Question

The quality control department of a company maintains ‘c’ chart to assess the quality of laptops. In this process, twenty laptops are examined randomly. The number of nonconformities observed per laptop is given in the table.

Laptop number	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Number of nonconformities	1	3	7	4	10	6	1	5	4	3	6	4	2	7	4	2	9	8	5	2

 

Based on the data, the upper control limit for the ‘c’ chart is ________ (up to two decimal places). 

Answer 1

Concept:

Upper control limit,

\(UCL = \overline{C} + 3\sqrt{\overline{C}}\)

Where,

\(Control\ limit\ CL = \overline{C} =\frac{∑ C}{n}\)

where, C = Number of noncoformities, n = number of samples

Calculation:

Given:

∑C = sum of non-conformities.

∑C = 93

n = 20

\(Control\ limit\ CL = \overline{C} =\frac{∑ C}{n}=\frac{93}{20}\)

\( \overline{C} = 4.65\)

\(UCL =4.65+3\times\sqrt{4.65}\)

UCL = 11.119

UCL = 11.12