Practice Problems: Quality Control Basics

Question 1:
A quality control engineer at a steel manufacturing plant is analyzing a production process for steel rods. A sample of 200 rods shows 8 defective units. The company's target defect rate is 3%.

What is the sample defect rate, and does it meet the company's target?

(a) 4.0%; does not meet target
(b) 3.5%; does not meet target
(c) 4.0%; meets target
(d) 3.5%; meets target

Question 2:
A manufacturing engineer is conducting acceptance sampling for a shipment of 5,000 electrical components. The sampling plan specifies a sample size of 125 units with an acceptance number of 3 defects. Upon inspection, 4 defective units are found in the sample.

What should be the engineer's decision regarding this shipment?

(a) Accept the shipment because the sample size is adequate
(b) Reject the shipment because defects exceed the acceptance number
(c) Accept the shipment with a warning notice
(d) Request a larger sample size for re-inspection

Question 3:
A process engineer is monitoring a bottling line where the target fill volume is 500 mL with a standard deviation of 5 mL. The process is normally distributed. The specification limits are 490 mL (LSL) and 510 mL (USL).

What is the process capability index (C_p)?

(a) 0.67
(b) 1.00
(c) 1.33
(d) 2.00

Question 4:
A quality control inspector is using a c-chart to monitor defects in printed circuit boards. Over 25 samples, a total of 150 defects were recorded, with each sample representing one circuit board.

What is the upper control limit (UCL) for this c-chart? (Use 3-sigma limits)

(a) 13.35
(b) 15.00
(c) 16.35
(d) 18.00

Question 5:
A manufacturing plant produces ball bearings with a target diameter of 10.00 mm. Analysis of 100 samples shows a mean diameter of 10.05 mm and a standard deviation of 0.03 mm. The specification limits are 9.94 mm to 10.06 mm.

What is the process capability index (C_pk)?

(a) 0.11
(b) 0.33
(c) 0.56
(d) 1.11

Question 6:
A quality engineer is implementing statistical process control on an assembly line. Sample data from 20 subgroups of size n = 5 shows that the average of sample ranges (R̄) is 12.5 units and the grand average (x̿) is 250 units.

What is the upper control limit (UCL) for the x̄-chart? (Use A₂ = 0.577 for n = 5)

(a) 257.2 units
(b) 262.5 units
(c) 267.2 units
(d) 272.5 units

Question 7:
A production facility uses an np-chart to monitor the number of defective items in samples of 50 units each. Historical data shows the process average fraction defective is 0.04.

What is the center line (CL) value for this np-chart?

(a) 0.04
(b) 0.50
(c) 2.00
(d) 4.00

Question 8:
A quality inspector is monitoring a process using a p-chart. In one sample of 200 items, 14 defective units were found. The process has a historical average fraction defective of 0.05.

What is the sample fraction defective (p) for this particular sample?

(a) 0.05
(b) 0.07
(c) 0.10
(d) 0.14

Question 9:
A process control engineer is analyzing a manufacturing process with specification limits of 45 ± 3 units. The process mean is centered at 45 units with a standard deviation of 0.75 units.

What is the process capability ratio (C_p)?

(a) 1.00
(b) 1.33
(c) 1.50
(d) 2.00

Question 10:
A quality manager receives a lot of 10,000 parts and implements single sampling with n = 200 and acceptance number c = 5. During inspection, 6 defective parts are found.

What action should the quality manager take?

(a) Accept the lot because the sample size is statistically valid
(b) Accept the lot because defects are less than 10
(c) Reject the lot because defects exceed the acceptance number
(d) Perform 100% inspection on remaining parts

Question 11:
A manufacturing engineer is using an R-chart to monitor process variability. For subgroups of size n = 4, the average range (R̄) is 8.5 units. The control chart factor D₄ = 2.282 for n = 4.

What is the upper control limit (UCL) for the R-chart?

(a) 10.78 units
(b) 15.50 units
(c) 19.40 units
(d) 22.82 units

Question 12:
A quality control team is analyzing defects in textile manufacturing using a u-chart. Over 15 inspection units of varying sizes, 180 total defects were found. The total area inspected was 300 square meters.

What is the average number of defects per square meter (ū)?

(a) 0.50
(b) 0.60
(c) 1.67
(d) 12.00

Question 13:
A process engineer evaluates a production line where the upper specification limit is 75 mm, lower specification limit is 65 mm, process mean is 72 mm, and standard deviation is 2 mm.

What is the lower process capability index (C_pk) value?

(a) 0.50
(b) 1.00
(c) 1.17
(d) 1.67

Question 14:
A quality inspector uses a p-chart to monitor defective rates. The process average is p̄ = 0.06 with sample size n = 100. Using 3-sigma control limits.

What is the upper control limit (UCL) for this p-chart?

(a) 0.087
(b) 0.131
(c) 0.156
(d) 0.180

Question 15:
A production supervisor monitors a packaging process using an x̄-chart. The grand average is 500 g, and R̄ = 15 g for subgroup size n = 6. The control chart factor A₂ = 0.483 for n = 6.

What is the lower control limit (LCL) for the x̄-chart?

(a) 485.0 g
(b) 490.5 g
(c) 492.8 g
(d) 495.0 g

Question 16:
A quality engineer analyzes a process where samples of n = 5 are taken every hour. After 25 subgroups, x̿ = 100 mm and R̄ = 10 mm. The control chart factor D₃ = 0 and D₄ = 2.114 for n = 5.

What is the lower control limit (LCL) for the R-chart?

(a) 0 mm
(b) 2.5 mm
(c) 5.0 mm
(d) 7.9 mm

Question 17:
A component manufacturer produces parts with specification limits of 50 ± 5 units. The process mean is 51 units with a standard deviation of 1.2 units.

What is the process capability index (C_pk)?

(a) 1.11
(b) 1.28
(c) 1.39
(d) 1.67

Question 18:
A quality control engineer uses acceptance sampling for incoming lots of 5,000 units. The sampling plan calls for n = 80 with an acceptance number c = 2. If 3 defective units are found in the sample.

What is the appropriate decision and the sample defect rate?

(a) Accept lot; 2.5% defect rate
(b) Accept lot; 3.75% defect rate
(c) Reject lot; 2.5% defect rate
(d) Reject lot; 3.75% defect rate

Question 19:
A plastics manufacturer monitors surface defects using a c-chart. Over 30 samples, the total number of defects recorded is 210. Each sample represents one molded panel.

What is the lower control limit (LCL) for this c-chart using 3-sigma limits?

(a) 0
(b) 0.07
(c) 2.13
(d) 4.26

Question 20:
A manufacturing plant produces bolts with a target diameter of 12.00 mm and specification limits of 11.85 mm to 12.15 mm. Process data shows μ = 12.00 mm and σ = 0.05 mm.

What is the process capability ratio (C_p)?

(a) 0.50
(b) 1.00
(c) 1.50
(d) 2.00