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**Please answer the question in the format listed below for each part. Please nu

ID: 375191 • Letter: #

Question

**Please answer the question in the format listed below for each part. Please number/letter answers. Provide explaination; if possible. Check numbers for accuracy.**

Ten samples of 15 parts each were taken from an ongoing process to establish a p-chart for control. The samples and the number of defectives in each are shown in the following table NUMBER OF DEFECTIVE ITEMS IN THE SAMPL SAMPLE n 1 15 2 15 3 15 4 15 5 15 6 15 715 8 15 9 15 10 15 a. Determine the P, S UCL and LCL for a p-chart of 95 percent confidence (1.96 standard deviations). (Leave no cells blank-be certain to enter "o" wherever required. Round your answers to 3 decimal places.) Sp UCL LCL b. What comments can you make about the process? O Process is out of statistical control O Process is in statistical control

Explanation / Answer

The appropriate control chart to use check whether number of defective items in samples are within control limits or not.

Here , Average number of defectives per sample = ( 0 + 2+ 1+1+1 +3 +1 +0+2+1 ) /10 =12/10 = 1.2

Hence proportion of defectives per sample = pbar = 1.2/15 = 0.08

Sample size = n = 15

Standard deviation of p chart = Sp = Square root ( pbar x ( 1 – pbar)/n)= Square root ( 0.08 x 0.92/15) = 0.07

Upper Control Limit = Pbar + Z.Sp = 0.08 + 1.96 x 0.07 = 0.08 + 0.137 = 0.217

Lower Control Limit = Maximum value ( 0, Pbar – Z.Sp) = Maximum value ( 0 , 0.08 – 0.137 ) = Maximum value ( 0 , - 0.057) = 0

Pbar = 0.08

Sp = 0.07

UCL = 0.217

LCL = 0

Since maximum permissible proportion of defectives is 0.217 ( value of UCL) , maximum number of defectives permissible in a sample of 15 will be

= 0.217 x 15 = 3.255

Since maximum value of number of defective items in sample is 3 which is less than 3.255, we can conclude that the process is in control

ANSWER : PROCESS IS IN STATISTICAL CONTROL

Pbar = 0.08

Sp = 0.07

UCL = 0.217

LCL = 0