Problem 13-8 A shirt manufacturer buys cloth by the 100 yard roll from a supplie
ID: 426975 • Letter: P
Question
Problem 13-8 A shirt manufacturer buys cloth by the 100 yard roll from a supplier. For setting up a control chart to manage the irregularities (e.g., loose threads and tears) the following data was collected from a sample provided by the supplier. SAMPLE IRREGULARITIES 2 3 5 4 5 6 5 6 2 4 1 2 3 4 5 67 8 9 10 a. Determine the?, sp, UCL and LCL for a c-chart with z = 2·(Leave no cells blank-be certain to enter o" wherever required. Round your answers to 2 decimal places.) UCL LCL b. Suppose the next five rolls from the supplier had four, four, four, three, and five irregularities. Is the supplier process under control? Yes NoExplanation / Answer
Solution:
Given: z = 2,
(a) Process mean, c-bar = Number of Irregularities / Total number of samples
c-bar = (2 + 3 + 5 + 4 + 5 + 6 + 5 + 6 + 2 + 4) / 10
c-bar = 42 / 10
c-bar = 4.2
Sp is calculated as;
Sp = SQRT (c-bar)
Sp = SQRT (4.2)
Sp = 2.05
The control chart limits of the process are calculated as;
UCL = c-bar + [z x SQRT (c-bar)]
UCL = 4.2 + [2 x SQRT (4.2)]
UCL = 8.30
LCL = c-bar - [z x SQRT (c-bar)]
LCL = 4.2 - [2 x SQRT (4.2)]
LCL = 0.10
(b) If the next five rolls from the supplier had 4, 4, 4, 3 and 5 irregularities, the supplier process WILL be under control because the Upper Control Limit (UCL) of the process is 8.30 and Lower Control Limit (LCL) is 0.10. The irregularities - 4, 4, 4, 3 and 5 lie within the control limits of the process.
Answer: Yes