A producer of specialty products uses a variety of natural and man-made materials to make unique countertops for kitchens and baths. One product line mixes concrete and natural river stone to make countertops that are polished to a high shine revealing unique patterns. Occasionally coarse sand will result in undesirable pitting and rough spots on surfaces. Consequently, as part of its quality control efforts, 8 by 4 metre polished slabs are checked periodically for imperfections. For each slab inspected the number of imperfections (pits, rough spots, etc.) is recorded. If the average number of imperfections per 8 by 4 metre polished slab is 2.6, the control limits for the appropriate control chart are
A) 0 and 7.44.
B) 0.98 and 4.21.
C) 0 and 9.89.
D) 1.24 and 3.96.
E) 1.24 and 4.21.

Question

Quizplus · Accepted Answer

The correct control limits for a Poisson distribution, which is appropriate for counting defects (imperfections in this case), are calculated using the formula LCL = μ - 3√μ and UCL = μ + 3√μ, where μ is the average number of defects. For μ = 2.6, LCL = 2.6 - 3√2.6 ≈ 0 (since it cannot be negative for counts of defects) and UCL = 2.6 + 3√2.6 ≈ 7.44.

A Producer of Specialty Products Uses a Variety of Natural