ISE235-HW2 - Solutions

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San Jose State University *

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235

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Industrial Engineering

Date

Jan 9, 2024

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pdf

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3

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1 ISE 235 Homework Assignment #2 – Solutions Problem #1: Exercise 6.19 (Exercise 6.41 of the 7 th Edition; Exercise 6.33 of the 6 th Edition; Exercise 5-33 of the 5 th Edition; 5-26 of the 4 th Edition). The exercise statement starts with, “ Control charts on X and R for samples of size n=5 are to be maintained on the tensile strength in pounds of a yarn. …..”. Note: For Part (b), treat the estimated mean and standard deviation as the true mean and true standard deviation. Then, use the technique of Standardization for Normal Distributions. Problem #2: Exercise 6.17 (Exercise 6.39 of the 7 th Edition; Exercise 6.31 of the 6 th Edition; Exercise 5-31 of the 5 th Edition; 5-24 of the 4 th Edition). The exercise statement starts with, “An X char has a center line of 100, uses three-sigma control limits, and is based on a sample size of four. …..” Note: We derived the formula – Equation (6.19) – in the class. The textbook has the same derivation (in section 6.2.6 and on page 238 of the 8 th Edition), although it has less detail. The derivation process requires the use of a common technique of Standardization of a Normal Random Variable. This technique can be found in all textbook on a first course on probability and statistics. This same technique is required for solving some of the other problems assigned in this HW and some future homework problems. Please review and master the technique.)
2 Problem #3: Exercise 6.30. (Exercise 6.55 of the 7 th Edition; Exercise 6.47 of the 6 th Edition; Exercise 5-47 of the 5 th Edition; 5-40 of the 4 th Edition). The exercise statement starts with, “ X and R charts with n = 4 are used to monitor a normally distributed quality characteristic. The control chart parameters are …..”. (This exercise illustrates the numerical process for developing the Operating Characteristic (OC) Curve of a control chart. An OC curve is simply a “Probability of Acceptance curve.”) Problem #4: and Exercise 6.31. (Exercise 6.56 of 7 th Edition; Exercise 6.48 of 6 th Edition; Exercise 5-48 of 5 th Edition; 5-41 of 4 th Edition). The exercise statement is, “ Consider the 𝑋 ̅ chart i n Exercise 6.55. Find the average run length for the chart.” Note: A more precise way of phrasing the question is the following: “What is the average run length for the chart to detect the shift to 790.”
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