56. The construction of the p chart described in this chapter requires specification of both UCL and LCL levels. Is the LCL meaningful in this context? In particular, what does it mean when an observed value of p is less than the LCL? If only the UCL is used to signal an out-of-control condition, should the calculation of the UCL be modified in any way? (Hint: The definition of the Type 1 error probability, a, will be different. The hypothesis test for determining if the process is in control is one-sided rather than two-sided.)

50 motor generators are inspected per day from a stable process. The best estimate of the fraction of nonconforming is 0.076. Determine the centeral line and control limits. On a particular day, 5 nonconforming generators were discovered. Is this process in or out of control? For the information given in the problem, construct a np-chart

7.  The school board is trying to evaluate a new math program introduced to​ second-graders in five elementary schools across the county this year. A sample of the student scores on standardized math tests in each elementary school yielded the following​ data:                                                       School No. of Test Errors A 48   B 21   C 32   D 40   E 52     For the test​ errors, the c​-chart with control limits that contain​ 99.73% of the random variation in test scores​ is: _____ Part 2 UCLc​= _______ ​(round your response to two decimal​ places). LCLc​= _______ ​(round your response to two decimal​ places). What does the chart tell you? Has the new math program been effective?

K The school board is trying to evaluate a new math program introduced to second-graders in five elementary schools across the county this year. A sample of the student scores on standardized math tests in each elementary school yielded the following data: School A 4 C E No. of Test Errors 48 21 32 40 52 For the test errors, the c-chart with control limits that contain 99.73% of the random variation in test scores is: UCL = errors (round your response to two decimal places).

Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. Use Exhibit 13.7. To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows. Use three-sigma control limits. SAMPLE NUMBER 1 H234STO OHN345 5 6 7 8 9 10 11 ΕΕΕΕΕ 12 13 14 15 READINGS (IN OHMS) 1097 1094 978 1013 976 1016 977 986 983 1026 988 1014 991 1030 995 991 1023 1014 982 970 1030 1027 1017 1004 995 982 994 1008 1001 1004 995 1015 1026 978 1017 984 995 1007 988 970 1004 1028 1019 983 990 1026 1017 1010 987 994 1030 974 995 1012 1016 1011 983 1018 981 1020

The results of inspection of DNA samples taken over the past 10 days are given below. Sample size is 100.                               Day 1 2 3 4 5 6 7 8 9 10 Defectives 3 5 5 6 3 3 0 4 6 2 ​a) The upper and lower 3 3​-sigma control chart limits​ are: UCLp ​= ___      LCLp ​=___

Boxes of Honey-Nut Oatmeal are produced to contain 15.0 ounces, with a standard deviation of 0.10 ounce. For a sample size of 49, the 3-sigma x chart control limits are: Upper Control Limit (UCL) = | ounces (round your response to two decimal places). Lower Control Limit (LCL;) = ounces (round your response to two decimal places).

An e-commerce website has received some complaints on Billing errors. Managers ask the accounting department to monitor the shipping process and make sure of the quality in their process. To monitor the process, for 10 consecutive weeks, they look into the first 100 shipments and count the number of Billing errors as shown in table below: 45 52 6 3 63 7 8 9 10 1 6 1 2 Construct a two-sigma limit control chart to show whether the shipping process in this e-commerce firm needs any improvement or performs at an acceptable level. (Round your answer to three decimal places.) Week 1 2 3 Number of Billing errors. 5 1 3 Upper Control Limit Lower Control Limit

A metal fabricator produces connecting rods with an outer diameter that has a 1 ± 0.04 inch specification. A machine operator takes several sample measurements over time and determines the sample mean outer diameter to be 1.003 inches with a standard deviation of 0.020 inch. Calculate the process capability index.