Process Capability & Statistics

A process has USL = 110 and LSL = 90, with a standard deviation of 2.5. What is the process potential capability Cp?

• A 2.00
• B 0.75
• C 1.00
• D 1.33 ✓

Answer: Cp = (USL - LSL) / (6 x sigma) = (110 - 90) / (6 x 2.5) = 20 / 15 = 1.33.

For the same process (USL = 110, LSL = 90, sigma = 2.5) with a mean of 104, what is Cpk?

• A 0.80 ✓
• B 1.07
• C 1.33
• D 1.87

Answer: Cpk = min[(USL - mean), (mean - LSL)] / (3 x sigma) = min[(110-104), (104-90)] / 7.5 = min[6, 14] / 7.5 = 0.80.

Under what condition does Cpk equal Cp for a process?

• A When the process is out of statistical control
• B When the process variation is very large
• C When the process mean is exactly centred between the specification limits ✓
• D When the sample size is below 30

Answer: Cpk equals Cp only when the process is perfectly centred between the specification limits; any off-centring makes Cpk less than Cp.

A process produces 15 defects across 1,000 units, where each unit has 5 defect opportunities. What is the DPMO (defects per million opportunities)?

• A 1,500
• B 3,000 ✓
• C 15,000
• D 300

Answer: DPMO = defects / (units x opportunities) x 1,000,000 = 15 / (1,000 x 5) x 1,000,000 = 0.003 x 1,000,000 = 3,000.

A process operating at a 'Six Sigma' level, accounting for the standard 1.5 sigma long-term shift, produces approximately how many defects per million opportunities?

• A 233
• B 6,210
• C 66,807
• D 3.4 ✓

Answer: A Six Sigma process corresponds to about 3.4 DPMO when the conventional 1.5 sigma shift is included.

For a normal distribution, approximately what percentage of the data falls within plus or minus one standard deviation of the mean (empirical rule)?

• A 95%
• B 99.7%
• C 50%
• D 68% ✓

Answer: By the empirical (68-95-99.7) rule, about 68% of values lie within one standard deviation of the mean, 95% within two, and 99.7% within three.