Question

Cupcakes are sensitive to temperature and humidity. Cupcakes must be cooked at a consistent temperature. To test the oven before using it to bake Cupcakes, we took temperature samples at regular intervals. The following measurements, in degrees Celsius, are the results.

Sample	X1	X2	X3	X4	X5	X6	X7	X8
1	172	163	164	175	168	161	168	160
2	172	162	163	173	172	174	172	176
3	165	179	179	178	160	169	165	172
4	163	174	167	177	176	173	178	175

a. Compute the upper control limit of x bar chart.

b. Compute the lower control limit of x bar chart.

c. Compute the upper control limit of R chart.

d. Compute the lower control limit of R chart.

e. is the process under control

Answer 1

Number of observations in sample = 8

From the reference table for xbar and rbar chart,

A₂ = 0.373

D₃ = 0.136

D₄ = 1.864

Formulas for x-bar chart -

Hence,

UCL for x bar chart = 170.156 + 0.373 * 15.75 = 176.03075

Center line = 170.156

LCL for x bar chart = 170.156 - 0.373 * 15.75 = 164.2812

Formulas for R chart,

Hence,

UCL for R chart = 1.864 x 15.75 = 29.358

LCL for R chart = 0.136 x 15.75 = 2.142

As per the data,

All the values of xbar lies under the UCL and LCL of the xbar chart.

All the values of R lies under the UCl and LCL of R chart.

Hence, the process is under control.