Chapter 7, Problem 9P

a)

Summary Introduction

To determine: The standard time for the operation.

Introduction: The amount of the dependency on human effort by an organization in terms of achieving its goals is given by the work design. It is directly linked to the productivity of an organization where good work design helps in achieving high productivity.

Answer to Problem 9P

The standard time for the operation is 5.80 minutes.

Explanation of Solution

Given information:

Performance rating	Observations (minutes per cycles)					Allowance
	1	2	3	4	5
0.9	1.4	1.42	1.39	1.38	1.41	0.10
1.2	2.1	2.05	2	1.85	1.8	0.10
1.11	1.6	1.4	1.5	1.45	1.55	0.10

Formula:

$\begin{array}{c}\text{Standard}\text{time}=\text{Normal}\text{time}\times \text{Allowance}\text{factor}\\ =\text{NT}\times \text{AF}\\ \text{NT}=\text{Observed}\text{time}\times \text{Performance}\text{Rating}\\ {\text{AF}}_{\text{job}}=\text{1}+\text{A}\end{array}$

Element	Performance rating	Observations (minutes per cycles)					Allowance	Observed time	Normal time	Afjob	Standard time
		1	2	3	4	5
A	0.9	1.4	1.42	1.39	1.38	1.4	0.10	1.4	1.26	1.10	1.39
B	1.2	2.1	2.05	2	1.85	1.8	0.10	1.96	2.352	1.10	2.59
C	1.11	1.6	1.4	1.5	1.45	1.6	0.10	1.5	1.665	1.10	1.83
	Standard time for operation										5.80

Calculation of standard time of operation:

Excel Worksheet:

Element A:

Normal time is calculated by multiplying observed timing, 1.4 and performance rating, 0.9 which yields 1.26 minutes.

Allowance factor is calculated by adding 1 with the allowance factor 0.10 to give 1.10.

$\begin{array}{c}\text{ST}=\text{NT}\times {\text{AF}}_{\text{job}}\\ =\text{1}\text{.26}\text{minutes}\times \text{1}\text{.10}\\ =1.39\text{minutes}\end{array}$

Standard time for element A is calculated by multiplying normal time of 1.26 minutes with allowance factor of 1.10 which gives 1.39 minutes.

Same process applies for element B and C which yields the standard times as 2.59 and 1.83. The standard time for operation is obtained by adding 1.39, 2.59 and 1.83 minutes which gives 5.80 minutes.

Hence, the standard time for the operation is 5.80 minutes.

b)

Summary Introduction

To determine: The number of observations for element A

Introduction: The amount of the dependency on human effort by an organization in terms of achieving its goals is given by the work design. It is directly linked to the productivity of an organization where good work design helps in achieving high productivity.

Answer to Problem 9P

The number of observations for element A is 1.

Explanation of Solution

Given information:

Performance rating	Observations (minutes per cycles)					Allowance
	1	2	3	4	5
0.9	1.4	1.42	1.39	1.38	1.41	0.10
1.2	2.1	2.05	2	1.85	1.8	0.10
1.11	1.6	1.4	1.5	1.45	1.55	0.10

Confidence= 98%

4% of true value

Formula:

$\text{n}={\left(\frac{\text{zs}}{\text{a}\overline{\text{x}}}\right)}^{\text{2}}$

$$ $\begin{array}{c}\text{z}=\text{Number of}\text{normal}\text{standard}\text{deviations}\text{for}\text{desired}\text{confidence}\\ \text{s}=\text{Sample}\text{standard}\text{deviation}\\ \overline{x}=\text{Sample mean}\\ \text{a}=\text{Desired accuracy}\end{array}$

Calculation of number of observations for element A:

In the above formula the sample standard deviation is calculated by,

Calculation of standard deviation:

Element A	Differences	Square of differences	Standard deviation
1.4	0	0	0.015811
1.42	0.02	0.0004
1.39	-0.01	0.0001
1.38	-0.02	0.0004
1.41	0.01	0.0001
Mean=1.4		SSQ=0.001

Excel worksheet:

Z value for confidence interval of 98% is 2.33.

The confidence interval $\frac{0.98}{2}$ gives 0.49, (z = 2.33).

Using z = 2.33:

$\begin{array}{c}\text{n}={\left(\frac{\text{2}\text{.33}\times 0.0158}{0.04\times 1.40}\right)}^{\text{2}}\\ =0.4322\end{array}$

The number of observations from the standard z table for confidence level of 98% is calculated by dividing the product of 2.33 and 0.0158 with product of 0.04 and 1.40 and squaring the resultant which gives 0.4322. Rounding off the value it gives the number of observation as 1.

Hence, the number of observation is 1.

c)

Summary Introduction

To determine: The number of observations for element C.

Introduction: The amount of the dependency on human effort by an organization in terms of achieving its goals is given by the work design. It is directly linked to the productivity of an organization where good work design helps in achieving high productivity.

Answer to Problem 9P

The number of observations for element C is 2.

Explanation of Solution

Given information:

Performance rating	Observations (minutes per cycles)					Allowance
	1	2	3	4	5
0.9	1.4	1.42	1.39	1.38	1.41	0.10
1.2	2.1	2.05	2	1.85	1.8	0.10
1.11	1.6	1.4	1.5	1.45	1.55	0.10

Confidence= 90%

0.10 minute of actual value.

Formula:

$\text{n}={\left(\frac{\text{zs}}{\text{e}}\right)}^{\text{2}}$

$$ $\begin{array}{l}\text{z}=\text{Number of}\text{normal}\text{standard}\text{deviations}\text{for}\text{desired}\text{confidence}\\ \text{s}=\text{Sample}\text{standard}\text{deviation}\\ \text{e}=\text{Maximum}\text{acceptable}\text{amount}\text{of}\text{time}\text{error}\end{array}$

Calculation of number of observations for element C:

In the above formula the sample standard deviation is calculated by,

Calculation of standard deviation:

Element C	Differences	Square of differences	Standard deviation
1.6	0.1	0.01	0.0791
1.4	-0.1	0.01
1.5	0	0
1.45	-0.05	0.0025
1.55	0.05	0.0025
Mean=1.5		SSQ=0.025

Excel worksheet:

Z value for confidence interval of 90% is 1.65.

The confidence interval $\frac{0.90}{2}$ gives 0.45, which is in the midway of 0.4495 (z = 1.64) and 0.4505 (z = 1.65).

• Using z = 1.64:

$\begin{array}{c}\text{n}={\left(\frac{1.64\times 0.0791}{0.10}\right)}^{\text{2}}\\ =1.6828\end{array}$

The number of observations from the standard z table for confidence level of 90 is calculated by dividing the product of 1.64 and 0.0791 with 0.10 and squaring the resultant which gives 1.6828.

• Using z = 1.65:

$\begin{array}{c}\text{n}={\left(\frac{1.65\times 0.0791}{0.10}\right)}^{\text{2}}\\ =1.7034\end{array}$

The number of observations from the standard z table for confidence level of 90 is calculated by dividing the product of 1.65 and 0.0791 with 0.10 and squaring the resultant which gives 1.7034.

Hence, the number of observations for element C is 2