The failure data of 10 electronic components are shown in the table given below:

Failure Number			1	2	3	4	5		6	7		8	9	10
Operating Time (in hours)			3	5	31	51	76		116	140		182	250	302

Estimate, the
i) reliability. 
ii) cumulative failure distribution.
iii) failure density. 
iv) failure rate functions.

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To estimate the reliability, we can use the following formula: R(t) = exp(-λt) where R(t) is the reliability at time t, and λ is the failure rate. To estimate λ, we can use the following formula: λ = (n - 1) / Σ(ti - ti-1) where n is the number of failures, ti is the operating time of the i-th failure, and ti-1 is the operating time of the (i-1)-th failure.

Using the given data, we can compute the values as follows:

i	ti	ti-1	ti - ti-1	λ	R(t)
1	3	0	3	0.003333	0.996675
2	5	3	2	0.003333	0.993362
3	31	5	26	0.001089	0.987318
4	51	31	20	0.001089	0.981311
5	76	51	25	0.001089	0.975331
6	116	76	40	0.000696	0.969377
7	140	116	24	0.000696	0.963450
8	182	140	42	0.000696	0.957550
9	250	182	68	0.000392	0.951678
10	302	250	52	0.000392	0.945832

(i) The estimated reliability values are shown in the above table under the column labeled "R(t)".

(ii) The cumulative failure distribution can be estimated as follows: F(t) = 1 - R(t) The estimated cumulative failure distribution values are shown in the table below:

i	t	F(t)
1	3	0.003325
2	5	0.006638
3	31	0.012682
4	51	0.018689
5	76	0.024669
6	116	0.030623
7	140	0.036550
8	182	0.042450
9	250	0.048322
10	302	0.054168

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Degree : PG DIPLOMA PROGRAMMES
Course Name : Post Graduate Diploma in Applied Statistics
Course Code : PGDAST
Subject Name : Industrial Statistics-I
Subject Code : MSTE 1
Year : 2023