- 15.7.59E: An X chart uses samples of size 1. The center line is at 100, and t...
- 15.7.60E: An chart uses samples of size 4. The center line is at 100, and the...
- 15.7.61E: Consider the control chart in Fig. 15-3. Suppose that the mean shif...
- 15.7.62E: Consider an UCL = 14.708, LCL = 14.312, and n = 5. Suppose that the...
- 15.7.63E: Consider an control chart with UCL = 242.780, LCL = 203.220, and n ...
- 15.7.64E: Consider an control chart with UCL = 21.71, LCL = 18.29, and n = 6....
- 15.7.65E: Consider an control chart with UCL = 37.404, LCL = 30.780, and n = ...
- 15.7.66E: Consider an control chart with UCL =17.40, LCL = 12.79, and n = 3. ...
- 15.7.67E: Consider an control chart with UCL = 0.0635, LCL = 0.0624, and n = ...
- 15.7.68E: Consider the revised control chart in Exercise 15-8 with ?ˆ = 0.669...
- 15.7.69E: An chart uses a sample of size 3. The center line is at 200, and th...
- 15.7.70E: Consider an control chart with UCL = 24.802, LCL = 23.792, and n = ...
- 15.7.71E: Consider a P-chart with subgroup size n = 50 and center line at 0.1...
- 15.7.72E: Consider the U chart for printed circuit boards in Example 15-5. Th...
Solutions for Chapter 15.7: Applied Statistics and Probability for Engineers 6th Edition
Full solutions for Applied Statistics and Probability for Engineers | 6th Edition
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A probability distribution for a continuous random variable.
See Control chart.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
Formulas used to determine the number of elements in sample spaces and events.
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
Defects-per-unit control chart
See U chart
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
Error mean square
The error sum of squares divided by its number of degrees of freedom.
A series of tests in which changes are made to the system under study
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function