A “six-sigma quality level” corresponds to process variation equal to half of the design tolerance, while allowing the mean to shift as much as ? standard deviations from the target

Question

A “six-sigma quality level” corresponds to process variation equal to half of the design tolerance, while allowing the mean to shift as much as   ?    standard deviations from the target

BlackTom AI · Accepted Answer

Cp (process capability) is defined as tolerance width divided by 6σ. If process variation equals half the design tolerance, then the full tolerance T = 12σ (because 6σ is half of T). Algebraically:
T/2 = 6σ  ⇒  T = 12σ.
Thus Cp = T/(6σ) = (12σ)/(6σ) = 2.

Let H denote the tolerance half‑width (distance from target to nearest spec): H = T/2 = 6σ. If the mean shifts by m standard deviations from the target, the remaining distance from the shifted mean to the nearest specification limit is H − m = 6σ − mσ. The question asks how large m can be while still meeting the “six‑sigma quality level” condition that process variation equals half the design tolerance. With H = 6σ, allowing a mean shift of m = 1σ leaves 6σ − 1σ = 5σ separation from the shifted mean to the nearest spec. In other words, starting from a design where tolerance half‑width = 6σ, a 1σ mean shift is tolerated while still retaining a very large separation (5σ) to the spec limits. This is the interpretation used in this statement: process variation = half tolerance with up to a 1σ mean shift.

Why the other choices are incorrect:
- 0σ: implies no mean shift is allowed; though conservative, the statement explicitly allows a nonzero shift.
- 2σ or 3σ: if the mean shifted that much, the distance to the nearest spec would be 4σ or 3σ respectively (6σ − 2σ = 4σ, 6σ − 3σ = 3σ), which does not match the conventional description given in the question.
- “None of the above” is incorrect because one of the numeric options is correct.

Therefore the mean may shift as much as 1 standard deviation from the target. This matches the provided answer: 1.

A “six-sigma quality level” corresponds to process variation equal to half of the design tolerance, while allowing the mean to shift as much as ? standard deviations from the target单项选择题

类似问题

The DMADV process incorporates the principal activities of the Design for Six Sigma. Which of the following activities included in DMADV focuses on identifying and understanding the market need or opportunity?

Amazon used which of the following to reduce errors in order fulfillment?

A project has a required return of 12.6 percent, an initial cash outflow of $42,100, and cash inflows of $16,500 in Year 1, $11,700 in Year 2, and $10,400 in Year 4. What is the net present value?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单