Section 2 Process Capability

Section 2 Process Capability 1) A process that is in statistical control will always yield products that meet their design specifications. Answer: FALSE Diff: 2 Key Term: Process capability ratio Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 2) The higher the process capability ratio, the greater the likelihood that process will be within design specifications. Answer: TRUE Diff: 2 Key Term: Process capability ratio Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 3) The Cpk index measures the difference between the desired and actual dimensions of goods or services produced. Answer: TRUE Diff: 2 Key Term: Process capability index Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 4) The process capability measures Cp and Cpk differ because: A) only one ensures the process mean is centered within the limits. B) Cp values above 1 indicate a capable process, while Cpk values above 2 indicate a capable process. C) They do not differ: both are identical. D) Cp values for a given process will always be greater than or equal to Cpk values. E) Both A and D are correct. Answer: E Diff: 3 Key Term: Process capability Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 5) A Cp value of 1.33 indicates a standard of how many standard deviations (sigmas)? A) 6 B) 1.33 C) 2 D) 3 E) 4 Answer: E Diff: 2 Key Term: Process capability ratio Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 6) Which of the following is true regarding the process capability index Cpk? A) A Cpk index value of 1 is the highest possible. B) The larger the Cpk, the more units meet specifications. C) The Cpk index can only be used when the process centerline is also the specification centerline. D) Positive values of the Cpk index are good; negative values are bad. E) Its value will always be at least as large as the Cp value for the same process. 29 Answer: B Diff: 2 Key Term: Process capability index Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 7) If the Cpk index exceeds 1: A) the AQL must be smaller than the LTPD. must be less than one-third of the absolute value of the difference between each specification limit and the process mean. C) the x-bar chart must indicate that the process is in control. D) the process is capable of Six Sigma quality. E) the process is characterized as "not capable." Answer: B Diff: 2 Key Term: Process capability index AACSB: Analytical thinking Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 8) The statistical definition of Six Sigma allows for 3.4 defects per million. This is achieved by what Cpk index value? A) 6 B) 1 C) 1.33 D) 1.67 E) 2 Answer: E Diff: 2 Key Term: Process capability index AACSB: Analytical thinking Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 9) A Cpk index of 1.00 equates to what defect rate? A) five percent B) 3.4 defects per million items C) 2.7 defects per 1,000 items D) 97.23 percent E) one percent Answer: C Diff: 3 Key Term: Process capability index AACSB: Analytical thinking Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 10) The term ________ is used to describe how well a process makes units within design specifications (or tolerances). Answer: process capability Diff: 2 Key Term: Process capability Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 30 11) A Cpk index greater than ________ is a capable process, one that generates fewer than 2.7 defects per Answer: unity, or 1 Diff: 2 Key Term: Process capability index Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 12) What does it mean for a process to be "capable"? Answer: Process capability refers to the ability of a process to meet design specifications, which are set by engineering design or customer requirements. Diff: 2 Key Term: Process capability Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 13) What is the difference between the process capability ratio Cp and the process capability index Cpk? Answer: The Cp ratio does not consider how well the process average is centered on the target value. However, Cpk does consider how well the process is centered. In particular, the Cp value will always be greater than or equal to the Cpk value, and a Cp value of 1 will not actually indicate ±3-sigma capability if the process is not centered. There's really no reason to use Cp instead of Cpk. Diff: 3 Key Term: Process capability AACSB: Reflective thinking Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 14) 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? Answer: The Cp ratio does not consider how well the process average is centered on the target value; its value is unaffected by the setting for the process mean. However, Cpk does consider how well the process is centered; with x-bar on the LSL, the formula guarantees a Cpk of zero. Diff: 2 Key Term: Process capability AACSB: Analytical thinking Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 31 15) The specifications for a manifold gasket that installs between two engine parts calls for a thickness of 2.500 mm ± .020 mm. The standard deviation of the process is estimated to be 0.004 mm. The process is currently operating at a mean thickness of 2.50 mm. (a) What are the upper and lower specification limits for this product? (b) What is the Cp for this process? (c) About what percent of all units of this gasket will meet specifications? Does this meet the technical definition of Six Sigma? Answer: (a) LSL = 2.48 mm, USL = 2.52 mm. (b) Cp = (2.52 - 2.48)/(6 0.004) = 1.67. (b) Each specification limit lies 5 standard deviations from the centerline, so practically 100 percent of units will meet specifications. However, this percentage is not quite as high as Six Sigma would call for. Diff: 2 Key Term: Process capability ratio AACSB: Analytical thinking Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 16) The specifications for a manifold gasket that installs between two engine parts calls for a thickness of 2.500 mm ± .020 mm. The standard deviation of the process is estimated to be 0.004 mm. The process is currently operating at a mean thickness of 2.50 mm. (a) What are the upper and lower specification limits for this product? (b) What is the Cp for this process? (c) The purchaser of these parts requires a capability index of 1.50. Is this process capable? Is this process good enough for the supplier? (d) If the process mean were to drift from its setting of 2.500 mm to a new mean of 2.497, would the process still be good enough for the supplier's needs? Answer: (a) LSL = 2.48 mm, USL = 2.52 mm. (b) Cp = (2.52 - 2.48)/(6 0.004) = 1.67. (c) Yes to both parts of the question. (d) The Cpk index is now relevant, and its value is the lesser of 1.917 and 1.417. The process is still capable, but not to the supplier's needs. Diff: 2 Key Term: Process capability AACSB: Analytical thinking Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 17) 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? Answer: LSL = 5.9 mm, USL = 6.1 mm. Cp is (6.1 - 5.9)/6(.02) = 1.67. Cpk is the lesser of = 1.17 and (6.03 - 5.9)/(3 0.02) = 2.17; therefore, 1.17. The upper specification limit lies more than 3 standard deviations from the centerline, and the lower specification limit is further away, so practically all units will meet specifications. Diff: 2 Key Term: Process capability AACSB: Analytical thinking Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 32 18) 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 are the Cp and Cpk values for this process? Is this process capable of producing the desired part? Answer: LSL = 5.8 inches, USL = 6.2 inches. Cp is (6.2-5.8)/6(.05) = 1.33. Cpk is the lesser of = .67 and (6.1 - 5.8)/(3 0.02) = 2.00; therefore, .67. The process is capable based upon the Cp. However, the process is not centered (based upon its Cpk) and based upon its current center is not producing parts that are of an acceptable quality. Diff: 2 Key Term: Process capability AACSB: Analytical thinking Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 19) 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. Answer: Cp = (21 - 19)/(6 .7) = .476 Cpk = min [(21 - 19.89)/(3 .7), (19.89 - 19)/(3 .7)] = .424 The very low capability metrics mean the process is not capable. The variability must be reduced. Diff: 2 Key Term: Process capability AACSB: Analytical thinking Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 20) At your first job out of college you have been assigned to the production of bottled 20 oz. soda. The process has upper and lower spec limits of 20.5 and 19.5 oz, respectively, with a mean of 19.8 oz and standard deviation of .1 oz. Your manager has requested the process produce no more than 3.4 defects per 1 million bottles produced. Calculate Cpk and then determine if the process is capable according to the manager's standard. Answer: Cpk = minimum [(20.5 - 19.8)/(3 .1),(19.8 - .5)/(3 .1)] = 1.0 oz The process is capable according to the typical 3-sigma standard of needing a Cpk is not capable according to the manager's six-sigma standard because Cpk is less than the 2.0 required for under 3.4 defects per million. Diff: 3 Key Term: Process capability index AACSB: Analytical thinking Objective: LO S6.6 Explain process capability and compute Cp and Cpk Learning Outcome: Apply basic statistical process control (SPC) methods 33