- 16-9.16-29: 16-29. Consider the control chart in Fig. 16-3. Suppose that the me...
- 16-9.16-30: An chart uses samples of size 4. The center line is at 100, and the...
- 16-9.16-31: Consider the revised control chart in Exercise 16-1 with , UCL 37.4...
- 16-9.16-32: Consider the control chart in Exercise 16-2(a) with , UCL 14.708, L...
- 16-9.16-33: 16-33. Consider the control chart in Exercise 16-3(a) with , UCL 15...
- 16-9.16-34: Consider the control chart in Exercise 16-4(a) with , UCL 21.88, LC...
- 16-9.16-35: 16-35. Consider the control chart in Exercise 16-5 with , UCL 242.7...
- 16-9.16-36: Consider the revised control chart in Exercise 16-7 with , UCL 0.06...
- 16-9.16-37: 16-37. Consider the revised control chart in Exercise 16-8 with , U...
Solutions for Chapter 16-9: CONTROL CHART PERFORMANCE
Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
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
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
The joint probability distribution of two random variables.
Bivariate normal distribution
The joint distribution of two normal random variables
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
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.
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
A probability distribution for a continuous random variable.
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 .
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
Another name for a probability density function
Discrete random variable
A random variable with a inite (or countably ininite) range.
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.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.