Concordia UniversityINSE 6220 — Fall 2014Advanced Statistical Approaches to QualityAssignment #1 – Due Date: October 10, 2014 Q.1 Let a random variable X denote the number of medication errors for a patient at a hospital. Experience shows that it occurs between 0 and 3 (inclusive) with the following probabilities: (a) Plot the probability mass function.(b) Calculate the mean μ and varia
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Concordia University
INSE 6220 — Fall 2014
Advanced Statistical Approaches to Quality
Assignment #1 – Due Date: October 10, 2014
Q.1 Let a random variable X denote the number of medication errors for a patient at a hospital. Experience shows that it occurs between 0 and 3 (inclusive) with the following probabilities:
(a) Plot the probability mass function.
(b) Calculate the mean μ and variance of the random variable X.
(c) Calculate the probability that X falls in the interval (μ − 6, μ + 6,).
Q.2 A quality control engineer is in charge of testing whether or not 90% of the Blue-ray disc players produced by his company conform to specifications. To do this, the engineer randomly selects a batch of 12 Blue-ray players from each day’s production. The day’s production is acceptable provided no more than 1 Blue-ray player fails to meet specifications. Otherwise, the entire day’s production has to be tested.
(A) What is the probability that the engineer incorrectly passes a day’s production as acceptable if only 80% of the day’s Blue-ray players actually conform to specification?
(b) What is the probability that the engineer unnecessarily requires the entire day’s production to be tested if in fact 90% of the Blue-ray players conform to specifications?
Q.3 A product-fill operation produces net weights that are normally distributed with mean μ = 8.06 ounces and standard deviation σ = 0.37 ounces.
(a) Estimate the percent of the containers that have a net weight less than 7.08 ounces.
(b) What is the probability that a sample of nine randomly selected containers will have an average net weight less than 7.08 ounces?
Q.4 An engineer wants to measure the bias in a pH meter. She uses the meter to measure the pH in 15 neutral substances (pH = 7.0) and obtains the following data:
7.04 7.0 7.03 7.01 6.97 7.00 6.95 7.00 6.99 7.04 6.97 7.07 7.04 6.97 7.08
(a) Check the assumption of normality for the pH meter data.
(b) Is there sufficient evidence to support the claim that the pH meter is not correctly calibrated at the 5% level of significance..
(c) Find the 95% two-sided confidence interval to estimate the mean. Comment on your result.
Q.5 A quality control supervisor in a cannery knows that the exact amount each can contains will vary, since there are certain uncontrollable factors that affect the amount of fill. Suppose regulatory agencies specify that the standard deviation of the amount of fill should be less that 0.1 ounce. The quality control supervisor sampled 10 cans and measured the amount of fill in each. The resulting data measurements are:
7.96 7.90 7.98 8.01 7.97 7.96 8.03 8.02 8.04 8.02
(a) Check the assumption of normality for the amount of fill data.
(b) Does this information, at the 0.05 level of significance, provide sufficient evidence to indicate that the standard deviation of the fill measurements is less than 0.1 ounce? Then, calculate the p-value.
(b) The Sample mean of the 10 can sample is
Q6 . The management of a luxurious hotel is concerned with increasing the return rate for hotel guests. One aspect of first impressions by guests relates to the time it takes to deliver the guest’s luggage to the room after check-in to the hotel. A random sample of 20 deliveries on a particular day was selected in Wing A of the hotel and a random sample of 20 deliveries was selected in Wing B.
Wing A: 10.70, 9.89, 11.83, 9.04, 9.37, 11.68, 8.36, 9.76, 13.67, 8.96, 9.51, 10.85, 10.57, 11.06, 8.91, 11.79, 10.59, 9.13, 12.37, 9.91.
Wing B: 7.20, 6.68, 9.29, 8.95, 6.61, 8.53, 8.92, 7.95, 7.57, 6.38, 8.89, 10.03, 9.30, 5.28, 9.23, 9.25, 8.44, 6.57, 10.61, 6.77.
(a) Check the assumption of normality for both delivery time data.
(b) Was there a difference in the mean delivery time in the two wings on the hotel?. Test with _ = 0.05.
(c) Determine whether the variance in luggage delivery time is the same for Wing A and Wing B of the hotel at the = 0.05 level of significance.
(d) Assume that delivery times to Wing A and Wing B are two independent normal populations with unknown variances and respectively. Construct a 90% two-sided confidence interval on the ratio of the two standard deviations Comment on your result.
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Q7.The management of a bank has embarked on a program of statistical process control and has decided to use variable control charts to study the waiting time of customers during the peak noon to 1 p.m. lunch hour to detect special causes of variation. Four customers are selected during the one-hour period; the first customer to enter the bank every 15 minutes. Each set of four measurements makes up a subgroup (sample). Table I lists the waiting time (operationally defined as the time from when the customer enters the line until he or she begins to be served by the teller) for 20 days.
TABLE I
Waiting Time for Customers at a Bank.
(a) Construct a table that shows the waiting time data along with the sample means and sample ranges.
(b) Estimate the process mean and standard deviation.
(c) Construct the R- and the X-charts. Identify the out-of-control points using all Western Electric rules. If necessary,
revise your control limits, assuming that any samples that violate Western Electric rules can de discarded.
(d) Assuming that the waiting times are normally distributed and and that specifications are 5 ± 3 minutes, calculate
Hence we conclude the Sample points are in range of the Control Limits of the Chart and The variation is in normal range and is caused due to internal errors .There is no need of remodeling the Western Electric rules system process.
(a) Assuming that the waiting times are normally distributed and and that specifications are 5 ± 3 minutes, calculate the process capability index and the proportion of the process that will not meet specifications.
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