QUESTION 2 Statistical Decision Making and Quality Control
Show all calculations/reason
(a) A company wishes to set control limits for monitoring the direct labour time to produce an important product. Over the past, the mean time has been 45 minutes with a standard deviation of 15 minutes and is believed to be normally distributed. The company proposes to collect random samples of 36 observations to monitor labour time.
1. If management wishes to establish x ¯ control limits covering the 95% confidence interval, calculate the appropriate UCL and LCL.
2. If management wishes to use smaller samples of 16 observations calculate the control limits covering the 95% confidence interval. (Round calculations to 2 decimal places)
(b) Quality control chart
Using the Excel Chart function prepare a quality control chart from the following sequential monthly cycle time data. The desired level of performance is 140, with an upper control limit of 160 and a lower control limit of 120.
Month Average Cycle Time
Explain whether the process is in control or whether corrective action is required.
Justify your conclusion.