11, 8, and 3 and the police chief wants a 90% confidence level, are the complaints in control?

Q: A department chair wants to monitor the percentage of failing students in classes in her department. Each class had an enrollment of 50 students last spring. The number of failing students in the 10 classes offered that term were 1, 4, 2, 0, 0, 0, 0, 0, 0, and 3, respectively. Compute the control limits for a p-chart at the 95% confidence level. Is the process in control?

Q: The specification for a plastic handle calls for a length of 6.0 inches .2 inches. The standard deviation of the process is estimated to be 0.05 inches. What are the upper and lower specification limits for this product? The process is known to operate at a mean thickness of 6.1 inches. What is the Cp and Cpk for this process? Is this process capable of producing the desired part?

Q: The specification for a plastic liner for concrete highway projects calls for a thickness of 6.0 mm 0.1 mm. The standard deviation of the process is estimated to be 0.02 mm. What are the upper and lower specification limits for this product? The process is known to operate at a mean thickness of 6.03 mm. What is the Cp and Cpk for this process? About what percent of all units of this liner will meet specifications?

Q: The width of a bronze bar is intended to be one-eighth of an inch (0.125 inches). Inspection samples contain five bars each. The average range of these samples is 0.01 inches. What are the upper and lower control limits for the x-bar and R-chart for this process, using 3-sigma limits?

Q: A woodworker is concerned about the quality of the finished appearance of her work. In sampling units of a split-willow hand-woven basket, she has found the following number of finish defects in ten units sampled: 4, 0, 3, 1, 2, 0, 1, 2, 0, 2.a. Calculate the average number of defects per basketb. If 3-sigma control limits are used, calculate the lower control limit, centerline, and upper control limit.

Q: Repeated sampling of a certain process shows the average of all sample ranges to be 1.0 cm. The sample size has been constant at n = 5. What are the 3-sigma control limits for this R-chart?

Q: A hospital-billing auditor has been inspecting patient bills. While almost all bills contain some errors, the auditor is looking now for large errors (errors in excess of $250). Among the last 100 bills inspected, the defect rate has been 16%. Calculate the upper and lower limits for the billing process for 99.7% confidence.

Q: If u03bc = 9 ounces, u03c3 = 0.5 ounces, and n = 9, calculate the 3-sigma control limits.

Q: The mean and standard deviations for a process are u03bc= 90 and u03c3 = 9. For the variable control chart, a sample size of 16 will be used. Calculate the standard deviation of the sampling distribution.

Q: The defect rate for a product has historically been about 1.6%. What are the upper and lower control chart limits for a p-chart, if you wish to use a sample size of 100 and 3-sigma limits?

Q: An operator trainee is attempting to monitor a filling process that has an overall average of 705 cc. The average range is 17 cc. If you use a sample size of 6, what are the upper and lower control limits for the x-bar and R chart?

Q: What four elements determine the value of average outgoing quality? Why does this curve rise, peak, and fall?

Q: What is the AOQ of an acceptance sampling plan?

Q: What is the purpose of the Operating Characteristics curve?

Q: What is acceptance sampling?

Q: A process is operating in such a manner that the mean of the process is exactly on the lower specification limit. What must be true about the two measures of capability for this process?

Q: What is the difference between the process capability ratio Cp and the process capability index Cpk?

Q: Why are x-bar and R-charts usually used hand in hand?

Q: What is the difference between natural and assignable causes of variation?

Q: What are the three possible results (or findings) from the use of control charts?

Q: Briefly explain what the Central Limit Theorem has to do with control charts.

Q: What is the basic objective of a process control system?

Q: The __________ is the percent defective in an average lot of goods inspected through acceptance sampling.

Q: The __________ is the lowest level of quality that we are willing to accept.

Q: A(n) __________ is a graph that describes how well an acceptance plan discriminates between good and bad lots.

Q: __________ is a method of measuring samples of lots or batches of product against predetermined standards.

Q: A Cpk index greater than __________ is a capable process, one that generates fewer than 2.7 defects per 1000 at the 3u03c3 level.

Q: The term __________ is used to describe how well a process makes units within design specifications (or tolerances).

Q: The __________ is a quality control chart used to control the number of defects per unit of output.

Q: The __________ are calculated to show how much allowance should be made for natural variation.

Q: The __________ is a quality control chart that indicates when changes occur in the central tendency of a production process.

Q: If a process has only natural variations, __________ percent of the time the sample averages will fall inside the (or ) control limits.

Q: The __________ is the chief way to control attributes.

Q: __________ is variation in a production process that can be traced to specific causes.

Q: Which of the following is true regarding the average outgoing quality level?A) An AOQ value of 1 is ideal, because all defects have been removed.B) AOQ is always greater than AQL but less than LTPD.C) AOQ rises (worsens) following inspection of failed lots.D) AOQ is very low (very good) for extremely poor quality lots.E) None of the above is true.

Q: Which of the following statements about acceptance sampling is true?A) The steeper an OC curve, the better it discriminates between good and bad lots.B) Acceptance sampling removes all defective items.C) Acceptance sampling of incoming lots is replacing statistical process control at the supplier.D) Acceptance sampling occurs continuously along the assembly line.E) All of the above are true.

Q: When a lot has been accepted by acceptance sampling, we know thatA) it has more defects than existed before the samplingB) it has had all its defects removed by 100% inspectionC) it will have the same defect percentage as the LTPDD) it has no defects presentE) All of the above are false.

Q: In most acceptance sampling plans, when a lot is rejected, the entire lot is inspected and all defective items are replaced. When using this technique the AOQA) worsens (AOQ becomes a larger fraction)B) improves (AOQ becomes a smaller fraction)C) is not affected, but the AQL is improvedD) is not affectedE) falls to zero

Q: A Type II error occurs whenA) a good lot is rejectedB) a bad lot is acceptedC) the population is worse than the LTPDD) the proportion of defectives is very smallE) none of the above

Q: A Type I error occurs whenA) a good lot is rejectedB) a bad lot is acceptedC) the number of defectives is very largeD) the population is worse than the AQLE) none of the above

Q: Average outgoing quality (AOQ) usuallyA) worsens with inspectionB) stays the same with inspectionC) improves with inspectionD) may either improve or worsen with inspectionE) is the average quality before inspectionAnswer: C

Q: Which of the following is true regarding the relationship between AOQ and the true population percent defective?A) AOQ is greater than the true percent defective.B) AOQ is the same as the true percent defective.C) AOQ is less than the true percent defective.D) There is no relationship between AOQ and the true percent defective.E) The relationship between these two cannot be determined.

Q: An operating characteristic (OC) curve describesA) how many defects per unit are permitted before rejection occursB) the sample size necessary to distinguish between good and bad lotsC) the most appropriate sampling plan for a given incoming product quality levelD) how well an acceptance sampling plan discriminates between good and bad lotsE) none of the above

Q: Acceptance sampling is usually used to controlA) the number of units output from one stage of a process which are then sent to the next stageB) the number of units delivered to the customerC) the quality of work-in-process inventoryD) incoming lots of purchased productsE) all of the above

Q: Which of the following statements on acceptance sampling is true?A) Acceptance sampling draws samples from a population of items, tests the sample, and accepts the entire population if the sample is good enough, and rejects it if the sample is poor enough.B) The sampling plan contains information about the sample size to be drawn and the critical acceptance or rejection numbers for that sample size.C) The steeper an operating characteristic curve, the better its ability to discriminate between good and bad lots.D) All of the above are true.E) All of the above are false.

Q: Acceptance samplingA) may involve inspectors taking random samples (or batches) of finished products and measuring them against predetermined standardsB) may involve inspectors taking random samples (or batches) of incoming raw materials and measuring them against predetermined standardsC) is more economical than 100% inspectionD) may be either of a variable or attribute type, although attribute inspection is more common in the business environmentE) All of the above are true.

Q: Acceptance samplingA) is the application of statistical techniques to the control of processesB) was developed by Walter Shewhart of Bell LaboratoriesC) is used to determine whether to accept or reject a lot of material based on the evaluation of a sampleD) separates the natural and assignable causes of variationE) all of the above

Q: A Cpk index of 1.00 equates to a defect rate ofA) five percentB) 3.4 defects per millionC) 2.7 per 1,000 itemsD) 97.23 percentE) one percent

Q: The statistical definition of Six Sigma allows for 3.4 defects per million. This is achieved by a Cpk index ofA) 0B) 1C) 1.33D) 1.67E) 2

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