Examine the Statistical Process Control outputs below. Answer the following questions.a. What is the sample size?b. What is the number of samples?c. What is the mean of sample 8; what is the range of sample 10?d. Is this process in control? Explain-a simple Yes or No is insufficient.e. What additional steps should the quality assurance team take? Mean Range UCL (Upper control limit) 12.6856 1.0193 CL (Center line) 12.36 0.67 LCL (Lower control limit) 10.0344 0 Sample Number Item 1 Item 2 Item 3 Item 4 Mean Range Sample 1 12.2 12.6 12 12.1 12.225 0.6 Sample 2 11.9 12.5 12.4 12.7 12.375 0.8 Sample 3 12 12.2 12.9 13.1 12.55 1.1 Sample 4 12.5 12.5 12.4 12.8 12.55 0.4 Sample 5 12.2 12.8 12.7 12 12.425 0.8 Sample 6 12.1 12.5 11.8 12.3 12.175 0.7 Sample 7 12.3 12.4 12.8 12.4 12.475 0.5 Sample 8 12 12.1 12.4 12.2 12.175 0.4 Sample 9 12.1 12.8 12.4 11.9 12.3 0.9 Sample 10 12.6 12.4 12.1 12.3 12.35 0.5 \begin{array}{|l|l|l|l|l|l|l|}\hline & & ext { Mean } & & ext { Range }\ ext { UCL (Upper control limit) } & & 12.6856 & & 1.0193\\hline ext { CL (Center line) } & & 12.36 & & 0.67\ ext { LCL (Lower control limit) } & & 10.0344 & & 0\ ext { Sample Number } & ext { Item 1 } & ext { Item 2 } & ext { Item 3} & ext { Item 4} & ext { Mean } & ext { Range }\\hline ext { Sample 1 } & 12.2 & 12.6 & 12 & 12.1 & 12.225 & 0.6 \ ext { Sample 2 } & 11.9 & 12.5 & 12.4 & 12.7 & 12.375 & 0.8 \ ext { Sample 3 } & 12 & 12.2 & 12.9 & 13.1 & 12.55 & 1.1 \ ext { Sample 4 } & 12.5 & 12.5 & 12.4 & 12.8 & 12.55 & 0.4 \ ext { Sample 5 } & 12.2 & 12.8 & 12.7 & 12 & 12.425 & 0.8 \ ext { Sample 6 } & 12.1 & 12.5 & 11.8 & 12.3 & 12.175 & 0.7 \ ext { Sample 7 } & 12.3 & 12.4 & 12.8 & 12.4 & 12.475 & 0.5 \ ext { Sample 8 } & 12 & 12.1 & 12.4 & 12.2 & 12.175 & 0.4 \ ext { Sample 9 } & 12.1 & 12.8 & 12.4 & 11.9 & 12.3 & 0.9 \ ext { Sample 10 } & 12.6 & 12.4 & 12.1 & 12.3 & 12.35 & 0.5 \\hline\end{array} UCL (Upper control limit) CL (Center line) LCL (Lower control limit) Sample Number Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 Sample 10 Item 1 12.2 11.9 12 12.5 12.2 12.1 12.3 12 12.1 12.6 Mean 12.6856 12.36 10.0344 Item 2 12.6 12.5 12.2 12.5 12.8 12.5 12.4 12.1 12.8 12.4 Item 3 12 12.4 12.9 12.4 12.7 11.8 12.8 12.4 12.4 12.1 Range 1.0193 0.67 0 Item 4 12.1 12.7 13.1 12.8 12 12.3 12.4 12.2 11.9 12.3 Mean 12.225 12.375 12.55 12.55 12.425 12.175 12.475 12.175 12.3 12.35 Range 0.6 0.8 1.1 0.4 0.8 0.7 0.5 0.4 0.9 0.5

Question

Examine the Statistical Process Control outputs below. Answer the following questions.a. What is the sample size?b. What is the number of samples?c. What is the mean of sample 8; what is the range of sample 10?d. Is this process in control? Explain-a simple Yes or No is insufficient.e. What additional steps should the quality assurance team take?    Mean   Range   UCL (Upper control limit)  12.6856 1.0193  CL (Center line)  12.36 0.67  LCL (Lower control limit)  10.0344 0  Sample Number   Item 1   Item 2   Item 3  Item 4  Mean   Range   Sample 1  12.2 12.6 12 12.1 12.225 0.6  Sample 2  11.9 12.5 12.4 12.7 12.375 0.8  Sample 3  12 12.2 12.9 13.1 12.55 1.1  Sample 4  12.5 12.5 12.4 12.8 12.55 0.4  Sample 5  12.2 12.8 12.7 12 12.425 0.8  Sample 6  12.1 12.5 11.8 12.3 12.175 0.7  Sample 7  12.3 12.4 12.8 12.4 12.475 0.5  Sample 8  12 12.1 12.4 12.2 12.175 0.4  Sample 9  12.1 12.8 12.4 11.9 12.3 0.9  Sample 10  12.6 12.4 12.1 12.3 12.35 0.5 \begin{array}{|l|l|l|l|l|l|l|}\hline & & 	ext { Mean }  & &  	ext { Range }\	ext { UCL (Upper control limit) } & & 12.6856 & & 1.0193\\hline	ext { CL (Center line) } & & 12.36 & & 0.67\	ext { LCL (Lower control limit) } & & 10.0344 & & 0\	ext { Sample Number } & 	ext { Item 1 } & 	ext { Item 2 } & 	ext { Item 3} & 	ext { Item 4} & 	ext { Mean }  &  	ext { Range }\\hline 	ext { Sample 1 }  &  12.2  &  12.6  &  12  &  12.1  &  12.225  &  0.6 \	ext { Sample 2 }  &  11.9  &  12.5  &  12.4  &  12.7  &  12.375  &  0.8 \	ext { Sample 3 }  &  12  &  12.2  &  12.9  &  13.1  &  12.55  &  1.1 \	ext { Sample 4 }  &  12.5  &  12.5  &  12.4  &  12.8  &  12.55  &  0.4 \	ext { Sample 5 }  &  12.2  &  12.8  &  12.7  &  12  &  12.425  &  0.8 \	ext { Sample 6 }  &  12.1  &  12.5  &  11.8  &  12.3  &  12.175  &  0.7 \	ext { Sample 7 }  &  12.3  &  12.4  &  12.8  &  12.4  &  12.475  &  0.5 \	ext { Sample 8 }  &  12  &  12.1  &  12.4  &  12.2  &  12.175  &  0.4 \	ext { Sample 9 }  &  12.1  &  12.8  &  12.4  &  11.9  &  12.3  &  0.9 \	ext { Sample 10 }  &  12.6  &  12.4  &  12.1  &  12.3  &  12.35  &  0.5 \\hline\end{array}  UCL (Upper control limit)   CL (Center line)   LCL (Lower control limit)   Sample Number   Sample 1   Sample 2   Sample 3   Sample 4   Sample 5   Sample 6   Sample 7   Sample 8   Sample 9   Sample 10  ​  Item 1  12.2 11.9 12 12.5 12.2 12.1 12.3 12 12.1 12.6 ​  Mean  12.6856 12.36 10.0344  Item 2  12.6 12.5 12.2 12.5 12.8 12.5 12.4 12.1 12.8 12.4 ​  Item 3 12 12.4 12.9 12.4 12.7 11.8 12.8 12.4 12.4 12.1 ​  Range  1.0193 0.67 0  Item 4 12.1 12.7 13.1 12.8 12 12.3 12.4 12.2 11.9 12.3 ​  Mean  12.225 12.375 12.55 12.55 12.425 12.175 12.475 12.175 12.3 12.35 ​  Range  0.6 0.8 1.1 0.4 0.8 0.7 0.5 0.4 0.9 0.5 ​ ​

Sarah Douglas · Accepted Answer

Final Answer : The sample size is 4; ten samples were taken. The mean of sample 8 is 12.175; the range of sample 10 is 0.5. This chart is built on 2-sigma limits, so the probability of a false signal is about 4.5%. The process is not in control-while all means are within limits, the range for sample 3 is too large. Investigate for assignable cause and eliminate that cause.

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