A normally distributed process uses 66.7% of the specification band. It is centered at the nominal dimension, located halfway between the upper and lower specification limits. (a) Estimate PCR and PCRk. Interpret these ratios. (b) What fallout level (fraction defective) is produced? 1
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2-1
SAMPLE SPACES AND EVENTS
2-2
INTERPRETATIONS OF PROBABILITY
2-3
ADDITION RULES
2-4
CONDITIONAL PROBABILITY
2-5
MULTIPLICATION AND TOTAL PROBABILITY RULES
2-6
INDEPENDENCE
2-7
BAYES THEOREM
2-8
RANDOM VARIABLES
3-1
DISCRETE RANDOM VARIABLES
3-2
PROBABILITY DISTRIBUTIONS AND PROBABILITY MASS FUNCTIONS
3-3
CUMULATIVE DISTRIBUTION FUNCTIONS
3-4
MEAN AND VARIANCE OF A DISCRETE RANDOM VARIABLE
3-5
DISCRETE UNIFORM DISTRIBUTION
3-6
BINOMIAL DISTRIBUTION
3-7
GEOMETRIC AND NEGATIVE BINOMIAL DISTRIBUTIONS
3-8
HYPERGEOMETRIC DISTRIBUTION
3-9
POISSON DISTRIBUTION
4-10
ERLANG AND GAMMA DISTRIBUTIONS
4-11
WEIBULL DISTRIBUTION
4-12
LOGNORMAL DISTRIBUTION
4-2
PROBABILITY DISTRIBUTIONS AND PROBABILITY DENSITY FUNCTIONS
4-3
CUMULATIVE DISTRIBUTION FUNCTIONS
4-4
MEAN AND VARIANCE OF A CONTINUOUS RANDOM VARIABLE
4-5
CONTINUOUS UNIFORM DISTRIBUTION
4-6
NORMAL DISTRIBUTION
4-7
NORMAL APPROXIMATION TO THE BINOMIAL AND POISSON DISTRIBUTIONS
4-8
CONTINUITY CORRECTIONS TO IMPROVE THE APPROXIMATION
4-9
EXPONENTIAL DISTRIBUTION
5-1
TWO DISCRETE RANDOM VARIABLES
5-10
CHEBYSHEVS INEQUALITY (CD ONLY)
5-2
MULTIPLE DISCRETE RANDOM VARIABLES
5-3
TWO CONTINUOUS RANDOM VARIABLES
5-4
MULTIPLE CONTINUOUS RANDOM VARIABLES
5-5
COVARIANCE AND CORRELATION
5-6
BIVARIATE NORMAL DISTRIBUTION
5-7
LINEAR COMBINATIONS OF RANDOM VARIABLES
5-8
FUNCTIONS OF RANDOM VARIABLES (CD ONLY)
5-9
MOMENT GENERATING FUNCTIONS (CD ONLY)
6-1
DATA SUMMARY AND DISPLAY
6-3
STEM-AND-LEAF DIAGRAMS
6-4
FREQUENCY DISTRIBUTIONS AND HISTOGRAMS
6-5
BOX PLOTS
6-6
TIME SEQUENCE PLOTS
6-7
PROBABILITY PLOTS
6-8
MORE ABOUT PROBABILITY PLOTTING (CD ONLY)
7-2
GENERAL CONCEPTS OF POINT ESTIMATION
7-3
METHODS OF POINT ESTIMATION
7-5
SAMPLING DISTRIBUTIONS OF MEANS
8-2
CONFIDENCE INTERVAL ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE KNOWN
8-3
CONFIDENCE INTERVAL ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE UNKNOWN
8-4
CONFIDENCE INTERVAL ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION
8-5
A LARGE-SAMPLE CONFIDENCE INTERVAL FOR A POPULATION PROPORTION
8-6
A PREDICTION INTERVAL FOR A FUTURE OBSERVATION
8-7
TOLERANCE INTERVALS FOR A NORMAL DISTRIBUTION
9-1
HYPOTHESIS TESTING
9-2
TESTS ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE KNOWN
9-3
TESTS ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE UNKNOWN
9-4
HYPOTHESIS TESTS ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION
9-5
TESTS ON A POPULATION PROPORTION
9-7
TESTING FOR GOODNESS OF FIT
10-3
INFERENCE FOR THE DIFFERENCE IN MEANS OF TWO NORMAL DISTRIBUTIONS, VARIANCES UNKNOWN
10-4
INFERENCE FOR THE DIFFERENCE IN MEANS OF TWO NORMAL DISTRIBUTIONS, VARIANCES UNKNOWN
10-5
INFERENCES ON THE VARIANCES OF TWO NORMAL POPULATIONS
10-6
INFERENCE ON TWO POPULATION PROPORTIONS
10-7
SUMMARY TABLE FOR INFERENCE PROCEDURES FOR TWO SAMPLES
10.2
INFERENCE FOR A DIFFERENCE IN MEANS OF TWO NORMAL DISTRIBUTIONS, VARIANCES KNOWN
11-11
CORRELATION
11-2
SIMPLE LINEAR REGRESSION
11-5
HYPOTHESIS TESTS IN SIMPLE LINEAR REGRESSION
11-7
PREDICTION OF NEW OBSERVATIONS
11-8
ADEQUACY OF THE REGRESSION MODEL
12-1
MULTIPLE LINEAR REGRESSION MODEL
12-2
MULTIPLE LINEAR REGRESSION MODEL
12-3
CONFIDENCE INTERVALS IN MULTIPLE LINEAR REGRESSION
12-5
MODEL ADEQUACY CHECKING
12-6
ASPECTS OF MULTIPLE REGRESSION MODELING
13-2
THE COMPLETELY RANDOMIZED SINGLE-FACTOR EXPERIMENT
13-4
RANDOMIZED COMPLETE BLOCK DESIGN
14-4
TWO-FACTOR FACTORIAL EXPERIMENTS
14-5
GENERAL FACTORIAL EXPERIMENTS
14-7
2k FACTORIAL DESIGNS
14-8
BLOCKING AND CONFOUNDING IN THE 2k DESIGN
14-9
FRACTIONAL REPLICATION OF THE 2k DESIGN
15-2
SIGN TEST
15-3
WILCOXON SIGNED-RANK TEST
15-4
WILCOXON RANK-SUM TEST
15-5
NONPARAMETRIC METHODS IN THE ANALYSIS OF VARIANCE
16-10
CUMULATIVE SUM CONTROL CHART
16-12
IMPLEMENTING SPC
16-5
x AND R OR S CONTROL CHARTS
16-6
CONTROL CHARTS FOR INDIVIDUAL MEASUREMENTS
16-7
PROCESS CAPABILITY
16-8
ATTRIBUTE CONTROL CHARTS
16-9
CONTROL CHART PERFORMANCE
33-3
THE RANDOM-EFFECTS MODEL
Textbook Solutions for Applied Statistics and Probability for Engineers
Chapter 16-7 Problem 16-23
Question
16-23. Reconsider 16-12. The viscosity specifications are at 500 25. Calculate estimates of the process capability ratios PCR and PCRk for this process and provide an interpretation.
Solution
The first step in solving 16-7 problem number 11 trying to solve the problem we have to refer to the textbook question: 16-23. Reconsider 16-12. The viscosity specifications are at 500 25. Calculate estimates of the process capability ratios PCR and PCRk for this process and provide an interpretation.
From the textbook chapter PROCESS CAPABILITY you will find a few key concepts needed to solve this.
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full solution
full solution
Title
Applied Statistics and Probability for Engineers 3
Author
Douglas C. Montgomery, George C. Runger
ISBN
9780471204541
16-23. Reconsider 16-12. The viscosity specifications are at 500 25. Calculate estimates
Chapter 16-7 textbook questions
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Chapter 16: Problem 16 Applied Statistics and Probability for Engineers 3
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Chapter 16: Problem 16 Applied Statistics and Probability for Engineers 3
Reconsider Exercise 16-1. Use the revised control limits and process estimates. (a) Estimate PCR and PCRk. Interpret these ratios. (b) What percentage of defectives is being produced by this process?
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Chapter 16: Problem 16 Applied Statistics and Probability for Engineers 3
Reconsider Exercise 16-2, where the specification limits are 14.50 0.50. (a) What conclusions can you draw about the ability of the process to operate within these limits? Estimate the percentage of defective items that will be produced. (b) Estimage PCR and PCRk. Interpret these ratios.
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Chapter 16: Problem 16 Applied Statistics and Probability for Engineers 3
Reconsider Exercise 16-3. Using the process estimates, what is the fallout level if the coded specifications are 10 5 mm? Estimate PCR and interpret this ratio.
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Chapter 16: Problem 16 Applied Statistics and Probability for Engineers 3
16-17. A normally distributed process uses 85% of the specification band. It is centered at the nominal dimension, located halfway between the upper and lower specification limits.
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Chapter 16: Problem 16 Applied Statistics and Probability for Engineers 3
Reconsider Exercise 16-5. Suppose that the quality characteristic is normally distributed with specification at 220 40. What is the fallout level? Estimate PCR and PCRk and interpret these ratios
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Chapter 16: Problem 16 Applied Statistics and Probability for Engineers 3
Reconsider Exercise 16-6. Suppose that the variable is normally distributed with specifications at 220 50. What is the proportion out of specifications? Estimate and interpret PCR and PCRk
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Chapter 16: Problem 16 Applied Statistics and Probability for Engineers 3
. Reconsider Exercise 16-4(a). Assuming that both charts exhibit statistical control and that the process specifications are at 20 5, estimate PCR and PCRk and interpret these ratios
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Chapter 16: Problem 16 Applied Statistics and Probability for Engineers 3
Reconsider Exercise 16-8. Given that the specifications are at 6.0 1.0, estimate PCR and PCRk and interpret these ratios
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Chapter 16: Problem 16 Applied Statistics and Probability for Engineers 3
Reconsider 16-7(b). What are the natural tolerance limits of this process?
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Chapter 16: Problem 16 Applied Statistics and Probability for Engineers 3
16-23. Reconsider 16-12. The viscosity specifications are at 500 25. Calculate estimates of the process capability ratios PCR and PCRk for this process and provide an interpretation.
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