Applied Statistics and Probability for Engineers 6th Edition solutions

Applied Statistics and Probability for Engineers 6
Problem 28E Suppose that a quality characteristic is normally distributed with specifications at 100 20. The process standard deviation is 6. (a) Suppose that the process mean is 100. What are the natural tolerance limits? What is the fraction defective? Calculate PCR and PCRk and interpret these

Applied Statistics and Probability for Engineers 6
Problem 29E Suppose that a quality characteristic is normally distributed with specifications from 20 to 32 units. (a) What value is needed for ? to achieve a PCR of 1.5? (b) What value for the process mean minimizes the fraction defective? Does this choice for the mean depend on the value of ? ?

Applied Statistics and Probability for Engineers 6
Problem 30E Suppose that a quality characteristic is normally distributed with specifications from 10 to 30 units. The process standard deviation is 2 units. (a) Calculate the natural tolerance limits, fraction defective, PCR, and PCRk when the process mean is 20. (b) Suppose that the process mean

Applied Statistics and Probability for Engineers 6
Problem 31E 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?

Applied Statistics and Probability for Engineers 6
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. (a) Estimate PCR and \(P C R_k\). Interpret these ratios. (b) What fallout level (fraction defective) is produced?

Applied Statistics and Probability for Engineers 6
Reconsider Exercise 15-1. Suppose that the quality characteristic is normally distributed with specification at \(220 \pm 40\). What is the fallout level? Estimate \(P C R \text { and } P C R_{k}\) and interpret these ratios. Equation Transcription: Text Transc

Applied Statistics and Probability for Engineers 6
Reconsider Exercise 15-2 in which the specification limits are \(14.50 \pm 0.50\) (a) What conclusions can you draw about the ability of the process to operate within these limits? Estimate the percentage of defective items that is produced. (b) Estimate \(P C R \text { and } P C R_{k}\). Interpr

Applied Statistics and Probability for Engineers 6
Reconsider Exercise 15-3. Suppose that the variable is normally distributed with specifications at \(220 \pm 50\). What is the proportion out of specifications? Estimate and interpret \(P C R \text { and } P C R_{k}\). Equation Transcription: Text Transcription

Applied Statistics and Probability for Engineers 6
Reconsider Exercise 15-4(a). Assuming that both charts exhibit statistical control and that the process specifications are at \(20 \pm 5\), estimate \(P C R \text { and } P C R_{k}\) and interpret these ratios. Equation Transcription: Text Transcription: 20 \pm 5 PCR

Applied Statistics and Probability for Engineers 6
Reconsider the diameter measurements in Exercise 15-7. Use the revised control limits and process estimates. (a) Estimate \(P C R \text { and } P C R_{k}\). Interpret these ratios. (b) What percentage of defectives is being produced by this process? Equation Transcription:

Applied Statistics and Probability for Engineers 6
Reconsider the copper-content measurements in Exercise 15-8. Given that the specifications are at \(6.0 \pm 1.0\), estimate \(P C R \text { and } P C R_{k}\) and interpret these ratios. Equation Transcription: Text Transcription: 6.0 \pm 1.0 PCR and PCR

Applied Statistics and Probability for Engineers 6
Reconsider the pull-strength measurements in Exercise 15-9. Estimate the fallout level if the specifications are \(16 \pm 5\). Estimate \(P C R\) and interpret this ratio. Equation Transcription: Text Transcription: 220 \pm 50 PCR

Applied Statistics and Probability for Engineers 6
Reconsider the syringe lengths in Exercise 15-10. Suppose that the specifications are set at \(4.90 \text { and } 5.00\) (a) Estimate the process standard deviation. (b) Calculate \(P C R \text { and } P C R_{k}\) for the process. Equation Transcription: T

Applied Statistics and Probability for Engineers 6
Reconsider the hardness measurements in Exercise 15-19. Suppose that the specifications are \(45 \text { to } 60\). (a) Estimate the process standard deviation. (b) Calculate \(P C R \text { and } P C R_{k}\) for the process. Equation Transcription: Tex

Applied Statistics and Probability for Engineers 6
Reconsider the viscosity measurements in Exercise 15-22. The specifications are \(500 \pm 25\). Calculate estimates of the process capability ratios PCR and \(P C R_{k}\) for this process and provide an interpretation.

Applied Statistics and Probability for Engineers 6
Problem 43E Suppose that a quality characteristic is normally distributed with specifications at 120 20. The process standard deviation is 6.5. (a) Suppose that the process mean is 120. What are the natural tolerance limits? What is the fraction defective? Calculate PCR and PCRk and interpret thes

Applied Statistics and Probability for Engineers 6
Problem 44E Suppose that a quality characteristic is normally distributed with specifications at 150 20. Natural tolerance limits for the process are 150 18. (a) Calculate the process standard deviation. (b) Calculate PCR and PCRk of the process. Calculate the percentage of the specification widt

Applied Statistics and Probability for Engineers 6
An \(\bar{X}\) control chart with 3-sigma control limits and subgroup size n=4 has control limits \(U C L=28.8\) and \(L C L= 24.6\). The process specification limits are (24,32). (a) Estimate the process standard deviation. (b) Calculate \(P C R\) and \(P C R_k\) for the process.

Applied Statistics and Probability for Engineers 6
A control chart for individual observations has 3-sigma control limits UCL=1.80 and LCL=1.62. The process specification limits are (1.64, 1.84). (a) Estimate the process standard deviation. (b) Calculate PCR and \(P C R_{\mathrm{k}}\) for the process.

Applied Statistics and Probability for Engineers 6
A process mean is centered between the specification limits and \(P C R=1.33\). Assume that the process mean increases by \(1.5 \sigma\). (a) Calculate \(P C R \text { and } P C R_{k}\) for the shifted process. (b) Calculate the estimated fallout from the shifted process and compare your result t

Applied Statistics and Probability for Engineers 6
The \(P C R \) for a measurement is 1.5 and the control limits for an \(\bar{X}\) chart with \(n=4 \) are 24.6 and 32.6. (a) Estimate the process standard deviation \(\sigma\). (b) Assume that the specification limits are centered around the process mean. Calculate the specification limits.