 16.2.6: In the case of known m and s, what control limits arenecessary for ...
 16.2.7: Consider a 3sigma control chart with a center line at m0and based ...
 16.2.8: The table below gives data on moisture content forspecimens of a ce...
 16.2.9: Refer to the data given in Exercise 8, and construct acontrol chart...
 16.2.10: When installing a bath faucet, it is important to properlyfasten th...
 16.2.11: The accompanying table gives sample means and standarddeviations, e...
 16.2.12: Refer to Exercise 11. An assignable cause was found forthe unusuall...
 16.2.13: Consider the control chart based on control limitsm0 6 2.81 syn.a. ...
 16.2.14: Threedimensional (3D) printing is a manufacturing technologythat a...
 16.2.15: Calculate control limits for the data of Exercise 8 usingthe robust...
Solutions for Chapter 16.2: Control Charts for Process Location
Full solutions for Probability and Statistics for Engineering and the Sciences  9th Edition
ISBN: 9781305251809
Solutions for Chapter 16.2: Control Charts for Process Location
Get Full SolutionsProbability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9781305251809. Since 10 problems in chapter 16.2: Control Charts for Process Location have been answered, more than 98875 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. Chapter 16.2: Control Charts for Process Location includes 10 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Arithmetic mean
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

Assignable cause
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

Bivariate normal distribution
The joint distribution of two normal random variables

Block
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

Center line
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

Contrast
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

Critical value(s)
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

Discrete distribution
A probability distribution for a discrete random variable

Error propagation
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

Expected value
The expected value of a random variable X is its longterm average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

Ftest
Any test of signiicance involving the F distribution. The most common Ftests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

Gamma function
A function used in the probability density function of a gamma random variable that can be considered to extend factorials

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

Geometric mean.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .