Practice Problems for Exam1S09

Bus. 142

PRACTICE PROBLEMS EXAM # 1

Spring 2009

1. Given the following information answer the questions (carrying to two decimals):

SAMPLE NO 3 4 8.0 8.0 7.9 7.8 7.9 8.0 47.6 8.1 8.0 7.9 7.7 8.0 8.1 47.8

1 8.0 7.9 7.9 8.0 7.9 8.1 Sigma X = X-bar = Sigma X/n = Sigma X-bar = X-double-bar = Sigma X-bar/s = 47.8

2 8.2 8.0 8.0 8.0 8.0 7.9 48.1

5 8.3 7.9 7.9 7.8 8.0 8.1 48.0

R1 = R2 = R3 = R4 = R5 =

Sigma R = R-bar = Sigma R/s =

a) What is the value for the grand mean (X-double-bar)? b) What is the value for the average range (R-bar)? c) What is the value for n? d) What are the values for UCLX-bar , LCLX-bar, UCLR , LCLR ? e) Draw rough mean and range charts. f) Does the process appear to be in control? Explain your answer! g) If the control limits of the mean chart were previously established as 8.48 and 8.01 and the control limits of the range chart were 0.48 and 0.0, does the process appear to be in control or out of control? Explain!

Bus. 142

PRACTICE PROBLEMS EXAM # 1

Spring 2009

2. Checkout time at a supermarket is monitored using a mean and a range chart. Six samples of n = 20 observations have been obtained and the sample means and ranges have already been computed. Sample Mean Range 1 3.06 0.42 2 3.15 0.50 3 3.11 0.41 4 3.13 0.46 5 3.06 0.46 6 3.09 0.45 Calculate upper and lower control limits for the mean chart and the range chart. Draw each chart showing upper control limits, lower control limits, chart means, and sample values. Is the process in control? Explain! Answers: 1a) 1b) 1c) 1d) 1f) 7.98 0.32 6 UCLX-bar = 8.13, LCLX-bar = 7.83, UCLR = 0.64, LCLR = 0 The process appears to be in control since all means and all ranges fall within the control limits. 1g) We have reason to believe that the process may be out of control since the means for samples 2 and 5 are below the lower control limit and the range for sample 5 is above the upper control limit. 2) UCLX-bar = 3.18, LCLX-bar = 3.02, UCLR = 0.72, LCLR = 0.18. Yes,...