Question

A new industrial oven has just been installed at Piatt Bakery. To develop experience regarding the oven temperature, an inspector reads the temperature at four different places inside the oven each half hour starting at 8:00 a.m. The last reading was at 10:30 a.m., for a total of six samples. The first reading, taken at 8:00 a.m., was 337 degrees Fahrenheit. (Only the last two digits are given in the following table to make the computations easier.)

Reading
Time		1			2			3			4
8:00 a.m.			37			43			44			40
8:30 a.m.			45			42			43			40
9:00 a.m.			43			49			40			44
9:30 a.m.			45			43			47			41
10:00 a.m.			35			48			49			63
10:30 a.m.			45			42			46			49

1. On the basis of this initial experience, determine the control limits for the range. (Round your intermediate calculations and final answers to 2 decimal places.)

LCL
UCL

2. For each time period, is the temperature out of control?

8:00 A.M.
8:30 A.M.
9:00 A.M.
9:30 A.M.
10:00 A.M.
10:30 A.M.

Thank you!!

Answer 1

Solution

Back-up Theory

Let xij represent the jth measurement at the ith interval, i = 1, 2, …., k and j = 1, 2, …., k.

The R Chart has:

Central line: CL = Rbar…………………………………………………………..(1a)

Lower Control Limit: LCL = D₃Rbar……………………………………(1b)

Upper Control Limit: UCL = D₄Rbar, ……………………………………(1c)

where

Rbar = (1/k)∑(i = 1, k)R_i, R_i = Max(xij) - min(xij)

A₂, D₃, D₄ , d2 are constants which can be directly obtained from standard Control Chart Constants Table…………………………………………………………………………..(2)

Now to work out the solution,

Part (a)

LCL = 0

UCL = ANSWER

[Details of calculations are given at the end]

Part (b)

All points are within limits. ANSWER

Details of calculations

	Reading
Time	1	2	3	4	Ri		Raw	Corrected
8:00 a.m.	37	43	44	40	7	Rbar	10.33	310.33
8:30 a.m.	45	42	43	40	5	D3 (4)	0	0
9:00 a.m.	43	49	40	44	9	D4 (4)	2.282	2.282
9:30 a.m.	45	43	47	41	6	LCL	0	0
10:00 a.m.	35	48	49	63	28	UCL	23.58	708.18
10:30 a.m.	45	42	46	49	7

NOTR: Figures under column ‘Raw’ are based on the given figures, which are original figures less 300. Corrected figures are based on the original figures.

DONE