IE 431
Practice Exercises 4
Industrial Engineering Department
Faculty of Engineering, King Abdulaziz University
IE 431: Industrial Quality Control
Practice Exercises # 4
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IE 431
Practice Exercises 4
1) A company that manufactures oil seals found the population mean to be
49.15 mm (1.935 in.), the population standard deviation to be 0.51 mm
(0.020 in.), and the data to be normally distributed. If the internal diameter
of the seal is below the lower specification limit of 47.80 mm, the part is
reworked. However, if it is above the upper specification limit of 49.80
mm, the seal is scrapped.
a) What percentage of the seals is reworked? What percentage is
scrapped?
b) For various reasons, the process average is changed to 48.50 mm.
With this new mean or process center, what percentage of the seals
is reworked? What percentage is scrapped? If rework is economically
feasible, is the change in the process center a wise decision?
2) Control charts for ̅
X R are to be established on a certain dimension part,
measured in millimeters. Data were collected in subgroup sizes of 6 and
are given below.
a) Determine the trial central line and control limits.
b) Assume assignable causes and revise the central line and limits.
c) Calculate is the process capability.
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IE 431
Practice Exercises 4
3) Control charts for ̅
X and s are to be established on the Brinell hardness of
hardened tool steel in kilograms per square millimeter. Data for subgroup
sizes of 3 are shown below.
a) Determine the trial central line and control limits for the ̅
X and s charts.
b) Assume that the out-of-control points have assignable causes.
Calculate the revised limits and central line.
4) Determine the trial central line and control limits for a moving-average and
moving-range chart using a time period of 3. Data in liters are as follows:
4.56, 4.65, 4.66, 4.34, 4.65, 4.40, 4.50, 4.55, 4.69, 4.29, 4.58, 4.71, 4.61,
4.66, 4.46, 4.70, 4.65, 4.61, 4.54, 4.55, 4.54, 4.54, 4.47, 4.64, 4.72, 4.47,
4.66, 4.51, 4.43, and 4.34. Are there any out-of-control points?
5) An X and MR chart is to be maintained on the pH value for the swimming
pool water of a leading motel. One reading is taken each day for 30 days.
Data are 7.8, 7.9, 7.7, 7.6, 7.4, 7.2, 6.9, 7.5, 7.8, 7.7, 7.5, 7.8, 8.0, 8.1,
8.0, 7.9, 8.2, 7.3, 7.8, 7.4, 7.2, 7.5, 6.8, 7.3, 7.4, 8.1, 7.6, 8.0, 7.4, and 7.0.
a) Plot the data on graph paper.
b) Determine the trial central line and limits, and evaluate the variation.
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IE 431
Practice Exercises 4
6) Determine the process capability of cypress bark bags in kilograms for
the data below. Also determine the Cp and Cpk for a USL of 130 kg and
an LSL of 75 kg.
7) Determine an EWMA chart for Exercise 2, using λ = 0.10 and λ = 0.20.
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