Question

The following data represent samples that were taken on 10 separate days. Each day has a varying sample size and the number of defects for the items sampled is listed. We want to see if this process is consistent and in control.

Day	Sample Size	Defects
1	100	6
2	110	4
3	190	10
4	190	7
5	240	15
6	255	8
7	105	3
8	175	6
9	245	22
10	265	27

a. Find the UCL.

b. Find the LCL.

c. Is the process in control? Why/why not?

Answer 1

Answer:-

Given That:-

The data represent samples that were taken on 10 separate days. Each day has a varying sample size and the number of defects for the items sampled is listed. We want to see if this process is consistent and in control.

Form given data

* The following data representation Samples that were taken on 10 separate days.

* Each day has a varying sample size and the number of defects for the items sampled is listed.

* We will use P chart (control for Proportion) to check for process in constant or not.

Day	Sample Size	Defects	Proportion of defects for 10 separate days.
1	100	6	6/100 = 0.062
2	110	4	4/110 = 0.036
3	190	10	10/190 = 0.052
4	190	7	7/190 = 0.036
5	240	15	15/240 = 0.062
6	255	8	8/255 = 0.031
7	105	3	3/105 = 0.028
8	175	6	6/175 = 0.034
9	245	22	22/245 = 0.089
10	265	27	27/265 = 0.101

* Center line, = 0.533/10

= 0.0533

Standard deviation of

=  

=

sd(P) = 0.7103

(a)

Find the UCL:

UCL = P + 3 * sd(P) = 0.0533 + 3*0.7103

= 2.1842

   UCL = 2.1842

(b)

Find the LCL:

LCL = P - 3 * sd(P) = 0.0533 - 3*0.7103 = -2.0776

LCL = 0 [The Proportion cannot be negative value]

(c)

Is the process in control? Why/why not

As all the sample Proportion of defectives are between LCL and UCL the process is in control.