Question

Twenty samples with 100 units each were taken; with the following number of defectives in each respective sample: 11, 2, 7, 5, 6, 7, 8, 5, 3, 6, 4, 3, 5, 6, 2, 5, 0, 9, 10, and 8.

1. Calculate the center line, upper control limit, and lower control limit for a 3s p-chart. (RE: As your starting point, recall that p-charts represent percentages of defects for samples.)
2. Plot the points on the chart.
3. Comment on whether the process is stable enough to begin using these data for quality control purposes. (SHOW WORK IN A EXCEL FILE) - List the steps of how to do the work as well.

Answer 1

Answer:

Answer a.

Plot the number of samples, Defective units in each sample out of 100 units in each sample.

Calculate the proportion (p%) for each sample using below formula

p% = (Defective units / No. of units in each sample)*100

Samples	Defective units	No. of units in each sample	p (%)
1	11	100	0.110
2	2	100	0.020
3	7	100	0.070
4	5	100	0.050
5	6	100	0.060
6	7	100	0.070
7	8	100	0.080
8	5	100	0.050
9	3	100	0.030
10	6	100	0.060
11	4	100	0.040
12	3	100	0.030
13	5	100	0.050
14	6	100	0.060
15	2	100	0.020
16	5	100	0.050
17	0	100	0.000
18	9	100	0.090
19	10	100	0.100
20	8	100	0.080
Average of all 20 observations p% (p bar) or Central Line	0.056	5.60%

Central Line = CL = p bar = Average of all 20 observations p% = 0.056

Sample size (n) =	100
p bar =	0.056
z= no. of standard deviation from process average as it is to be calculated for 3σ	3

Standard Deviation (σ) = √[p bar * (1- p bar)]/n

σ = √[0.056 * (1- 0.056)]/100

σ = 0.0230

UCL (Upper Control Limit) = p bar+3σ = 0.056 + (3*0.0230) = 0.1250

LCL (Lower Control Limit) = p bar-3σ = 0.056 - (3*0.0230) = -0.0130

Answer b.

Make following table in Excel:

STEPS

In Excel, use following graph:

Select all data of the above table.

Click on “Insert” tab and then “Line”

Following chart will appear:

Answer c.

The process is stable for quality control purposes as it well within the UCL & LCL.

For getting the above chart use following steps:

STEPS

In Excel, use following graph:

Select all data of the above table.

Click on “Insert” tab and then “Line”