/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q1E A control chart for thickness of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 16: Q1E (page 680)

A control chart for thickness of rolled-steel sheets is based on an upper control limit of .0520 in. and a lower limit of .0475 in. The first ten values of the quality statistic (in this case X, the sample mean thickness of n 5 5 sample sheets) are .0506, .0493, .0502, .0501, .0512, .0498, .0485, .0500, .0505, and .0483. Construct the initial part of the quality control chart, and comment on its appearance.

Short Answer

Expert verified

There are no out of control signals.

Step by step solution

01

solving using graph:

We notice that all ten value of the statistic \(\bar X\)are between the UCL and LCL which means that there are no out of control signals.

02

final answer:

There are no out of control signals.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Refer to Exercise 34 and consider the plan with \(n = 100\)and \(c = 2\). Calculate \(P(A)\) for \(p = .01,.02, \ldots ,.05\), and sketch the two OC curves on the same set of axes. Which of the two plans is preferable (leaving aside the cost of sampling) and why?

The accompanying table gives sample means and standard deviations, each based on\(n = 6\)observations of the refractive index of fiber-optic cable. Construct a control chart, and comment on its appearance. (Hint:\(\Sigma {\bar x_i} = 2317.07\)and\(\left. {\Sigma {s_i} = 30.34.} \right)\)

\(\begin{aligned}{*{20}{l}}{Day\;\;\;\;\;\;\;bar\left( x \right)\;\;\;\;s\;\;\;\;\;\;\;\;\;\;\;\;Day\;\;\;\;\;\;\;bar\left( x \right)\;\;\;\;s}\\{1\;\;\;\;\;\;\;\;\;\;\;\;95.47\;\;\;\;1.30\;\;\;\;\;\;13\;\;\;\;\;\;\;\;\;\;97.02\;\;\;\;1.28}\\{2\;\;\;\;\;\;\;\;\;\;\;\;97.38\;\;\;\;.88\;\;\;\;\;\;\;\;14\;\;\;\;\;\;\;\;\;\;95.55\;\;\;\;1.14}\\{3\;\;\;\;\;\;\;\;\;\;\;\;96.85\;\;\;\;1.43\;\;\;\;\;\;15\;\;\;\;\;\;\;\;\;\;96.29\;\;\;\;1.37}\\{4\;\;\;\;\;\;\;\;\;\;\;\;96.64\;\;\;\;1.59\;\;\;\;\;\;16\;\;\;\;\;\;\;\;\;\;96.80\;\;\;\;1.40}\\{5\;\;\;\;\;\;\;\;\;\;\;\;96.87\;\;\;\;1.52\;\;\;\;\;\;17\;\;\;\;\;\;\;\;\;\;96.01\;\;\;\;1.58}\\{6\;\;\;\;\;\;\;\;\;\;\;\;96.52\;\;\;\;1.27\;\;\;\;\;\;18\;\;\;\;\;\;\;\;\;\;95.39\;\;\;\;.98}\\{7\;\;\;\;\;\;\;\;\;\;\;\;96.08\;\;\;\;1.16\;\;\;\;\;\;19\;\;\;\;\;\;\;\;\;\;96.58\;\;\;\;1.21}\\{8\;\;\;\;\;\;\;\;\;\;\;\;96.48\;\;\;\;.79\;\;\;\;\;\;\;\;20\;\;\;\;\;\;\;\;\;\;96.43\;\;\;\;.75}\\{9\;\;\;\;\;\;\;\;\;\;\;\;96.63\;\;\;\;1.48\;\;\;\;\;\;21\;\;\;\;\;\;\;\;\;\;97.06\;\;\;\;1.34}\\{10\;\;\;\;\;\;\;\;\;\;96.50\;\;\;\;.80\;\;\;\;\;\;\;\;22\;\;\;\;\;\;\;\;\;\;98.34\;\;\;\;1.60}\\{11\;\;\;\;\;\;\;\;\;\;97.22\;\;\;\;1.42\;\;\;\;\;\;23\;\;\;\;\;\;\;\;\;\;96.42\;\;\;\;1.22}\\{12\;\;\;\;\;\;\;\;\;\;96.55\;\;\;\;1.65\;\;\;\;\;\;24\;\;\;\;\;\;\;\;\;\;95.99\;\;\;\;1.18\;\;\;\;\;\;\;}\end{aligned}\)

When the out-of-control ARL corresponds to a shift of 1 standard deviation in the process mean, what are the characteristics of the CUSUM procedure that has ARLs of 250 and \(4.8\), respectively, for the in-control and out of-control conditions?

When\({S^2}i\)s the sample variance of a normal random sample,\((n - 1){S^2}/{\sigma ^2}\)has a chi-squared distribution with\(n - 1df\), so

\(P\left( {\chi _{.999,n - 1}^2 < \frac{{(n - 1){S^2}}}{{{\sigma ^2}}} < \chi _{.001,n - 1}^2} \right) = .998\)

from which

\(P\left( {\frac{{{\sigma ^2}\chi _{.999,n - 1}^2}}{{n - 1}} < {S^2} < \frac{{{\sigma ^2}\chi _{.001,n - 1}^2}}{{n - 1}}} \right) = .998\)

This suggests that an alternative chart for controlling process variation involves plotting the sample variances and using the control limits

\(\begin{aligned}{l}LCL = \overline {{s^2}} {\chi _{ - 999_{ - n - 1}^2}}/(n - 1)\\UCL = \overline {{s^2}} \chi _{.001,n - 1}^2/(n - 1)\end{aligned}\)

Construct the corresponding chart for the data of Exercise\(11\). (Hint: The lower- and upper-tailed chi-squared critical values for\(5\)df are\(.210\)and\(20.515\), respectively.)

When installing a bath faucet, it is important to properly fasten the threaded end of the faucet stem to the water supply line. The threaded stem dimensions must meet product specifications, otherwise malfunction and leakage may occur. Authors of "Improving the Process Capability of a Boring Operation by the Application of Statistical Techniques" (Intl. J. Sci. Engr. Research, Vol. 3, Issue\(5\), May\(2012\)) investigated the production process of a particular bath faucet manufactured in India. The article reported the threaded stem diameter (target value being\(13\;mm\)) of each faucet in\(25\)samples of size\(4\)as shown here:

\(\begin{aligned}{*{20}{c}}{Subgroup}&{x\_(1)}&{x\_(2)}&{x\_(3)}&{x\_(4)}\\1&{13.02}&{12.95}&{12.92}&{12.99}\\2&{13.02}&{13.10}&{12.96}&{12.96}\\3&{13.04}&{13.08}&{13.05}&{13.10}\\4&{13.04}&{12.96}&{12.96}&{12.97}\\5&{12.96}&{12.97}&{12.90}&{13.05}\\6&{12.90}&{12.88}&{13.00}&{13.05}\\7&{12.97}&{12.96}&{12.96}&{12.99}\\8&{13.04}&{13.02}&{13.05}&{12.97}\\9&{13.05}&{13.10}&{12.98}&{12.96}\\{10}&{12.96}&{13.00}&{12.99}&{12.99}\\{11}&{12.90}&{13.05}&{12.98}&{12.88}\\{12}&{12.96}&{12.98}&{12.97}&{13.02}\end{aligned}\)

\(\begin{aligned}{*{20}{c}}{ }&{}&{}&{}&{}\\{13}&{13.00}&{12.96}&{12.99}&{12.90}\\{14}&{12.88}&{12.94}&{13.05}&{13.00}\\{15}&{12.96}&{12.96}&{13.04}&{12.98}\\{16}&{12.99}&{12.94}&{13.00}&{13.05}\\{17}&{13.05}&{13.02}&{12.88}&{12.96}\\{18}&{13.08}&{13.06}&{13.10}&{13.05}\\{19}&{13.02}&{13.05}&{13.04}&{12.97}\\{20}&{12.96}&{12.90}&{12.97}&{13.05}\\{21}&{12.98}&{12.99}&{12.96}&{13.00}\\{22}&{12.97}&{13.02}&{12.96}&{12.99}\\{23}&{13.04}&{13.00}&{12.98}&{13.10}\\{24}&{13.02}&{12.90}&{13.05}&{12.97}\\{25}&{12.93}&{12.88}&{12.91}&{12.90}\end{aligned}\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.