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CPU of a computer chip. The central processing unit (CPU)
Chapter 13, Problem 15E(choose chapter or problem)
Problem 15E
CPU of a computer chip. The central processing unit (CPU) of a microcomputer is a computer chip containing millions of transistors. Connecting the transistors are slender circuit paths only .5 to .85 micrometer wide. A manufacturer of CPU chips knows that if the circuit paths are not .5–.85 micrometer wide, a variety of problems will arise in the chips’ performance. The manufacturer sampled four CPU chips six times a day (every 90 minutes from 8:00 a.m. until 4:30 p.m.) for 5 consecutive days and measured the circuit path widths. These data and Minitab were used to construct the shown below. a. Assuming that = .335, calculate the chart’s upper and lower control limits, the upper and lower A–B boundaries, and the upper and lower B–C boundaries. b. What does the chart suggest about the stability of the process used to put circuit paths on the CPU chip? Justify your answer. c. Should the control limits be used to monitor future process output? Explain.
Questions & Answers
QUESTION:
Problem 15E
CPU of a computer chip. The central processing unit (CPU) of a microcomputer is a computer chip containing millions of transistors. Connecting the transistors are slender circuit paths only .5 to .85 micrometer wide. A manufacturer of CPU chips knows that if the circuit paths are not .5–.85 micrometer wide, a variety of problems will arise in the chips’ performance. The manufacturer sampled four CPU chips six times a day (every 90 minutes from 8:00 a.m. until 4:30 p.m.) for 5 consecutive days and measured the circuit path widths. These data and Minitab were used to construct the shown below. a. Assuming that = .335, calculate the chart’s upper and lower control limits, the upper and lower A–B boundaries, and the upper and lower B–C boundaries. b. What does the chart suggest about the stability of the process used to put circuit paths on the CPU chip? Justify your answer. c. Should the control limits be used to monitor future process output? Explain.
ANSWER:
Step 1 of 4
Here the circuit path widths are measured for the four CPU chips six times a day for 5
consecutive days. Thus, we have n = 4.
From the given control chart, we observed that the center line exists at 
Using control chart constants table, we observe 
a) We assumed that
By definitions, the upper and lower control limits are defined as 
Therefore,
