Piston rings for an automotive engine are produced by a forging process. We wish to monitor the inside diameter of the rings manufactured by this process, using an x̄ and an s control chart. Samples of size 8 are to be taken at regular intervals, and the sample means and standard deviations are computed and plotted on the charts in time order. The target values for the inside diameter are a mean of μ = 75 mm and a standard deviation of σ = 0.38 mm. A table containing control chart constants is reproduced below.
Q1: The center line for the three sigma x̄ control chart would be
Q2: The upper control limit for the x̄ control chart would be
Q3: The lower control limit for the x̄ control chart would be
Q4: The center line for the three sigma s chart would be
Q5: The lower control limit for the three sigma s chart would be
Q6: The upper control limit for the three sigma s chart would be
Q7:
Suppose we use a "run of nine" rule, that is, we declare the process out of control if nine consecutive points are all above the center line of the x̄ or if nine consecutive points are all below the center line of the x̄ chart. If the process is in statistical control, then with any particular collection of nine consecutive points, the probability that we declare the process out of control using this rule is (approximately):
I need help figuring out how to answer these questions. I don't just want the answers, I would like to know how to solve for them, as I am feeling completely lost. Please!!
The control limits for the chart are
CL=
UCL=+A2
LCL=-A2
A2=0.373 (From table of Control Chart constants)
Hence
Q1. Ans.:CL==75
Q2.Ans:UCL=+A2=75+(0.373x0.38)=75.14
Q3. Ans. LCL=-A2=75-(0.373x.38)=74.85
The control limits for s chart are:
CL=S
UCL=B4S
LCL=B3S
B4=1.815 and B3=0.185 (From table of Control Chart constants)
Q4. Ans: CL=S=0.38
Q5.Ans:LCL=B3S=0.185x0.38=0.073
Q6: Ans:UCL=B4S=1.815x0.38=0.6897
Piston rings for an automotive engine are produced by a forging process. We wish to monitor...
Parts manufactured by an injection-molding process are subjected to a compressive strength test. We wish to monitor the compressive strength of the parts manufactured by this process, using an x̄ and an s control chart. Samples of size 9 are to be taken at regular intervals, and their mean compressive strength (in psi = pounds per square inch) and standard deviation are plotted on the charts in time order. The target values for the compressive strengths are a mean of...
Smith and Johnson Industries has decided to use a p-Chart with 3-sigma control limits to monitor the proportion of defective galvanized pipes produced by their production process. The quality control manager randomly samples 150 galvanized pipes at 16 successively selected time periods and counts the number of defective galvanized pipes in the sample. Step 1 of 8: What is the Center Line of the control chart? Round your answer to three decimal places. Step 2 of 8: What value of...
8.4 14 *9. Suppose that we are using an T-chart with subgroups of size n - 5 in an idealized setting in which the data is Normally distributed with known mean μ and standard deviation σ. We know that σ,-sd(X)-4. Use also the facts that and Assume that the process is under control and that subgroups are indepen- dent. Suppose that 100 subgroup means are plotted onto the chart over the course of a day. (a) What is the probability...
The Money Pit Mortgage Company is interested in monitoring the performance of the mortgage process. Fifteen samples of five completed mortgage transactions each were taken during a period when the process was believed to be in control. The times to complete the transactions were measured. The means and ranges of the mortgage process transaction times, measured in days, are as follows: b. Sample123456789 10 11 12 13 14 15 Mean 5 103 7 8 13 14 9 9 9 5...
A gear has been designed to have a diameter of 3 inches. The standard deviation of the process is 0.3 inch. A control chart is shown. Each chart has horizontal lines drawn at the mean, μ, μ 2o, and at μ 3G. Determine if the process shown is in control or out of control. Explain Is the process in control or out of control? Select all that apply A. Out of control, because a point lies more than three standard...
A marathoner is now running his marathons with an average time of 3 hours, and 15 minutes, and a standard deviation of 15 minute and her times follow a normal distribution. What is the probability of the marathoner running a marathon time of exactly 2 hours and 58 minutes? 0.00 0.05 0.15 0.12 Which of the following would indicate a process has special causes of variation? A point is above the lower control limit and below the upper control limit...
better quality image O Is the process in control or out of control? Choose the correct answer below. A liquid-dispensing machine has been designed to fill bottles with 10 liter of liquid. The standard deviation of the process is 0.2 liter. A control chart is shown. The chart has horizontal lines drawn at the mean, H. att 20, and at 30. Determine if the process shown is in control or out of control. Explain. Liquid Dispenser Liquid dispensed (in ters)...
Use the following data for problems 7 and 9. The number of ounces of water is a water bottle is normally distributed with a mean of 16.9oz and a standard deviation of 0.25oz. What is the probability that a randomly selected water bottle will have exactly 16.8oz of water in it? 0.3446 0.6554 0.0000 0.2500 What is the probability that a randomly selected water bottle with have between 16.7oz and 17.18oz of water in it? 0.7500 0.3432 0.0000 0.6568 If...
Judy Holmes Industries has decided to use a p-Chart to monitor the proportion of defective castings produced by their production process. The control limits on these charts will be designed to include 95%95% of the sample proportions when the process is In Control. The operations manager randomly samples 400400 castings at 1616 successively selected time periods and counts the number of defective castings in the sample. Table Control Chart Copy Table Step 8 of 8 : You, acting as the...
A control chart is used for monitoring a process mean ( 7 ) that is normally distributed with a mean of u and a standard deviation of o, and the sample size is n = 5. A 3-sigma limit (u +30z) is used as control limits. Two decision rules are given here. Rule 1: If one or more of the next seven samples yield values of the sample average that fall outside the control limits, conclude that the process is...