Question

Work Sampling Exercise This study is focusing on machine operations. Using the following observed data, machine setup 2 rna ashinon fdemels fer h ihine idle Find the adequate sample sizes to make the occurrence probabilities of idle and setup time fall within ±3% of the occurrence error. (Use 2σ limits) 3. Observed Data: Machine running Remove scrap Change tool Change material Adjust die Wait for maintenance service Wait for next material 48 S 17 5 12 5 23 S 53 I 25工 Total number of random initial observations: 400

For a industrial and systems engineering class

Answer 1

1.

The machine idle activities are Wait for maintenance service and Wait for next material

The machine set up activities are Remove Scrap, Change tool, Change material, Adjust die.

2.

Occurrence probability for machine idle activities = (53 + 25) / 400 = 0.195

Occurrence probability for machine set up activities = (48 + 17 + 12 + 23) / 400 = 0.25

Standard error of Occurrence probability for machine idle activities = $\sqrt{0.195*(1-0.195)/400}$ = 0.0198

Standard error of Occurrence probability for machine set up activities = $\sqrt{0.25*(1-0.25)/400}$ = 0.02165

z value for 95% confidence interval is 1.96

95% confidence interval for the Occurrence probability for machine idle activities is,

(0.195 - 1.96 * 0.0198,  0.195 + 1.96 * 0.0198)

(0.1562, 0.2338)

95% confidence interval for the Occurrence probability for machine set up activities is,

(0.25 - 1.96 * 0.02165,  0.25 + 1.96 * 0.02165)

(0.2076, 0.2924)

(c)

Given Margin of error = 3% = 0.03

For 2$\sigma$ limits, z = 2

Adequate sample size for machine idle activities = (z / E)² * p(1 - p)

= (2 / 0.03)² * 0.195 * (1 - 0.195) = 698 (Rounding to nearest integer)

Adequate sample size for machine set up activities = (z / E)² * p(1 - p)

= (2 / 0.03)² * 0.25 * (1 - 0.25) = 833   (Rounding to nearest integer)